Research ArticleMultiobjective Combinatorial Auctions inTransportation Procurement

Joshua Ignatius1 Seyyed-Mahdi Hosseini-Motlagh2 Mark Goh34

Mohammad Mehdi Sepehri5 Adli Mustafa1 and Amirah Rahman1

1 School of Mathematical Sciences Universiti Sains Malaysia 11800 Penang Malaysia2 School of Industrial Engineering Iran University of Science and Technology Tehran 16846-13114 Iran3NUS Business School National University of Singapore Singapore 1196774 School of Management University of South Australia Adelaide SA 5000 Australia5 Department of Industrial Engineering Tarbiat Modares University Tehran 14117-13114 Iran

Correspondence should be addressed to Joshua Ignatius joshua ignatiushotmailcom

Received 25 September 2013 Accepted 29 November 2013 Published 16 February 2014

Academic Editor Kim-Hua Tan

Copyright copy 2014 Joshua Ignatius et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents a multiobjective winner determination combinatorial auctionmechanism for transportation carriers to presentmultiple transport lanes and bundle the lanes as packet bids to the shippers for the purposes of ocean freight This then allows thecarriers to maximize their network of resources and pass some of the cost savings onto the shipper Specifically we formulate threemulti-objective optimization models (weighted objective model preemptive goal programming and compromise programming)under three criteria of cost marketplace fairness and themarketplace confidence in determining thewinning packagesWe developsolutions on the three models and perform a sensitivity analysis to show the options the shipper can use depending on the existingconditions at the point of awarding the transport lanes

1 Introduction

Shippers often rely on an auction or a tendering mechanismto attract the transport carriers to provide cost competitivelogistics services on transport lanes either singly or as abundle In such an auction of transportation procurementservices the stakeholders often comprise shippers and carri-ers who attend to an electronic transportationmarket (ETM)involving a bid preparation stage (see Sheffi [1] for the details)In the maritime industry a transport lane is treated as ashipping lane used to move a defined number of containersfrom origin port to destination port In this situation thecarriers would bid for the right (usually at the lowest costand with the best delivery time window reliability) to shipconsigned goods for the shipper The shipper has to decidewhich lanes (either all or part of them) to award to whichcarrier the goods can completely be shipped in full and

directly from source to destination with one carrier or itspartners in the shipping conference or shipped to destinationusing transshipment ports

Shipping with a carrier using partner transport servicesnaturally raises concerns of the quality of service and reli-ability of delivery Sometimes such shipments experiencedelays increased cost at the transit container terminals off-loading of container boxes due to the lack of volume into thedestination port and higher than expected demurrage due topeak season surcharges All of these affect the track record ofthe carrier who can offer the lowest price but less than desiredquality of service to the shipper [2] Also for operationalreasons carriers tend to go into anETMsignaling the numberof containers they can transport within a certain volumerange so as to justify their cost of operations and achieve thebest economies of scale for their and their partnerrsquos network(see [3])

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 951783 9 pageshttpdxdoiorg1011552014951783

2 Mathematical Problems in Engineering

Therefore given the various operational and businessconstraints there exist variations in the auction design Forinstance Forster and Strasser [4] have studied auctions wherethe shipper opens up a list of individual transport lanes to thecarriers to bid and uses a strict price criterion as the primarymeasure of carrier selection (the winner of the auction)More recently Sheffi [1] presents a combinatorial auctionmechanism whereby shippers request bids for a group(s) oflanes rather than individual transport lanes to eke out bettercost efficiencies and economies of scale A one-shipper tomulticarrier network is considered as a combinatorial auction(CA) if the carriers are allowed to submit a combination ofindividual transport lanes as a packet

To date combinatorial auctions conducted effectivelyhave contributed to cost reduction and mutual satisfactionbetween the shipper and carriers as a main source of costis the asset repositioning cost that involves a carrier havingto relocate its resources (ships) to service a transport lanefrom one shipper to another [5] This is observed fromthe empty backhaul movements when servicing a particulartrade lane in the transport network Nair [6] reports thateven the most sophisticated carrier would have some excesscapacity Indeed theUSmarket contributed toUS$165 billionin total estimated industry loss due to capacity inefficiencies[7]

Under a CA setting a shipper typically offers a seriesof lanes that they wish to ldquobuyrdquo separately and each carrierwill run their carrier routing optimization to determine thepreferred packages that they can offer In order to be com-petitive each carrier would rationally try to offer the lowestprice possible subject to operational and capacity constraintsIdeally the bids tendered shouldminimize the carriersrsquo emptyload movements throughout its own network [8 9] andreduce the need to reposition the ships to another port forthe pick-up of more committed freight Cost uncertainty andshipment uncertainty are also covered in the literature of CA(see [10 11])

The CA approach has been noted to also allow a carrierto complement its network and pass of the cost savings tothe shipper For instance in Table 1 consider a case wherea carrier is interested to bid for lanes P

1a P3a P5a and P7a

In a single auction structure the carrier has to place eachinterested lane (P

1a P3a P5a or P7a) as a bid If lane P7a is

not part of the carrierrsquos winning bid then the carrier will haveto return from location J to its origin P with an empty loadthus incurring higher transportation costs Contrastingly ina combinatorial auctionmarket the carrier can place a bid forlane P

7b and refuse the entire package if one of the lanes is notpart of the winning bid

Thus the rationale for bidding based on packages isbased on the complementarity property where the packageis valued more than the sum of the individual lanes to thecarrier In addition by allowing for carriers the option ofdenying an entire package when one of their lanes is notaccepted in the bidding transaction eliminates a carrierrsquosasset repositioning costs and in return for this the carriertypically offers shippers more competitive rates This form ofbusiness transaction between the shipper and the carriers isoften facilitated by an internet-based ETM The auctioneer

can be the shipper or any third party service provider Todate combinatorial auctions for transportation procurementfocus on a single objective cost minimization model In thispaper we propose to include two other important criteriain the long-term sustainability of an auction market Theseare (i) marketplace fairness and (ii) the shipperrsquos confidenceof the carrierrsquos ability to provide the requisite service giventhat not all carriers have their own transit terminals and thussuffer from varying service times at the transit points that isquality of service To handle these objectives we will applythree multiobjective decision-makingmodels to compare thesolution approaches

The rest of the paper is organized as follows Section 2provides the relevant review on multiobjective optimizationmodels the weighted objective goal programming and com-promise programming Section 3 presents the mathematicalprogramming framework for the three models in the contextof transportation procurementThe data preparation and testprocedures are provided in Section 4 Section 5 discusses thesolutions and concludes the paper

2 Multiobjective Optimization

With conflicting and multiple objectives in an actual realworld decision-making context optimizing a single objectiveis no longer viable [12] In the case of combinatorial auctionsthe auctioneer usually needs to maintain other objectivesfor scenario planning For instance awarding lane contractsbased on cost alone may lead to only a selected few largecarriers being chosen as they have the needed capacity andnetwork reach This prevents other smaller players and otherregional players from engaging in the marketplace Otheroptimizing considerations include the quality of serviceand maintaining a ready pool of carriers through strategicresource allocation of containers We now review somemultiobjective mathematical programming techniques thatwe will use for this paper

21 Weighted Objectives Model (WOM) The WOM consid-ered to be the oldest method representing multiple objectivesin a linear programmingmodel [13] seeks to approximate theefficient set and provides a crude way of generating efficientsolutions by varying their weights Consider

max 119885 =

119869

sum

119894=1

119908119894119891119894(119909)

st 119909 isin 119883

(1)

where 119908119894is the positive weight of the objective 119891

119894(119909)

22 Goal Programming (GP) Goal programming extendsthe basic LP and keeps part of the kernel of MODM Itguides a decisionmaker to attain a closest solution possible tothe various conflicting objectives [14] Today GP techniqueshave been applied across disciplines ranging from vendorselection [15] to berth allocation in ports [16] Metaheuristicapproaches have been used to solve the GP routines such

Mathematical Problems in Engineering 3

Table 1 Simple versus combinatorial auction

Lanes offered Carrierrsquos bids in simple auction Carrierrsquos bids in CA

K

SP

J

P1a (PrarrK)P2a (KrarrP)P3a (Krarr S)P4a (SrarrK)P5a (Srarr J)P6a (Jrarr S)P7a (JrarrP)

P1b (PrarrK KrarrP)P2b (Krarr S Srarr J)

P3b (PrarrK Krarr S SrarrK KrarrP)P4b (Srarr J Jrarr S)

P5b (Krarr S Srarr J Jrarr S SrarrK)P6b (PrarrK Krarr S Srarr J Jrarr S SrarrK KrarrP)

P7b (PrarrK Krarr S Srarr J JrarrP)

as simulated annealing genetic algorithms and Tabu search[17] Since GP allows one to adjust the target values andorweights flexibly it can also be used for scenario planningThis is especially useful in the context of CA especially forthe shipper who may wish to reshift focus on other nonpriceconsiderations after the bid exercise Two forms of GP existweighted and preemptive The former assigns weights tounwanted deviations thus effectively allowing the decisionmaker to state their relative importance of the objectivesThe objective is singly minimized as an Archimedean sum asfollows

min 119885 =

119898

sum

119894=1

119908minus

119894119889minus

119894+ 119908+

119894119889+

119894

st 119891119894(119909) + 119889

minus

119894minus 119889+

119894= 119887119894 119894 = 1 2 3 119909 isin 119883

(2)

where119891119894(119909) is the linear objective function with a target value

of 119887119894 while 119908

minus

119894and 119908

+

119894are nonzero weights attached to the

respective positive 119889+119894(overachievement) and negative devia-

tions 119889minus119894(underachievement) This technique minimizes the

sum of deviations from the target valueThe second goal formulation minimizes deviations hier-

archically 1198751(119909) gt 119875

2(119909) gt sdot sdot sdot gt 119875

119904(119909) This is akin to

optimizing fully a goal that has a higher importance beforemoving to the next goal In short the goal of a higher orderpriority is infinitely more important than the goals of lowerpriority Thus the objective function in (2) can be replacedwith

min 119885 =

119869

sum

119894=1

119875119904(119908minus

119894119889minus

119894+ 119908+

119894119889+

119894) (3)

23 Compromise Programming (CP) CP models conflictingobjectives as a distance minimizing function so as to reacha point nearest to the ideal solution The ideal solutionis gathered by optimizing each objective with the hardconstraints individually while ignoring all other objectivesThe CP approach can be viewed as an extension of the GPtechnique with somemodifications to the deviation variableswhile fixing the root at unity [18]Themathematical model isas follows

min 119885 =

119898

sum

119894=1

[119908119901

119894(119887119894minus 119891119894(119909)

Δ119894

)

119901

]

1119901

st 119909 isin 119883

(4)

where 119908119901

119894are the nonpreemptive weights of the 119901th metric

while Δ119894

= 119891+

119894(119909) minus 119891

minus

119894(119909) are the normalizing constants

obtained by the distance between the maximum and mini-mum anchors for each objective function 119894 Tamiz et al [12]show that for 119901 = 120572 it is equivalent to solving

min 120572

st 120572 ge119908119894

Δ119894

[119887lowast

119894minus 119891119894(119909)] 119894 = 1 2 119909 isin 119883

(5)

where 119887lowast119894is obtained by maximizing 119891

119894(119909)

3 Modelling the TransportationProcurement Problem

We now model the combinatorial auction transportationprocurement problem that supports multiple lanes multiplepackages and multiple bidders whereby the shipper attractsbids for a set of lanes as single packages that have differ-ent prices for each unit of volume in each lane (origin-destination) The volumes submitted for each package variesaccording to the carriersrsquo resource capacities We introducethe following notation

31 Indices

I Set of shipping origins

J Set of shipping destinations

K Set of packages

C Set of carriers

32 Parameters The set of bid bundles119888119861119896 can be specified

as a 4-tuple (119888119886119896119888119901119896119888119871119896119888119880119896) where

(i)119888119886119896= (119888119886119896

11 119888119886119896

119894119895 119888119886119896

119898119899) with

119888119886119896isin (R+)

119898times119899

119888119886119896

119894119895is the load volume per unit time (week) received

from carrier 119888 on transport lane from origin 119894 todestination 119895 that are being bid out as part of package119896

(ii)119888119901119896= (11988811990111989611 119888119901119896119894119895 119888119901119896119898119899

)with119888119901119896isin (R+)

119898times119899

119888119901119896119894119895is the bid price per load on lane 119894 to 119895 received

from carrier 119888 as part of package bid 119896

4 Mathematical Problems in Engineering

(iii)119888119871119896= (119888119871119896

11 119888119871119896

119894119895 119888119871119896

119898119899) with

119888119871119896isin (R+)

119898times119899

119888119871119896

119894119895is the lower bound in loads on lane 119894 to 119895 that

carrier 119888 is willing to accept as part of package bid 119896

(iv)119888119880119896

= (119888119880119896

11 119888119880119896

119894119895 119888119880119896

119898119899) with

119888119880119896

isin

(R+)119898times119899119888119880119896

119894119895is the upper bound in loads on lane 119894 to

119895 that carrier 119888 is willing to accept as part of packagebid 119896

Each bundle bid119888119861119896 is a placement order that is services that

are to be sold by the auctioneer

33 Decision Variables We define the decision variable cor-responding to each lane as

119888119909119896

119894119895 where

119888119909119896

119894119895is fraction of load

per time unit (week) on lane 119894 to 119895 from carrier 119888 on packagebid 119896

Subsequently each package is denoted as119888119910119896 where

119888119910119896

denotes that if carrier 119888 is assigned package bid 119896 then119888119910119896=

1 otherwise119888119910119896= 0

34TheModel Formulation We seek to simultaneously min-imize cost maximize marketplace fairness and maximizeshipperrsquos confidenceCost Objective The total cost of the accepted bids is mini-mized as

1198911(119909) = Min

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895 (6)

Marketplace Fairness Objective The total number of acceptedpackages is maximized as

1198912(119909) = Max

sellersum

119888=1

package

sum

119896=1

119888119910119896 (7)

Marketplace Confidence ObjectiveThedifference between thelower bound volume sought by the carrier and the upperbound volume sought by the auctioneer is minimized asfollows

1198913(119909) = Min

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816 (8)

Supply-Demand Constraint The total volume accepted aswinning packagesmust be no less than the volume auctionedthat is

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895 119888119909119896

119894119895

ge

destinationsum

119896=1

origin

sum

119894=1

119886119896

119894119895119909119896

119894119895forall119894 isin origin 119895 isin destination

(9)

Transactional Constraints Equation (10) allows the auction-eer to transact the entire package within a particular volumerange specified by the carriers The variable 1

119888119910119896

in (10)ensures that the carrier must offer all lanes within thepackage if one of the lanes is approved as a winning lane bythe auctioneer Consider

minus119872119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination

minus119888119871119861119896

119894119895 119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination

119888119880119861119896

119894119895 119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(10)

Business Guarantee Constraint A shipper might not wantto rely too heavily on a small number of winning carriersIn the longer term it might be prudent for a shipper toensure that the amount of traffic won by a carrier is within acertain bound This will create a higher potential for carriersto revisit the marketplace to bid The scope of the carrier setcoverage is measured by the amount of volume (loads) wonThe constraints below ensure that all carriers are awardedbusiness within some preset volume bounds Consider

119888Min Value le

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895

le119888Max Value

(11)

Carrier Base Size Constraints This is an extension to thebusiness guarantee constraint with the restriction on thenumber of winning carriers for each lane The system-based(or hard) approach adds the following constraints to limit thenumber of carriers assigned at the lane level

minus119872119888119908119894+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(12)

sellersum

119888=1

119888119908119894le 119871119894

forall119894 isin origin (13)

minus119872119888119911 +119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(14)

sellersum

119888=1

119888119911 le 119878 (15)

Mathematical Problems in Engineering 5

The number of carriers winning the right to haul at origin 119894

is denoted as 119871119894in (13) while 119878 is the system limit of winning

carriers for the entire auction

Simple Reload Bids Constraint This constraint denotes thatthe ratio of outbound volume to inbound volume must be atleast119888120573119895 Consider

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119895119894 119888119888119896

119895119894

ge119888120573119895lowast

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895 119888119909119896

119894119895forall119888 119896

(16)

Nonnegativity and Binary Constraints As the decision vari-ables are expressed as percentages we define

119888119909119896

119894119895in (17) as

real numbers Carrier 119888 is assigned package bid 119896when 119888119910119896 =

1 (or 0 otherwise) (18) Carrier 119888 is assigned to origin 119894 when119888119908119894= 1 (or 0 else) (19) Also carrier 119888 is assigned to a network

when119888119911119894= 1 (or 0 otherwise) (20) Consider

119888119909119896

119894119895isin 119877+ (17)

119888119910119896= 0 1 (18)

119888119908119894= 0 1 (19)

119888119911 = 0 1 (20)

We now present the three models for the CA transportprocurement problem WOM preemptive GP and CPWOM Consider

Min 1199081(

sellersum

119888=1

packag

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895)

minus 1199082(

sellersum

119888=1

package

sum

119896=1

119888119910119896)

+ 1199083(

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816)

st (9)ndash(20) (21)

Preemptive Goal Model (PGM) Consider

Min 1198751119889+

1+ 1198752119889minus

2+ 1198753119889+

3 1198751gt 1198752gt 119875119904(119909)

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895+ 119889minus

1minus 119889+

1

= Cost Goal

sellersum

119888=1

package

sum

119896=1

119888119910119896+119889minus

2minus 119889+

2

= Marketplace Reputation Goal

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816+ 119889minus

3minus 119889+

3

= Shipperrsquos Confidence Goal

st (9)ndash(20) (22)

where 119889minus119894and 119889

+

119894are the underachievement and overachieve-

ment deviations of the 119894th goal

CPM The combinatorial auction transportation procure-ment model in a CP is as follows

Min

1199081((

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895

minus 119888lowast

119894) times (119888

lowast

119894)minus1

)

119875

minus 1199082(

sumseller119888=1

sumpackage119896=1 119888

119910119896minus119903lowast

119894

119903lowast

119894

)

119875

+ 1199083((

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816

minus119904lowast

119894) times (119904

lowast

119894)minus1

)

119875

1119875

st (9)ndash(20) (23)

where 119901 = 1 2 infin The ideal values of cost marketplacefairness and shipperrsquos confidence are gathered from 119888

lowast

119894=

min1198911(119909) 119903lowast

119894= max119891

2(119909) and 119904

lowast

119894= min119891

3(119909) respec-

tively (see (6)ndash(8)) The larger deviations receive greaterimportance as 119901 increases This is the penalizing effectplaced on larger deviations from their respective ideal solu-tions The compromise solutions satisfy 1 le 119901 le infin

6 Mathematical Problems in Engineering

Table 2 Results experimental runs

Test Model Cost ($) Marketplace fairness Shipperrsquos confidence1 Ideal cost 116650 4 158382 Ideal marketplace fairness 2589176 100 2724223 Ideal shipperrsquos confidence 673384 34 04 Preemptive GP 129611 4 737575 Equal weight 194505 12 2783

CP (equal weights)6 119901 = 1 441444 27 23087 119901 = 2 153932 5 20388 119901 = infin 129441 4 74755

The solution at 119901 = infin indicates that the largest deviationamong all objectives is the most dominant in the optimalsolutionrsquos distance function

4 Solution and Analysis

The following steps detail our dataset generation procedureand analysis

Step 1 (generate shipperrsquos lane offerings) The condition ofCA requires each shipper to put the amount of volume fora set of lanes on offer in separate auction markets We set[119878+]1times119899

as the shipperrsquos volume required in a CA of 119899 lanesThe maximum amount of loads available for carriers to bidon each 119894-119895 origin-destination (lane) or cell 0119886

119894119895isin [119878+]1times119899

is randomly generated from [1000 10000] using a uniformdistribution

Step 2 (generate carriersrsquo bids) We assume that the carriersare able to view the total available volumes for each lane andset their bids accordingly For our simulated carrierrsquos amountof loads we generate a seed number 120572 between [1 100] foreach lane A value of 120572 greater than 50 enforces the rule ofempty cells and signifies the refusal of a carrier to accepta particular lane If 120572 lt 50 another random number 120573 isgenerated between [06 1] where 120573 lowast

0119886119894119895=1119886119894119895and 1119888119886119894119895isin

[119862+]119898times119899

correspond to the amount of loads offered by the119898thcarrier of the 119899th lane

Step 3 (solving routines) The buy and sell prices of each laneare fixed at $3 and $1 per unit of load respectivelyThe datasetis solved by WOM PGM and CPM respectively on Lingoversion 8

Step 4 (results and sensitivity analysis) Table 2 shows theresults where a series of 8 tests were run The ideal valuesof each objective are obtained by analyzing each objectiveindependently while keeping all the constraints in themodelWe observe that the model that optimises the cost yieldsthe lowest cost ($11665) out of all models tested This trendcontinues with models that optimise marketplace fairnessand shipperrsquos confidence respectively yielding the best resultfor marketplace fairness (100) and shipperrsquos confidence (0)when compared with other models We define shipperrsquos

confidence to be the distance between the carriersrsquo bidvolume and the shipperrsquos request The value of 0 indicates nodistance and denotes that all requested volumes by shippercan be met

In the PGM the preemptive weights are specified in thefollowing order of importance cost marketplace fairnessand shipperrsquos confidence Here the cost value is close to theideal cost as this objective was stated to be infinitely moreimportant than the other objectivesThe value ofmarketplacefairness in Test 4 is the same as Test 1 However the differencein shipperrsquos confidence is expected as its inclusion as anobjective renders that cost will be sacrificed by 129611 minus

116650 = $12961 Thus in considering the 3 objectiveshierarchically the feasible solution sacrificed in cost waspassed onto satisfying shipperrsquos confidence This can be seenfrom the reduced unawarded volume of 73757 (Test 4) from15838 (Test 1)

InTest 5 we formulated aweighted-objectivesmodelwith1199081

= 1199082

= 1199083

= 13 to optimize a set of objectivessimultaneously with the same priority for all objectives

A sensitivity analysis is conducted on the WOM byvarying the weights of each objective while the other 2objectives are restricted to sharing the remainder weightsequally (Tables 3ndash5) The results of the WOMmodel are alsocompared directly against the CP model since the weights ofthe three objectives are standardized to be equal across thetwo techniques It is observed that the CPmethod dominateson cost and shipperrsquos confidence The CPM solution isobtained when 119901 is set to infin Further as 119901 rarr infin the costand shipperrsquos confidence objectives improve at the expenseof marketplace fairness (Table 2 Tests 6 to 8) However theWOM results are not necessarily inferior to the CPM asthe shipper now can now choose between the solutions ofTest 5 or Test 8 Test 5 produces 12 winning bids whileTest 8 produces 4 winning bids If all 12 winning bidsare won by a single carrier in Test 5 but the 4 winningbids of Test 8 are won by different carriers the shippermay strategically select the CPM solution On the otherhand if some of the winning bids in Test 5 are won by aprominent carrier that is not part of the winning carrier inTest 8 the shipper may opt for the Test 5 WOM solutioninstead to keep the service relationship intact as much aspossible

Mathematical Problems in Engineering 7

Table 3 Varying cost objective weights WOMmethod

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 1166496 1166496 1166496 1166496 1166496 1166496 123742 194505 265986 758231 3052837 3052837Marketplace fairness 4 4 4 4 4 4 5 12 18 39 100 100Marketplace confidence 15838 15838 15838 15838 15838 15838 16924 2783 38234 109119864 minus 04 0 0

Table 4 Varying marketplace fairness weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 2589176 244227 244227 244227 1752309 7371432 3894 1945048 14262 1166496 1166496 1166496Marketplace fairness 100 100 100 100 82 45 27 12 7 4 4 4Marketplace confidence 272422 358248 358248 358248 256872 108082 55576 2783 19708 15838 15838 15838

Table 5 Varying marketplace confidence weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 673384 200191 200191 200191 200191 200191 1950118 1945048 217084 2408288 2532848 3047688Marketplace fairness 34 100 100 100 100 100 11 12 14 16 17 21Marketplace confidence 0 0 0 0 0 0 18462 2783 31358 3474 3647 43678

Table 6 Varying cost objective weights CP method

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 116650 118066 119614 121316 123194 125278 127647 129441 130421 133686 137680 911812Marketplace fairness 4 4 4 4 4 4 4 4 4 4 4 38Marketplace confidence 158380 148941 138614 127269 114748 100855 85695 74755 68988 49782 27313 1119864 minus 04

Table 7 Varying marketplace fairness weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 763739 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441Marketplace fairness 42 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 10459 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755

8 Mathematical Problems in Engineering

Table 8 Varying marketplace confidence weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 911812 141246 139581 137823 135860 133686 131261 129441 128466 125278 121454 116649Marketplace fairness 38 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 1119864 minus 04 7986 16752 26517 37424 49783 64046 74755 80572 100855 126351 158380

The solutions of Table 6 can be compared directly toTable 3 as can be Tables 7 and 4 as well as Tables 8 and 5respectively Generally when the weights for the cost objec-tive are reduced on a 005 step decrease from 1 to 0 the costvalue steadily increases for the CPM This trend is also truefor marketplace confidence However the WOM model isinsensitive to weight changes when the cost weights are in[05 1] The same pattern is found for marketplace fairnessand shipperrsquos confidence where varying weights between[0 015] and [005 025] for the respective objectives didnot change the values of those objectives (Tables 4 and5) The CPM quickly reaches a minimum for marketplacefairness with a slight change in weights from the maximum1 Choosing a different 119875 value will alter marketplace fairnessThus theWOMcan provide solutions quickly for eachweightvariation However the CPM can provide many solutionsfor the same weight variations albeit having to vary theparameter 119901

5 Conclusions

While research on transportation procurement has benefitedfrom the use of CA the literature does not explicitly providemodel solutions and formulation for the multiobjective con-textThismay be due to the difficulty in operationalising con-cepts such as marketplace fairness and shipperrsquos confidenceThis paper treating the MODM problem in the context asa multiobjective optimization model allows the shipper toinclude nonfinancial carrier selection measures Future workcan consider a service index that can be incorporated andupdated from one auction to another to allow carriers tobe tracked on performance Our results suggest that there isno dominant MODM technique However this is good forthe shipper as shipper now has at its disposal a variety oftechniques to compare against when making a final decisionon the winner for the auction Alternatively the shipper canuse the results for a further bargaining process with thecarriers There may be a situation where the shipper intendsto use a particular carrier who has a high quality service levelbut has a higher service cost too The shipper may then askthe carrier whether it could provide the service at the nextlower price For incorporating a bargaining phase into a CAmechanism readers may be interested in the work of Huanget al [19] Another alternative would be to introduce trust-based mechanism by observing the discrepancy between theresults and the services offered One step further would be

to use this as a means to validate the sensitivity resultsTrust mechanisms have been used in agent-based researchto support decisions made on economic exchange (see [20])Future workmay also include soft computing approaches thatallow the shipper to automate and filter the solutions based onother criteria such as the business relationships

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y Sheffi ldquoCombinatorial auctions in the procurement of trans-portation servicesrdquo Interfaces vol 34 no 4 pp 245ndash252 2004

[2] Y Guo A Lim B Rodrigues and Y Zhu ldquoCarrier assignmentmodels in transportation procurementrdquo Journal of the Opera-tional Research Society vol 57 no 12 pp 1472ndash1481 2006

[3] S M H Motlagh M M Sepehri J Ignatius and A MustafaldquoOptimizing trade in transportation procurement is combi-natorial double auction approach truly betterrdquo InternationalJournal of Innovative Computing Information and Control vol6 no 6 pp 2537ndash2550 2010

[4] J R Forster and S Strasser ldquoCarrier modal selection factorsthe shipper carrier paradoxrdquo Transportation Research Forumvol 31 no 1 pp 206ndash212 1991

[5] W Elmaghraby and P Keskinocak ldquoCombinatorial auctionsin procurementrdquo Tech Rep School of Industrial and SystemsEngineering Georgia Institute of Technology 2002

[6] A Nair ldquoEmerging internet-enabled auction mechanisms insupply chainrdquo Supply ChainManagement vol 10 no 3 pp 162ndash168 2005

[7] O Ergun G Kuyzu and M Savelsbergh ldquoShipper collabora-tionrdquo Computers and Operations Research vol 34 no 6 pp1551ndash1560 2007

[8] C Caplice Optimization-based bidding a new framework forshipper-carrier relationships [PhD dissertation] MIT Cam-bridge Mass USA 1996

[9] C Caplice and Y Sheffi ldquoOptimization based procurement fortransportation servicesrdquo Journal of Business Logistics vol 24 no2 pp 109ndash128 2004

[10] J Ignatius Y-J Lai SMHosseini-MotlaghMM Sepehri andA Mustafa ldquoModeling fuzzy combinatorial auctionrdquo ExpertSystems with Applications vol 38 pp 11482ndash11488 2011

Mathematical Problems in Engineering 9

[11] N Remli and M Rekik ldquoA robust winner determination prob-lem for combinatorial transportation auctions under uncertainshipment volumesrdquo Transportation Research C vol 35 no 10pp 204ndash217 2013

[12] M Tamiz D Jones and C Romero ldquoGoal programming fordecision making an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 111 no 3 pp569ndash581 1998

[13] A M Geoffrion ldquoProper efficiency and the theory of vectormaximizationrdquo Journal of Mathematical Analysis and Applica-tions vol 22 no 3 pp 618ndash630 1968

[14] A Charnes andW W CooperManagement Models and Indus-trial Applications of Linear Programming John Wiley amp SonsNew York NY USA 1961

[15] VWadhwa andA R Ravindran ldquoVendor selection in outsourc-ingrdquo Computers and Operations Research vol 34 no 12 pp3725ndash3737 2007

[16] A Imai E Nishimura and S Papadimitriou ldquoBerth allocationwith service priorityrdquo Transportation Research B vol 37 no 5pp 437ndash457 2003

[17] D F Jones S K Mirrazavi and M Tamiz ldquoMulti-objectivemeta-heuristics an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 137 no 1 pp 1ndash92002

[18] A Charnes and W W Cooper ldquoGoal programming and multi-objective optimization Part 1rdquo European Journal of OperationalResearch vol 1 no 1 pp 39ndash54 1977

[19] HHuang R J KauffmanH Xu and L Zhao ldquoA hybridmecha-nism for heterogeneous e-procurement involving a combinato-rial auction and bargainingrdquo Electronic Commerce Research andApplications vol 12 no 3 pp 181ndash194 2013

[20] Y Yang S Singhal and Y Xu ldquoAlternate strategies for a win-win seeking agent in agent-human negotiationsrdquo Journal ofManagement Information Systems vol 29 no 3 pp 223ndash2552012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

Therefore given the various operational and businessconstraints there exist variations in the auction design Forinstance Forster and Strasser [4] have studied auctions wherethe shipper opens up a list of individual transport lanes to thecarriers to bid and uses a strict price criterion as the primarymeasure of carrier selection (the winner of the auction)More recently Sheffi [1] presents a combinatorial auctionmechanism whereby shippers request bids for a group(s) oflanes rather than individual transport lanes to eke out bettercost efficiencies and economies of scale A one-shipper tomulticarrier network is considered as a combinatorial auction(CA) if the carriers are allowed to submit a combination ofindividual transport lanes as a packet

To date combinatorial auctions conducted effectivelyhave contributed to cost reduction and mutual satisfactionbetween the shipper and carriers as a main source of costis the asset repositioning cost that involves a carrier havingto relocate its resources (ships) to service a transport lanefrom one shipper to another [5] This is observed fromthe empty backhaul movements when servicing a particulartrade lane in the transport network Nair [6] reports thateven the most sophisticated carrier would have some excesscapacity Indeed theUSmarket contributed toUS$165 billionin total estimated industry loss due to capacity inefficiencies[7]

Under a CA setting a shipper typically offers a seriesof lanes that they wish to ldquobuyrdquo separately and each carrierwill run their carrier routing optimization to determine thepreferred packages that they can offer In order to be com-petitive each carrier would rationally try to offer the lowestprice possible subject to operational and capacity constraintsIdeally the bids tendered shouldminimize the carriersrsquo emptyload movements throughout its own network [8 9] andreduce the need to reposition the ships to another port forthe pick-up of more committed freight Cost uncertainty andshipment uncertainty are also covered in the literature of CA(see [10 11])

The CA approach has been noted to also allow a carrierto complement its network and pass of the cost savings tothe shipper For instance in Table 1 consider a case wherea carrier is interested to bid for lanes P

1a P3a P5a and P7a

In a single auction structure the carrier has to place eachinterested lane (P

1a P3a P5a or P7a) as a bid If lane P7a is

not part of the carrierrsquos winning bid then the carrier will haveto return from location J to its origin P with an empty loadthus incurring higher transportation costs Contrastingly ina combinatorial auctionmarket the carrier can place a bid forlane P

7b and refuse the entire package if one of the lanes is notpart of the winning bid

Thus the rationale for bidding based on packages isbased on the complementarity property where the packageis valued more than the sum of the individual lanes to thecarrier In addition by allowing for carriers the option ofdenying an entire package when one of their lanes is notaccepted in the bidding transaction eliminates a carrierrsquosasset repositioning costs and in return for this the carriertypically offers shippers more competitive rates This form ofbusiness transaction between the shipper and the carriers isoften facilitated by an internet-based ETM The auctioneer

can be the shipper or any third party service provider Todate combinatorial auctions for transportation procurementfocus on a single objective cost minimization model In thispaper we propose to include two other important criteriain the long-term sustainability of an auction market Theseare (i) marketplace fairness and (ii) the shipperrsquos confidenceof the carrierrsquos ability to provide the requisite service giventhat not all carriers have their own transit terminals and thussuffer from varying service times at the transit points that isquality of service To handle these objectives we will applythree multiobjective decision-makingmodels to compare thesolution approaches

The rest of the paper is organized as follows Section 2provides the relevant review on multiobjective optimizationmodels the weighted objective goal programming and com-promise programming Section 3 presents the mathematicalprogramming framework for the three models in the contextof transportation procurementThe data preparation and testprocedures are provided in Section 4 Section 5 discusses thesolutions and concludes the paper

2 Multiobjective Optimization

With conflicting and multiple objectives in an actual realworld decision-making context optimizing a single objectiveis no longer viable [12] In the case of combinatorial auctionsthe auctioneer usually needs to maintain other objectivesfor scenario planning For instance awarding lane contractsbased on cost alone may lead to only a selected few largecarriers being chosen as they have the needed capacity andnetwork reach This prevents other smaller players and otherregional players from engaging in the marketplace Otheroptimizing considerations include the quality of serviceand maintaining a ready pool of carriers through strategicresource allocation of containers We now review somemultiobjective mathematical programming techniques thatwe will use for this paper

21 Weighted Objectives Model (WOM) The WOM consid-ered to be the oldest method representing multiple objectivesin a linear programmingmodel [13] seeks to approximate theefficient set and provides a crude way of generating efficientsolutions by varying their weights Consider

max 119885 =

119869

sum

119894=1

119908119894119891119894(119909)

st 119909 isin 119883

(1)

where 119908119894is the positive weight of the objective 119891

119894(119909)

22 Goal Programming (GP) Goal programming extendsthe basic LP and keeps part of the kernel of MODM Itguides a decisionmaker to attain a closest solution possible tothe various conflicting objectives [14] Today GP techniqueshave been applied across disciplines ranging from vendorselection [15] to berth allocation in ports [16] Metaheuristicapproaches have been used to solve the GP routines such

Mathematical Problems in Engineering 3

Table 1 Simple versus combinatorial auction

Lanes offered Carrierrsquos bids in simple auction Carrierrsquos bids in CA

K

SP

J

P1a (PrarrK)P2a (KrarrP)P3a (Krarr S)P4a (SrarrK)P5a (Srarr J)P6a (Jrarr S)P7a (JrarrP)

P1b (PrarrK KrarrP)P2b (Krarr S Srarr J)

P3b (PrarrK Krarr S SrarrK KrarrP)P4b (Srarr J Jrarr S)

P5b (Krarr S Srarr J Jrarr S SrarrK)P6b (PrarrK Krarr S Srarr J Jrarr S SrarrK KrarrP)

P7b (PrarrK Krarr S Srarr J JrarrP)

as simulated annealing genetic algorithms and Tabu search[17] Since GP allows one to adjust the target values andorweights flexibly it can also be used for scenario planningThis is especially useful in the context of CA especially forthe shipper who may wish to reshift focus on other nonpriceconsiderations after the bid exercise Two forms of GP existweighted and preemptive The former assigns weights tounwanted deviations thus effectively allowing the decisionmaker to state their relative importance of the objectivesThe objective is singly minimized as an Archimedean sum asfollows

min 119885 =

119898

sum

119894=1

119908minus

119894119889minus

119894+ 119908+

119894119889+

119894

st 119891119894(119909) + 119889

minus

119894minus 119889+

119894= 119887119894 119894 = 1 2 3 119909 isin 119883

(2)

where119891119894(119909) is the linear objective function with a target value

of 119887119894 while 119908

minus

119894and 119908

+

119894are nonzero weights attached to the

respective positive 119889+119894(overachievement) and negative devia-

tions 119889minus119894(underachievement) This technique minimizes the

sum of deviations from the target valueThe second goal formulation minimizes deviations hier-

archically 1198751(119909) gt 119875

2(119909) gt sdot sdot sdot gt 119875

119904(119909) This is akin to

optimizing fully a goal that has a higher importance beforemoving to the next goal In short the goal of a higher orderpriority is infinitely more important than the goals of lowerpriority Thus the objective function in (2) can be replacedwith

min 119885 =

119869

sum

119894=1

119875119904(119908minus

119894119889minus

119894+ 119908+

119894119889+

119894) (3)

23 Compromise Programming (CP) CP models conflictingobjectives as a distance minimizing function so as to reacha point nearest to the ideal solution The ideal solutionis gathered by optimizing each objective with the hardconstraints individually while ignoring all other objectivesThe CP approach can be viewed as an extension of the GPtechnique with somemodifications to the deviation variableswhile fixing the root at unity [18]Themathematical model isas follows

min 119885 =

119898

sum

119894=1

[119908119901

119894(119887119894minus 119891119894(119909)

Δ119894

)

119901

]

1119901

st 119909 isin 119883

(4)

where 119908119901

119894are the nonpreemptive weights of the 119901th metric

while Δ119894

= 119891+

119894(119909) minus 119891

minus

119894(119909) are the normalizing constants

obtained by the distance between the maximum and mini-mum anchors for each objective function 119894 Tamiz et al [12]show that for 119901 = 120572 it is equivalent to solving

min 120572

st 120572 ge119908119894

Δ119894

[119887lowast

119894minus 119891119894(119909)] 119894 = 1 2 119909 isin 119883

(5)

where 119887lowast119894is obtained by maximizing 119891

119894(119909)

3 Modelling the TransportationProcurement Problem

We now model the combinatorial auction transportationprocurement problem that supports multiple lanes multiplepackages and multiple bidders whereby the shipper attractsbids for a set of lanes as single packages that have differ-ent prices for each unit of volume in each lane (origin-destination) The volumes submitted for each package variesaccording to the carriersrsquo resource capacities We introducethe following notation

31 Indices

I Set of shipping origins

J Set of shipping destinations

K Set of packages

C Set of carriers

32 Parameters The set of bid bundles119888119861119896 can be specified

as a 4-tuple (119888119886119896119888119901119896119888119871119896119888119880119896) where

(i)119888119886119896= (119888119886119896

11 119888119886119896

119894119895 119888119886119896

119898119899) with

119888119886119896isin (R+)

119898times119899

119888119886119896

119894119895is the load volume per unit time (week) received

from carrier 119888 on transport lane from origin 119894 todestination 119895 that are being bid out as part of package119896

(ii)119888119901119896= (11988811990111989611 119888119901119896119894119895 119888119901119896119898119899

)with119888119901119896isin (R+)

119898times119899

119888119901119896119894119895is the bid price per load on lane 119894 to 119895 received

from carrier 119888 as part of package bid 119896

4 Mathematical Problems in Engineering

(iii)119888119871119896= (119888119871119896

11 119888119871119896

119894119895 119888119871119896

119898119899) with

119888119871119896isin (R+)

119898times119899

119888119871119896

119894119895is the lower bound in loads on lane 119894 to 119895 that

carrier 119888 is willing to accept as part of package bid 119896

(iv)119888119880119896

= (119888119880119896

11 119888119880119896

119894119895 119888119880119896

119898119899) with

119888119880119896

isin

(R+)119898times119899119888119880119896

119894119895is the upper bound in loads on lane 119894 to

119895 that carrier 119888 is willing to accept as part of packagebid 119896

Each bundle bid119888119861119896 is a placement order that is services that

are to be sold by the auctioneer

33 Decision Variables We define the decision variable cor-responding to each lane as

119888119909119896

119894119895 where

119888119909119896

119894119895is fraction of load

per time unit (week) on lane 119894 to 119895 from carrier 119888 on packagebid 119896

Subsequently each package is denoted as119888119910119896 where

119888119910119896

denotes that if carrier 119888 is assigned package bid 119896 then119888119910119896=

1 otherwise119888119910119896= 0

34TheModel Formulation We seek to simultaneously min-imize cost maximize marketplace fairness and maximizeshipperrsquos confidenceCost Objective The total cost of the accepted bids is mini-mized as

1198911(119909) = Min

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895 (6)

Marketplace Fairness Objective The total number of acceptedpackages is maximized as

1198912(119909) = Max

sellersum

119888=1

package

sum

119896=1

119888119910119896 (7)

Marketplace Confidence ObjectiveThedifference between thelower bound volume sought by the carrier and the upperbound volume sought by the auctioneer is minimized asfollows

1198913(119909) = Min

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816 (8)

Supply-Demand Constraint The total volume accepted aswinning packagesmust be no less than the volume auctionedthat is

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895 119888119909119896

119894119895

ge

destinationsum

119896=1

origin

sum

119894=1

119886119896

119894119895119909119896

119894119895forall119894 isin origin 119895 isin destination

(9)

Transactional Constraints Equation (10) allows the auction-eer to transact the entire package within a particular volumerange specified by the carriers The variable 1

119888119910119896

in (10)ensures that the carrier must offer all lanes within thepackage if one of the lanes is approved as a winning lane bythe auctioneer Consider

minus119872119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination

minus119888119871119861119896

119894119895 119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination

119888119880119861119896

119894119895 119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(10)

Business Guarantee Constraint A shipper might not wantto rely too heavily on a small number of winning carriersIn the longer term it might be prudent for a shipper toensure that the amount of traffic won by a carrier is within acertain bound This will create a higher potential for carriersto revisit the marketplace to bid The scope of the carrier setcoverage is measured by the amount of volume (loads) wonThe constraints below ensure that all carriers are awardedbusiness within some preset volume bounds Consider

119888Min Value le

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895

le119888Max Value

(11)

Carrier Base Size Constraints This is an extension to thebusiness guarantee constraint with the restriction on thenumber of winning carriers for each lane The system-based(or hard) approach adds the following constraints to limit thenumber of carriers assigned at the lane level

minus119872119888119908119894+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(12)

sellersum

119888=1

119888119908119894le 119871119894

forall119894 isin origin (13)

minus119872119888119911 +119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(14)

sellersum

119888=1

119888119911 le 119878 (15)

Mathematical Problems in Engineering 5

The number of carriers winning the right to haul at origin 119894

is denoted as 119871119894in (13) while 119878 is the system limit of winning

carriers for the entire auction

Simple Reload Bids Constraint This constraint denotes thatthe ratio of outbound volume to inbound volume must be atleast119888120573119895 Consider

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119895119894 119888119888119896

119895119894

ge119888120573119895lowast

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895 119888119909119896

119894119895forall119888 119896

(16)

Nonnegativity and Binary Constraints As the decision vari-ables are expressed as percentages we define

119888119909119896

119894119895in (17) as

real numbers Carrier 119888 is assigned package bid 119896when 119888119910119896 =

1 (or 0 otherwise) (18) Carrier 119888 is assigned to origin 119894 when119888119908119894= 1 (or 0 else) (19) Also carrier 119888 is assigned to a network

when119888119911119894= 1 (or 0 otherwise) (20) Consider

119888119909119896

119894119895isin 119877+ (17)

119888119910119896= 0 1 (18)

119888119908119894= 0 1 (19)

119888119911 = 0 1 (20)

We now present the three models for the CA transportprocurement problem WOM preemptive GP and CPWOM Consider

Min 1199081(

sellersum

119888=1

packag

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895)

minus 1199082(

sellersum

119888=1

package

sum

119896=1

119888119910119896)

+ 1199083(

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816)

st (9)ndash(20) (21)

Preemptive Goal Model (PGM) Consider

Min 1198751119889+

1+ 1198752119889minus

2+ 1198753119889+

3 1198751gt 1198752gt 119875119904(119909)

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895+ 119889minus

1minus 119889+

1

= Cost Goal

sellersum

119888=1

package

sum

119896=1

119888119910119896+119889minus

2minus 119889+

2

= Marketplace Reputation Goal

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816+ 119889minus

3minus 119889+

3

= Shipperrsquos Confidence Goal

st (9)ndash(20) (22)

where 119889minus119894and 119889

+

119894are the underachievement and overachieve-

ment deviations of the 119894th goal

CPM The combinatorial auction transportation procure-ment model in a CP is as follows

Min

1199081((

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895

minus 119888lowast

119894) times (119888

lowast

119894)minus1

)

119875

minus 1199082(

sumseller119888=1

sumpackage119896=1 119888

119910119896minus119903lowast

119894

119903lowast

119894

)

119875

+ 1199083((

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816

minus119904lowast

119894) times (119904

lowast

119894)minus1

)

119875

1119875

st (9)ndash(20) (23)

where 119901 = 1 2 infin The ideal values of cost marketplacefairness and shipperrsquos confidence are gathered from 119888

lowast

119894=

min1198911(119909) 119903lowast

119894= max119891

2(119909) and 119904

lowast

119894= min119891

3(119909) respec-

tively (see (6)ndash(8)) The larger deviations receive greaterimportance as 119901 increases This is the penalizing effectplaced on larger deviations from their respective ideal solu-tions The compromise solutions satisfy 1 le 119901 le infin

6 Mathematical Problems in Engineering

Table 2 Results experimental runs

Test Model Cost ($) Marketplace fairness Shipperrsquos confidence1 Ideal cost 116650 4 158382 Ideal marketplace fairness 2589176 100 2724223 Ideal shipperrsquos confidence 673384 34 04 Preemptive GP 129611 4 737575 Equal weight 194505 12 2783

CP (equal weights)6 119901 = 1 441444 27 23087 119901 = 2 153932 5 20388 119901 = infin 129441 4 74755

The solution at 119901 = infin indicates that the largest deviationamong all objectives is the most dominant in the optimalsolutionrsquos distance function

4 Solution and Analysis

The following steps detail our dataset generation procedureand analysis

Step 1 (generate shipperrsquos lane offerings) The condition ofCA requires each shipper to put the amount of volume fora set of lanes on offer in separate auction markets We set[119878+]1times119899

as the shipperrsquos volume required in a CA of 119899 lanesThe maximum amount of loads available for carriers to bidon each 119894-119895 origin-destination (lane) or cell 0119886

119894119895isin [119878+]1times119899

is randomly generated from [1000 10000] using a uniformdistribution

Step 2 (generate carriersrsquo bids) We assume that the carriersare able to view the total available volumes for each lane andset their bids accordingly For our simulated carrierrsquos amountof loads we generate a seed number 120572 between [1 100] foreach lane A value of 120572 greater than 50 enforces the rule ofempty cells and signifies the refusal of a carrier to accepta particular lane If 120572 lt 50 another random number 120573 isgenerated between [06 1] where 120573 lowast

0119886119894119895=1119886119894119895and 1119888119886119894119895isin

[119862+]119898times119899

correspond to the amount of loads offered by the119898thcarrier of the 119899th lane

Step 3 (solving routines) The buy and sell prices of each laneare fixed at $3 and $1 per unit of load respectivelyThe datasetis solved by WOM PGM and CPM respectively on Lingoversion 8

Step 4 (results and sensitivity analysis) Table 2 shows theresults where a series of 8 tests were run The ideal valuesof each objective are obtained by analyzing each objectiveindependently while keeping all the constraints in themodelWe observe that the model that optimises the cost yieldsthe lowest cost ($11665) out of all models tested This trendcontinues with models that optimise marketplace fairnessand shipperrsquos confidence respectively yielding the best resultfor marketplace fairness (100) and shipperrsquos confidence (0)when compared with other models We define shipperrsquos

confidence to be the distance between the carriersrsquo bidvolume and the shipperrsquos request The value of 0 indicates nodistance and denotes that all requested volumes by shippercan be met

In the PGM the preemptive weights are specified in thefollowing order of importance cost marketplace fairnessand shipperrsquos confidence Here the cost value is close to theideal cost as this objective was stated to be infinitely moreimportant than the other objectivesThe value ofmarketplacefairness in Test 4 is the same as Test 1 However the differencein shipperrsquos confidence is expected as its inclusion as anobjective renders that cost will be sacrificed by 129611 minus

116650 = $12961 Thus in considering the 3 objectiveshierarchically the feasible solution sacrificed in cost waspassed onto satisfying shipperrsquos confidence This can be seenfrom the reduced unawarded volume of 73757 (Test 4) from15838 (Test 1)

InTest 5 we formulated aweighted-objectivesmodelwith1199081

= 1199082

= 1199083

= 13 to optimize a set of objectivessimultaneously with the same priority for all objectives

A sensitivity analysis is conducted on the WOM byvarying the weights of each objective while the other 2objectives are restricted to sharing the remainder weightsequally (Tables 3ndash5) The results of the WOMmodel are alsocompared directly against the CP model since the weights ofthe three objectives are standardized to be equal across thetwo techniques It is observed that the CPmethod dominateson cost and shipperrsquos confidence The CPM solution isobtained when 119901 is set to infin Further as 119901 rarr infin the costand shipperrsquos confidence objectives improve at the expenseof marketplace fairness (Table 2 Tests 6 to 8) However theWOM results are not necessarily inferior to the CPM asthe shipper now can now choose between the solutions ofTest 5 or Test 8 Test 5 produces 12 winning bids whileTest 8 produces 4 winning bids If all 12 winning bidsare won by a single carrier in Test 5 but the 4 winningbids of Test 8 are won by different carriers the shippermay strategically select the CPM solution On the otherhand if some of the winning bids in Test 5 are won by aprominent carrier that is not part of the winning carrier inTest 8 the shipper may opt for the Test 5 WOM solutioninstead to keep the service relationship intact as much aspossible

Mathematical Problems in Engineering 7

Table 3 Varying cost objective weights WOMmethod

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 1166496 1166496 1166496 1166496 1166496 1166496 123742 194505 265986 758231 3052837 3052837Marketplace fairness 4 4 4 4 4 4 5 12 18 39 100 100Marketplace confidence 15838 15838 15838 15838 15838 15838 16924 2783 38234 109119864 minus 04 0 0

Table 4 Varying marketplace fairness weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 2589176 244227 244227 244227 1752309 7371432 3894 1945048 14262 1166496 1166496 1166496Marketplace fairness 100 100 100 100 82 45 27 12 7 4 4 4Marketplace confidence 272422 358248 358248 358248 256872 108082 55576 2783 19708 15838 15838 15838

Table 5 Varying marketplace confidence weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 673384 200191 200191 200191 200191 200191 1950118 1945048 217084 2408288 2532848 3047688Marketplace fairness 34 100 100 100 100 100 11 12 14 16 17 21Marketplace confidence 0 0 0 0 0 0 18462 2783 31358 3474 3647 43678

Table 6 Varying cost objective weights CP method

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 116650 118066 119614 121316 123194 125278 127647 129441 130421 133686 137680 911812Marketplace fairness 4 4 4 4 4 4 4 4 4 4 4 38Marketplace confidence 158380 148941 138614 127269 114748 100855 85695 74755 68988 49782 27313 1119864 minus 04

Table 7 Varying marketplace fairness weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 763739 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441Marketplace fairness 42 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 10459 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755

8 Mathematical Problems in Engineering

Table 8 Varying marketplace confidence weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 911812 141246 139581 137823 135860 133686 131261 129441 128466 125278 121454 116649Marketplace fairness 38 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 1119864 minus 04 7986 16752 26517 37424 49783 64046 74755 80572 100855 126351 158380

The solutions of Table 6 can be compared directly toTable 3 as can be Tables 7 and 4 as well as Tables 8 and 5respectively Generally when the weights for the cost objec-tive are reduced on a 005 step decrease from 1 to 0 the costvalue steadily increases for the CPM This trend is also truefor marketplace confidence However the WOM model isinsensitive to weight changes when the cost weights are in[05 1] The same pattern is found for marketplace fairnessand shipperrsquos confidence where varying weights between[0 015] and [005 025] for the respective objectives didnot change the values of those objectives (Tables 4 and5) The CPM quickly reaches a minimum for marketplacefairness with a slight change in weights from the maximum1 Choosing a different 119875 value will alter marketplace fairnessThus theWOMcan provide solutions quickly for eachweightvariation However the CPM can provide many solutionsfor the same weight variations albeit having to vary theparameter 119901

5 Conclusions

While research on transportation procurement has benefitedfrom the use of CA the literature does not explicitly providemodel solutions and formulation for the multiobjective con-textThismay be due to the difficulty in operationalising con-cepts such as marketplace fairness and shipperrsquos confidenceThis paper treating the MODM problem in the context asa multiobjective optimization model allows the shipper toinclude nonfinancial carrier selection measures Future workcan consider a service index that can be incorporated andupdated from one auction to another to allow carriers tobe tracked on performance Our results suggest that there isno dominant MODM technique However this is good forthe shipper as shipper now has at its disposal a variety oftechniques to compare against when making a final decisionon the winner for the auction Alternatively the shipper canuse the results for a further bargaining process with thecarriers There may be a situation where the shipper intendsto use a particular carrier who has a high quality service levelbut has a higher service cost too The shipper may then askthe carrier whether it could provide the service at the nextlower price For incorporating a bargaining phase into a CAmechanism readers may be interested in the work of Huanget al [19] Another alternative would be to introduce trust-based mechanism by observing the discrepancy between theresults and the services offered One step further would be

to use this as a means to validate the sensitivity resultsTrust mechanisms have been used in agent-based researchto support decisions made on economic exchange (see [20])Future workmay also include soft computing approaches thatallow the shipper to automate and filter the solutions based onother criteria such as the business relationships

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y Sheffi ldquoCombinatorial auctions in the procurement of trans-portation servicesrdquo Interfaces vol 34 no 4 pp 245ndash252 2004

[2] Y Guo A Lim B Rodrigues and Y Zhu ldquoCarrier assignmentmodels in transportation procurementrdquo Journal of the Opera-tional Research Society vol 57 no 12 pp 1472ndash1481 2006

[3] S M H Motlagh M M Sepehri J Ignatius and A MustafaldquoOptimizing trade in transportation procurement is combi-natorial double auction approach truly betterrdquo InternationalJournal of Innovative Computing Information and Control vol6 no 6 pp 2537ndash2550 2010

[4] J R Forster and S Strasser ldquoCarrier modal selection factorsthe shipper carrier paradoxrdquo Transportation Research Forumvol 31 no 1 pp 206ndash212 1991

[5] W Elmaghraby and P Keskinocak ldquoCombinatorial auctionsin procurementrdquo Tech Rep School of Industrial and SystemsEngineering Georgia Institute of Technology 2002

[6] A Nair ldquoEmerging internet-enabled auction mechanisms insupply chainrdquo Supply ChainManagement vol 10 no 3 pp 162ndash168 2005

[7] O Ergun G Kuyzu and M Savelsbergh ldquoShipper collabora-tionrdquo Computers and Operations Research vol 34 no 6 pp1551ndash1560 2007

[8] C Caplice Optimization-based bidding a new framework forshipper-carrier relationships [PhD dissertation] MIT Cam-bridge Mass USA 1996

[9] C Caplice and Y Sheffi ldquoOptimization based procurement fortransportation servicesrdquo Journal of Business Logistics vol 24 no2 pp 109ndash128 2004

[10] J Ignatius Y-J Lai SMHosseini-MotlaghMM Sepehri andA Mustafa ldquoModeling fuzzy combinatorial auctionrdquo ExpertSystems with Applications vol 38 pp 11482ndash11488 2011

Mathematical Problems in Engineering 9

[11] N Remli and M Rekik ldquoA robust winner determination prob-lem for combinatorial transportation auctions under uncertainshipment volumesrdquo Transportation Research C vol 35 no 10pp 204ndash217 2013

[12] M Tamiz D Jones and C Romero ldquoGoal programming fordecision making an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 111 no 3 pp569ndash581 1998

[13] A M Geoffrion ldquoProper efficiency and the theory of vectormaximizationrdquo Journal of Mathematical Analysis and Applica-tions vol 22 no 3 pp 618ndash630 1968

[14] A Charnes andW W CooperManagement Models and Indus-trial Applications of Linear Programming John Wiley amp SonsNew York NY USA 1961

[15] VWadhwa andA R Ravindran ldquoVendor selection in outsourc-ingrdquo Computers and Operations Research vol 34 no 12 pp3725ndash3737 2007

[16] A Imai E Nishimura and S Papadimitriou ldquoBerth allocationwith service priorityrdquo Transportation Research B vol 37 no 5pp 437ndash457 2003

[17] D F Jones S K Mirrazavi and M Tamiz ldquoMulti-objectivemeta-heuristics an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 137 no 1 pp 1ndash92002

[18] A Charnes and W W Cooper ldquoGoal programming and multi-objective optimization Part 1rdquo European Journal of OperationalResearch vol 1 no 1 pp 39ndash54 1977

[19] HHuang R J KauffmanH Xu and L Zhao ldquoA hybridmecha-nism for heterogeneous e-procurement involving a combinato-rial auction and bargainingrdquo Electronic Commerce Research andApplications vol 12 no 3 pp 181ndash194 2013

[20] Y Yang S Singhal and Y Xu ldquoAlternate strategies for a win-win seeking agent in agent-human negotiationsrdquo Journal ofManagement Information Systems vol 29 no 3 pp 223ndash2552012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

Table 1 Simple versus combinatorial auction

Lanes offered Carrierrsquos bids in simple auction Carrierrsquos bids in CA

K

SP

J

P1a (PrarrK)P2a (KrarrP)P3a (Krarr S)P4a (SrarrK)P5a (Srarr J)P6a (Jrarr S)P7a (JrarrP)

P1b (PrarrK KrarrP)P2b (Krarr S Srarr J)

P3b (PrarrK Krarr S SrarrK KrarrP)P4b (Srarr J Jrarr S)

P5b (Krarr S Srarr J Jrarr S SrarrK)P6b (PrarrK Krarr S Srarr J Jrarr S SrarrK KrarrP)

P7b (PrarrK Krarr S Srarr J JrarrP)

as simulated annealing genetic algorithms and Tabu search[17] Since GP allows one to adjust the target values andorweights flexibly it can also be used for scenario planningThis is especially useful in the context of CA especially forthe shipper who may wish to reshift focus on other nonpriceconsiderations after the bid exercise Two forms of GP existweighted and preemptive The former assigns weights tounwanted deviations thus effectively allowing the decisionmaker to state their relative importance of the objectivesThe objective is singly minimized as an Archimedean sum asfollows

min 119885 =

119898

sum

119894=1

119908minus

119894119889minus

119894+ 119908+

119894119889+

119894

st 119891119894(119909) + 119889

minus

119894minus 119889+

119894= 119887119894 119894 = 1 2 3 119909 isin 119883

(2)

where119891119894(119909) is the linear objective function with a target value

of 119887119894 while 119908

minus

119894and 119908

+

119894are nonzero weights attached to the

respective positive 119889+119894(overachievement) and negative devia-

tions 119889minus119894(underachievement) This technique minimizes the

sum of deviations from the target valueThe second goal formulation minimizes deviations hier-

archically 1198751(119909) gt 119875

2(119909) gt sdot sdot sdot gt 119875

119904(119909) This is akin to

optimizing fully a goal that has a higher importance beforemoving to the next goal In short the goal of a higher orderpriority is infinitely more important than the goals of lowerpriority Thus the objective function in (2) can be replacedwith

min 119885 =

119869

sum

119894=1

119875119904(119908minus

119894119889minus

119894+ 119908+

119894119889+

119894) (3)

23 Compromise Programming (CP) CP models conflictingobjectives as a distance minimizing function so as to reacha point nearest to the ideal solution The ideal solutionis gathered by optimizing each objective with the hardconstraints individually while ignoring all other objectivesThe CP approach can be viewed as an extension of the GPtechnique with somemodifications to the deviation variableswhile fixing the root at unity [18]Themathematical model isas follows

min 119885 =

119898

sum

119894=1

[119908119901

119894(119887119894minus 119891119894(119909)

Δ119894

)

119901

]

1119901

st 119909 isin 119883

(4)

where 119908119901

119894are the nonpreemptive weights of the 119901th metric

while Δ119894

= 119891+

119894(119909) minus 119891

minus

119894(119909) are the normalizing constants

obtained by the distance between the maximum and mini-mum anchors for each objective function 119894 Tamiz et al [12]show that for 119901 = 120572 it is equivalent to solving

min 120572

st 120572 ge119908119894

Δ119894

[119887lowast

119894minus 119891119894(119909)] 119894 = 1 2 119909 isin 119883

(5)

where 119887lowast119894is obtained by maximizing 119891

119894(119909)

3 Modelling the TransportationProcurement Problem

We now model the combinatorial auction transportationprocurement problem that supports multiple lanes multiplepackages and multiple bidders whereby the shipper attractsbids for a set of lanes as single packages that have differ-ent prices for each unit of volume in each lane (origin-destination) The volumes submitted for each package variesaccording to the carriersrsquo resource capacities We introducethe following notation

31 Indices

I Set of shipping origins

J Set of shipping destinations

K Set of packages

C Set of carriers

32 Parameters The set of bid bundles119888119861119896 can be specified

as a 4-tuple (119888119886119896119888119901119896119888119871119896119888119880119896) where

(i)119888119886119896= (119888119886119896

11 119888119886119896

119894119895 119888119886119896

119898119899) with

119888119886119896isin (R+)

119898times119899

119888119886119896

119894119895is the load volume per unit time (week) received

from carrier 119888 on transport lane from origin 119894 todestination 119895 that are being bid out as part of package119896

(ii)119888119901119896= (11988811990111989611 119888119901119896119894119895 119888119901119896119898119899

)with119888119901119896isin (R+)

119898times119899

119888119901119896119894119895is the bid price per load on lane 119894 to 119895 received

from carrier 119888 as part of package bid 119896

4 Mathematical Problems in Engineering

(iii)119888119871119896= (119888119871119896

11 119888119871119896

119894119895 119888119871119896

119898119899) with

119888119871119896isin (R+)

119898times119899

119888119871119896

119894119895is the lower bound in loads on lane 119894 to 119895 that

carrier 119888 is willing to accept as part of package bid 119896

(iv)119888119880119896

= (119888119880119896

11 119888119880119896

119894119895 119888119880119896

119898119899) with

119888119880119896

isin

(R+)119898times119899119888119880119896

119894119895is the upper bound in loads on lane 119894 to

119895 that carrier 119888 is willing to accept as part of packagebid 119896

Each bundle bid119888119861119896 is a placement order that is services that

are to be sold by the auctioneer

33 Decision Variables We define the decision variable cor-responding to each lane as

119888119909119896

119894119895 where

119888119909119896

119894119895is fraction of load

per time unit (week) on lane 119894 to 119895 from carrier 119888 on packagebid 119896

Subsequently each package is denoted as119888119910119896 where

119888119910119896

denotes that if carrier 119888 is assigned package bid 119896 then119888119910119896=

1 otherwise119888119910119896= 0

34TheModel Formulation We seek to simultaneously min-imize cost maximize marketplace fairness and maximizeshipperrsquos confidenceCost Objective The total cost of the accepted bids is mini-mized as

1198911(119909) = Min

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895 (6)

Marketplace Fairness Objective The total number of acceptedpackages is maximized as

1198912(119909) = Max

sellersum

119888=1

package

sum

119896=1

119888119910119896 (7)

Marketplace Confidence ObjectiveThedifference between thelower bound volume sought by the carrier and the upperbound volume sought by the auctioneer is minimized asfollows

1198913(119909) = Min

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816 (8)

Supply-Demand Constraint The total volume accepted aswinning packagesmust be no less than the volume auctionedthat is

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895 119888119909119896

119894119895

ge

destinationsum

119896=1

origin

sum

119894=1

119886119896

119894119895119909119896

119894119895forall119894 isin origin 119895 isin destination

(9)

Transactional Constraints Equation (10) allows the auction-eer to transact the entire package within a particular volumerange specified by the carriers The variable 1

119888119910119896

in (10)ensures that the carrier must offer all lanes within thepackage if one of the lanes is approved as a winning lane bythe auctioneer Consider

minus119872119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination

minus119888119871119861119896

119894119895 119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination

119888119880119861119896

119894119895 119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(10)

Business Guarantee Constraint A shipper might not wantto rely too heavily on a small number of winning carriersIn the longer term it might be prudent for a shipper toensure that the amount of traffic won by a carrier is within acertain bound This will create a higher potential for carriersto revisit the marketplace to bid The scope of the carrier setcoverage is measured by the amount of volume (loads) wonThe constraints below ensure that all carriers are awardedbusiness within some preset volume bounds Consider

119888Min Value le

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895

le119888Max Value

(11)

Carrier Base Size Constraints This is an extension to thebusiness guarantee constraint with the restriction on thenumber of winning carriers for each lane The system-based(or hard) approach adds the following constraints to limit thenumber of carriers assigned at the lane level

minus119872119888119908119894+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(12)

sellersum

119888=1

119888119908119894le 119871119894

forall119894 isin origin (13)

minus119872119888119911 +119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(14)

sellersum

119888=1

119888119911 le 119878 (15)

Mathematical Problems in Engineering 5

The number of carriers winning the right to haul at origin 119894

is denoted as 119871119894in (13) while 119878 is the system limit of winning

carriers for the entire auction

Simple Reload Bids Constraint This constraint denotes thatthe ratio of outbound volume to inbound volume must be atleast119888120573119895 Consider

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119895119894 119888119888119896

119895119894

ge119888120573119895lowast

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895 119888119909119896

119894119895forall119888 119896

(16)

Nonnegativity and Binary Constraints As the decision vari-ables are expressed as percentages we define

119888119909119896

119894119895in (17) as

real numbers Carrier 119888 is assigned package bid 119896when 119888119910119896 =

1 (or 0 otherwise) (18) Carrier 119888 is assigned to origin 119894 when119888119908119894= 1 (or 0 else) (19) Also carrier 119888 is assigned to a network

when119888119911119894= 1 (or 0 otherwise) (20) Consider

119888119909119896

119894119895isin 119877+ (17)

119888119910119896= 0 1 (18)

119888119908119894= 0 1 (19)

119888119911 = 0 1 (20)

We now present the three models for the CA transportprocurement problem WOM preemptive GP and CPWOM Consider

Min 1199081(

sellersum

119888=1

packag

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895)

minus 1199082(

sellersum

119888=1

package

sum

119896=1

119888119910119896)

+ 1199083(

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816)

st (9)ndash(20) (21)

Preemptive Goal Model (PGM) Consider

Min 1198751119889+

1+ 1198752119889minus

2+ 1198753119889+

3 1198751gt 1198752gt 119875119904(119909)

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895+ 119889minus

1minus 119889+

1

= Cost Goal

sellersum

119888=1

package

sum

119896=1

119888119910119896+119889minus

2minus 119889+

2

= Marketplace Reputation Goal

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816+ 119889minus

3minus 119889+

3

= Shipperrsquos Confidence Goal

st (9)ndash(20) (22)

where 119889minus119894and 119889

+

119894are the underachievement and overachieve-

ment deviations of the 119894th goal

CPM The combinatorial auction transportation procure-ment model in a CP is as follows

Min

1199081((

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895

minus 119888lowast

119894) times (119888

lowast

119894)minus1

)

119875

minus 1199082(

sumseller119888=1

sumpackage119896=1 119888

119910119896minus119903lowast

119894

119903lowast

119894

)

119875

+ 1199083((

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816

minus119904lowast

119894) times (119904

lowast

119894)minus1

)

119875

1119875

st (9)ndash(20) (23)

where 119901 = 1 2 infin The ideal values of cost marketplacefairness and shipperrsquos confidence are gathered from 119888

lowast

119894=

min1198911(119909) 119903lowast

119894= max119891

2(119909) and 119904

lowast

119894= min119891

3(119909) respec-

tively (see (6)ndash(8)) The larger deviations receive greaterimportance as 119901 increases This is the penalizing effectplaced on larger deviations from their respective ideal solu-tions The compromise solutions satisfy 1 le 119901 le infin

6 Mathematical Problems in Engineering

Table 2 Results experimental runs

Test Model Cost ($) Marketplace fairness Shipperrsquos confidence1 Ideal cost 116650 4 158382 Ideal marketplace fairness 2589176 100 2724223 Ideal shipperrsquos confidence 673384 34 04 Preemptive GP 129611 4 737575 Equal weight 194505 12 2783

CP (equal weights)6 119901 = 1 441444 27 23087 119901 = 2 153932 5 20388 119901 = infin 129441 4 74755

The solution at 119901 = infin indicates that the largest deviationamong all objectives is the most dominant in the optimalsolutionrsquos distance function

4 Solution and Analysis

The following steps detail our dataset generation procedureand analysis

Step 1 (generate shipperrsquos lane offerings) The condition ofCA requires each shipper to put the amount of volume fora set of lanes on offer in separate auction markets We set[119878+]1times119899

as the shipperrsquos volume required in a CA of 119899 lanesThe maximum amount of loads available for carriers to bidon each 119894-119895 origin-destination (lane) or cell 0119886

119894119895isin [119878+]1times119899

is randomly generated from [1000 10000] using a uniformdistribution

Step 2 (generate carriersrsquo bids) We assume that the carriersare able to view the total available volumes for each lane andset their bids accordingly For our simulated carrierrsquos amountof loads we generate a seed number 120572 between [1 100] foreach lane A value of 120572 greater than 50 enforces the rule ofempty cells and signifies the refusal of a carrier to accepta particular lane If 120572 lt 50 another random number 120573 isgenerated between [06 1] where 120573 lowast

0119886119894119895=1119886119894119895and 1119888119886119894119895isin

[119862+]119898times119899

correspond to the amount of loads offered by the119898thcarrier of the 119899th lane

Step 3 (solving routines) The buy and sell prices of each laneare fixed at $3 and $1 per unit of load respectivelyThe datasetis solved by WOM PGM and CPM respectively on Lingoversion 8

Step 4 (results and sensitivity analysis) Table 2 shows theresults where a series of 8 tests were run The ideal valuesof each objective are obtained by analyzing each objectiveindependently while keeping all the constraints in themodelWe observe that the model that optimises the cost yieldsthe lowest cost ($11665) out of all models tested This trendcontinues with models that optimise marketplace fairnessand shipperrsquos confidence respectively yielding the best resultfor marketplace fairness (100) and shipperrsquos confidence (0)when compared with other models We define shipperrsquos

confidence to be the distance between the carriersrsquo bidvolume and the shipperrsquos request The value of 0 indicates nodistance and denotes that all requested volumes by shippercan be met

In the PGM the preemptive weights are specified in thefollowing order of importance cost marketplace fairnessand shipperrsquos confidence Here the cost value is close to theideal cost as this objective was stated to be infinitely moreimportant than the other objectivesThe value ofmarketplacefairness in Test 4 is the same as Test 1 However the differencein shipperrsquos confidence is expected as its inclusion as anobjective renders that cost will be sacrificed by 129611 minus

116650 = $12961 Thus in considering the 3 objectiveshierarchically the feasible solution sacrificed in cost waspassed onto satisfying shipperrsquos confidence This can be seenfrom the reduced unawarded volume of 73757 (Test 4) from15838 (Test 1)

InTest 5 we formulated aweighted-objectivesmodelwith1199081

= 1199082

= 1199083

= 13 to optimize a set of objectivessimultaneously with the same priority for all objectives

A sensitivity analysis is conducted on the WOM byvarying the weights of each objective while the other 2objectives are restricted to sharing the remainder weightsequally (Tables 3ndash5) The results of the WOMmodel are alsocompared directly against the CP model since the weights ofthe three objectives are standardized to be equal across thetwo techniques It is observed that the CPmethod dominateson cost and shipperrsquos confidence The CPM solution isobtained when 119901 is set to infin Further as 119901 rarr infin the costand shipperrsquos confidence objectives improve at the expenseof marketplace fairness (Table 2 Tests 6 to 8) However theWOM results are not necessarily inferior to the CPM asthe shipper now can now choose between the solutions ofTest 5 or Test 8 Test 5 produces 12 winning bids whileTest 8 produces 4 winning bids If all 12 winning bidsare won by a single carrier in Test 5 but the 4 winningbids of Test 8 are won by different carriers the shippermay strategically select the CPM solution On the otherhand if some of the winning bids in Test 5 are won by aprominent carrier that is not part of the winning carrier inTest 8 the shipper may opt for the Test 5 WOM solutioninstead to keep the service relationship intact as much aspossible

Mathematical Problems in Engineering 7

Table 3 Varying cost objective weights WOMmethod

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 1166496 1166496 1166496 1166496 1166496 1166496 123742 194505 265986 758231 3052837 3052837Marketplace fairness 4 4 4 4 4 4 5 12 18 39 100 100Marketplace confidence 15838 15838 15838 15838 15838 15838 16924 2783 38234 109119864 minus 04 0 0

Table 4 Varying marketplace fairness weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 2589176 244227 244227 244227 1752309 7371432 3894 1945048 14262 1166496 1166496 1166496Marketplace fairness 100 100 100 100 82 45 27 12 7 4 4 4Marketplace confidence 272422 358248 358248 358248 256872 108082 55576 2783 19708 15838 15838 15838

Table 5 Varying marketplace confidence weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 673384 200191 200191 200191 200191 200191 1950118 1945048 217084 2408288 2532848 3047688Marketplace fairness 34 100 100 100 100 100 11 12 14 16 17 21Marketplace confidence 0 0 0 0 0 0 18462 2783 31358 3474 3647 43678

Table 6 Varying cost objective weights CP method

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 116650 118066 119614 121316 123194 125278 127647 129441 130421 133686 137680 911812Marketplace fairness 4 4 4 4 4 4 4 4 4 4 4 38Marketplace confidence 158380 148941 138614 127269 114748 100855 85695 74755 68988 49782 27313 1119864 minus 04

Table 7 Varying marketplace fairness weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 763739 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441Marketplace fairness 42 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 10459 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755

8 Mathematical Problems in Engineering

Table 8 Varying marketplace confidence weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 911812 141246 139581 137823 135860 133686 131261 129441 128466 125278 121454 116649Marketplace fairness 38 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 1119864 minus 04 7986 16752 26517 37424 49783 64046 74755 80572 100855 126351 158380

The solutions of Table 6 can be compared directly toTable 3 as can be Tables 7 and 4 as well as Tables 8 and 5respectively Generally when the weights for the cost objec-tive are reduced on a 005 step decrease from 1 to 0 the costvalue steadily increases for the CPM This trend is also truefor marketplace confidence However the WOM model isinsensitive to weight changes when the cost weights are in[05 1] The same pattern is found for marketplace fairnessand shipperrsquos confidence where varying weights between[0 015] and [005 025] for the respective objectives didnot change the values of those objectives (Tables 4 and5) The CPM quickly reaches a minimum for marketplacefairness with a slight change in weights from the maximum1 Choosing a different 119875 value will alter marketplace fairnessThus theWOMcan provide solutions quickly for eachweightvariation However the CPM can provide many solutionsfor the same weight variations albeit having to vary theparameter 119901

5 Conclusions

While research on transportation procurement has benefitedfrom the use of CA the literature does not explicitly providemodel solutions and formulation for the multiobjective con-textThismay be due to the difficulty in operationalising con-cepts such as marketplace fairness and shipperrsquos confidenceThis paper treating the MODM problem in the context asa multiobjective optimization model allows the shipper toinclude nonfinancial carrier selection measures Future workcan consider a service index that can be incorporated andupdated from one auction to another to allow carriers tobe tracked on performance Our results suggest that there isno dominant MODM technique However this is good forthe shipper as shipper now has at its disposal a variety oftechniques to compare against when making a final decisionon the winner for the auction Alternatively the shipper canuse the results for a further bargaining process with thecarriers There may be a situation where the shipper intendsto use a particular carrier who has a high quality service levelbut has a higher service cost too The shipper may then askthe carrier whether it could provide the service at the nextlower price For incorporating a bargaining phase into a CAmechanism readers may be interested in the work of Huanget al [19] Another alternative would be to introduce trust-based mechanism by observing the discrepancy between theresults and the services offered One step further would be

to use this as a means to validate the sensitivity resultsTrust mechanisms have been used in agent-based researchto support decisions made on economic exchange (see [20])Future workmay also include soft computing approaches thatallow the shipper to automate and filter the solutions based onother criteria such as the business relationships

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y Sheffi ldquoCombinatorial auctions in the procurement of trans-portation servicesrdquo Interfaces vol 34 no 4 pp 245ndash252 2004

[2] Y Guo A Lim B Rodrigues and Y Zhu ldquoCarrier assignmentmodels in transportation procurementrdquo Journal of the Opera-tional Research Society vol 57 no 12 pp 1472ndash1481 2006

[3] S M H Motlagh M M Sepehri J Ignatius and A MustafaldquoOptimizing trade in transportation procurement is combi-natorial double auction approach truly betterrdquo InternationalJournal of Innovative Computing Information and Control vol6 no 6 pp 2537ndash2550 2010

[4] J R Forster and S Strasser ldquoCarrier modal selection factorsthe shipper carrier paradoxrdquo Transportation Research Forumvol 31 no 1 pp 206ndash212 1991

[5] W Elmaghraby and P Keskinocak ldquoCombinatorial auctionsin procurementrdquo Tech Rep School of Industrial and SystemsEngineering Georgia Institute of Technology 2002

[6] A Nair ldquoEmerging internet-enabled auction mechanisms insupply chainrdquo Supply ChainManagement vol 10 no 3 pp 162ndash168 2005

[7] O Ergun G Kuyzu and M Savelsbergh ldquoShipper collabora-tionrdquo Computers and Operations Research vol 34 no 6 pp1551ndash1560 2007

[8] C Caplice Optimization-based bidding a new framework forshipper-carrier relationships [PhD dissertation] MIT Cam-bridge Mass USA 1996

[9] C Caplice and Y Sheffi ldquoOptimization based procurement fortransportation servicesrdquo Journal of Business Logistics vol 24 no2 pp 109ndash128 2004

[10] J Ignatius Y-J Lai SMHosseini-MotlaghMM Sepehri andA Mustafa ldquoModeling fuzzy combinatorial auctionrdquo ExpertSystems with Applications vol 38 pp 11482ndash11488 2011

Mathematical Problems in Engineering 9

[11] N Remli and M Rekik ldquoA robust winner determination prob-lem for combinatorial transportation auctions under uncertainshipment volumesrdquo Transportation Research C vol 35 no 10pp 204ndash217 2013

[12] M Tamiz D Jones and C Romero ldquoGoal programming fordecision making an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 111 no 3 pp569ndash581 1998

[13] A M Geoffrion ldquoProper efficiency and the theory of vectormaximizationrdquo Journal of Mathematical Analysis and Applica-tions vol 22 no 3 pp 618ndash630 1968

[14] A Charnes andW W CooperManagement Models and Indus-trial Applications of Linear Programming John Wiley amp SonsNew York NY USA 1961

[15] VWadhwa andA R Ravindran ldquoVendor selection in outsourc-ingrdquo Computers and Operations Research vol 34 no 12 pp3725ndash3737 2007

[16] A Imai E Nishimura and S Papadimitriou ldquoBerth allocationwith service priorityrdquo Transportation Research B vol 37 no 5pp 437ndash457 2003

[17] D F Jones S K Mirrazavi and M Tamiz ldquoMulti-objectivemeta-heuristics an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 137 no 1 pp 1ndash92002

[18] A Charnes and W W Cooper ldquoGoal programming and multi-objective optimization Part 1rdquo European Journal of OperationalResearch vol 1 no 1 pp 39ndash54 1977

[19] HHuang R J KauffmanH Xu and L Zhao ldquoA hybridmecha-nism for heterogeneous e-procurement involving a combinato-rial auction and bargainingrdquo Electronic Commerce Research andApplications vol 12 no 3 pp 181ndash194 2013

[20] Y Yang S Singhal and Y Xu ldquoAlternate strategies for a win-win seeking agent in agent-human negotiationsrdquo Journal ofManagement Information Systems vol 29 no 3 pp 223ndash2552012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

(iii)119888119871119896= (119888119871119896

11 119888119871119896

119894119895 119888119871119896

119898119899) with

119888119871119896isin (R+)

119898times119899

119888119871119896

119894119895is the lower bound in loads on lane 119894 to 119895 that

carrier 119888 is willing to accept as part of package bid 119896

(iv)119888119880119896

= (119888119880119896

11 119888119880119896

119894119895 119888119880119896

119898119899) with

119888119880119896

isin

(R+)119898times119899119888119880119896

119894119895is the upper bound in loads on lane 119894 to

119895 that carrier 119888 is willing to accept as part of packagebid 119896

Each bundle bid119888119861119896 is a placement order that is services that

are to be sold by the auctioneer

33 Decision Variables We define the decision variable cor-responding to each lane as

119888119909119896

119894119895 where

119888119909119896

119894119895is fraction of load

per time unit (week) on lane 119894 to 119895 from carrier 119888 on packagebid 119896

Subsequently each package is denoted as119888119910119896 where

119888119910119896

denotes that if carrier 119888 is assigned package bid 119896 then119888119910119896=

1 otherwise119888119910119896= 0

34TheModel Formulation We seek to simultaneously min-imize cost maximize marketplace fairness and maximizeshipperrsquos confidenceCost Objective The total cost of the accepted bids is mini-mized as

1198911(119909) = Min

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895 (6)

Marketplace Fairness Objective The total number of acceptedpackages is maximized as

1198912(119909) = Max

sellersum

119888=1

package

sum

119896=1

119888119910119896 (7)

Marketplace Confidence ObjectiveThedifference between thelower bound volume sought by the carrier and the upperbound volume sought by the auctioneer is minimized asfollows

1198913(119909) = Min

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816 (8)

Supply-Demand Constraint The total volume accepted aswinning packagesmust be no less than the volume auctionedthat is

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895 119888119909119896

119894119895

ge

destinationsum

119896=1

origin

sum

119894=1

119886119896

119894119895119909119896

119894119895forall119894 isin origin 119895 isin destination

(9)

Transactional Constraints Equation (10) allows the auction-eer to transact the entire package within a particular volumerange specified by the carriers The variable 1

119888119910119896

in (10)ensures that the carrier must offer all lanes within thepackage if one of the lanes is approved as a winning lane bythe auctioneer Consider

minus119872119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination

minus119888119871119861119896

119894119895 119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination

119888119880119861119896

119894119895 119888119910119896+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(10)

Business Guarantee Constraint A shipper might not wantto rely too heavily on a small number of winning carriersIn the longer term it might be prudent for a shipper toensure that the amount of traffic won by a carrier is within acertain bound This will create a higher potential for carriersto revisit the marketplace to bid The scope of the carrier setcoverage is measured by the amount of volume (loads) wonThe constraints below ensure that all carriers are awardedbusiness within some preset volume bounds Consider

119888Min Value le

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895

le119888Max Value

(11)

Carrier Base Size Constraints This is an extension to thebusiness guarantee constraint with the restriction on thenumber of winning carriers for each lane The system-based(or hard) approach adds the following constraints to limit thenumber of carriers assigned at the lane level

minus119872119888119908119894+119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(12)

sellersum

119888=1

119888119908119894le 119871119894

forall119894 isin origin (13)

minus119872119888119911 +119888119886119896

119894119895 119888119909119896

119894119895le 0

forall119888 isin seller 119896 isin package 119894 isin origin 119895 isin destination(14)

sellersum

119888=1

119888119911 le 119878 (15)

Mathematical Problems in Engineering 5

The number of carriers winning the right to haul at origin 119894

is denoted as 119871119894in (13) while 119878 is the system limit of winning

carriers for the entire auction

Simple Reload Bids Constraint This constraint denotes thatthe ratio of outbound volume to inbound volume must be atleast119888120573119895 Consider

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119895119894 119888119888119896

119895119894

ge119888120573119895lowast

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895 119888119909119896

119894119895forall119888 119896

(16)

Nonnegativity and Binary Constraints As the decision vari-ables are expressed as percentages we define

119888119909119896

119894119895in (17) as

real numbers Carrier 119888 is assigned package bid 119896when 119888119910119896 =

1 (or 0 otherwise) (18) Carrier 119888 is assigned to origin 119894 when119888119908119894= 1 (or 0 else) (19) Also carrier 119888 is assigned to a network

when119888119911119894= 1 (or 0 otherwise) (20) Consider

119888119909119896

119894119895isin 119877+ (17)

119888119910119896= 0 1 (18)

119888119908119894= 0 1 (19)

119888119911 = 0 1 (20)

We now present the three models for the CA transportprocurement problem WOM preemptive GP and CPWOM Consider

Min 1199081(

sellersum

119888=1

packag

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895)

minus 1199082(

sellersum

119888=1

package

sum

119896=1

119888119910119896)

+ 1199083(

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816)

st (9)ndash(20) (21)

Preemptive Goal Model (PGM) Consider

Min 1198751119889+

1+ 1198752119889minus

2+ 1198753119889+

3 1198751gt 1198752gt 119875119904(119909)

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895+ 119889minus

1minus 119889+

1

= Cost Goal

sellersum

119888=1

package

sum

119896=1

119888119910119896+119889minus

2minus 119889+

2

= Marketplace Reputation Goal

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816+ 119889minus

3minus 119889+

3

= Shipperrsquos Confidence Goal

st (9)ndash(20) (22)

where 119889minus119894and 119889

+

119894are the underachievement and overachieve-

ment deviations of the 119894th goal

CPM The combinatorial auction transportation procure-ment model in a CP is as follows

Min

1199081((

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895

minus 119888lowast

119894) times (119888

lowast

119894)minus1

)

119875

minus 1199082(

sumseller119888=1

sumpackage119896=1 119888

119910119896minus119903lowast

119894

119903lowast

119894

)

119875

+ 1199083((

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816

minus119904lowast

119894) times (119904

lowast

119894)minus1

)

119875

1119875

st (9)ndash(20) (23)

where 119901 = 1 2 infin The ideal values of cost marketplacefairness and shipperrsquos confidence are gathered from 119888

lowast

119894=

min1198911(119909) 119903lowast

119894= max119891

2(119909) and 119904

lowast

119894= min119891

3(119909) respec-

tively (see (6)ndash(8)) The larger deviations receive greaterimportance as 119901 increases This is the penalizing effectplaced on larger deviations from their respective ideal solu-tions The compromise solutions satisfy 1 le 119901 le infin

6 Mathematical Problems in Engineering

Table 2 Results experimental runs

Test Model Cost ($) Marketplace fairness Shipperrsquos confidence1 Ideal cost 116650 4 158382 Ideal marketplace fairness 2589176 100 2724223 Ideal shipperrsquos confidence 673384 34 04 Preemptive GP 129611 4 737575 Equal weight 194505 12 2783

CP (equal weights)6 119901 = 1 441444 27 23087 119901 = 2 153932 5 20388 119901 = infin 129441 4 74755

The solution at 119901 = infin indicates that the largest deviationamong all objectives is the most dominant in the optimalsolutionrsquos distance function

4 Solution and Analysis

The following steps detail our dataset generation procedureand analysis

Step 1 (generate shipperrsquos lane offerings) The condition ofCA requires each shipper to put the amount of volume fora set of lanes on offer in separate auction markets We set[119878+]1times119899

as the shipperrsquos volume required in a CA of 119899 lanesThe maximum amount of loads available for carriers to bidon each 119894-119895 origin-destination (lane) or cell 0119886

119894119895isin [119878+]1times119899

is randomly generated from [1000 10000] using a uniformdistribution

Step 2 (generate carriersrsquo bids) We assume that the carriersare able to view the total available volumes for each lane andset their bids accordingly For our simulated carrierrsquos amountof loads we generate a seed number 120572 between [1 100] foreach lane A value of 120572 greater than 50 enforces the rule ofempty cells and signifies the refusal of a carrier to accepta particular lane If 120572 lt 50 another random number 120573 isgenerated between [06 1] where 120573 lowast

0119886119894119895=1119886119894119895and 1119888119886119894119895isin

[119862+]119898times119899

correspond to the amount of loads offered by the119898thcarrier of the 119899th lane

Step 3 (solving routines) The buy and sell prices of each laneare fixed at $3 and $1 per unit of load respectivelyThe datasetis solved by WOM PGM and CPM respectively on Lingoversion 8

Step 4 (results and sensitivity analysis) Table 2 shows theresults where a series of 8 tests were run The ideal valuesof each objective are obtained by analyzing each objectiveindependently while keeping all the constraints in themodelWe observe that the model that optimises the cost yieldsthe lowest cost ($11665) out of all models tested This trendcontinues with models that optimise marketplace fairnessand shipperrsquos confidence respectively yielding the best resultfor marketplace fairness (100) and shipperrsquos confidence (0)when compared with other models We define shipperrsquos

confidence to be the distance between the carriersrsquo bidvolume and the shipperrsquos request The value of 0 indicates nodistance and denotes that all requested volumes by shippercan be met

In the PGM the preemptive weights are specified in thefollowing order of importance cost marketplace fairnessand shipperrsquos confidence Here the cost value is close to theideal cost as this objective was stated to be infinitely moreimportant than the other objectivesThe value ofmarketplacefairness in Test 4 is the same as Test 1 However the differencein shipperrsquos confidence is expected as its inclusion as anobjective renders that cost will be sacrificed by 129611 minus

116650 = $12961 Thus in considering the 3 objectiveshierarchically the feasible solution sacrificed in cost waspassed onto satisfying shipperrsquos confidence This can be seenfrom the reduced unawarded volume of 73757 (Test 4) from15838 (Test 1)

InTest 5 we formulated aweighted-objectivesmodelwith1199081

= 1199082

= 1199083

= 13 to optimize a set of objectivessimultaneously with the same priority for all objectives

A sensitivity analysis is conducted on the WOM byvarying the weights of each objective while the other 2objectives are restricted to sharing the remainder weightsequally (Tables 3ndash5) The results of the WOMmodel are alsocompared directly against the CP model since the weights ofthe three objectives are standardized to be equal across thetwo techniques It is observed that the CPmethod dominateson cost and shipperrsquos confidence The CPM solution isobtained when 119901 is set to infin Further as 119901 rarr infin the costand shipperrsquos confidence objectives improve at the expenseof marketplace fairness (Table 2 Tests 6 to 8) However theWOM results are not necessarily inferior to the CPM asthe shipper now can now choose between the solutions ofTest 5 or Test 8 Test 5 produces 12 winning bids whileTest 8 produces 4 winning bids If all 12 winning bidsare won by a single carrier in Test 5 but the 4 winningbids of Test 8 are won by different carriers the shippermay strategically select the CPM solution On the otherhand if some of the winning bids in Test 5 are won by aprominent carrier that is not part of the winning carrier inTest 8 the shipper may opt for the Test 5 WOM solutioninstead to keep the service relationship intact as much aspossible

Mathematical Problems in Engineering 7

Table 3 Varying cost objective weights WOMmethod

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 1166496 1166496 1166496 1166496 1166496 1166496 123742 194505 265986 758231 3052837 3052837Marketplace fairness 4 4 4 4 4 4 5 12 18 39 100 100Marketplace confidence 15838 15838 15838 15838 15838 15838 16924 2783 38234 109119864 minus 04 0 0

Table 4 Varying marketplace fairness weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 2589176 244227 244227 244227 1752309 7371432 3894 1945048 14262 1166496 1166496 1166496Marketplace fairness 100 100 100 100 82 45 27 12 7 4 4 4Marketplace confidence 272422 358248 358248 358248 256872 108082 55576 2783 19708 15838 15838 15838

Table 5 Varying marketplace confidence weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 673384 200191 200191 200191 200191 200191 1950118 1945048 217084 2408288 2532848 3047688Marketplace fairness 34 100 100 100 100 100 11 12 14 16 17 21Marketplace confidence 0 0 0 0 0 0 18462 2783 31358 3474 3647 43678

Table 6 Varying cost objective weights CP method

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 116650 118066 119614 121316 123194 125278 127647 129441 130421 133686 137680 911812Marketplace fairness 4 4 4 4 4 4 4 4 4 4 4 38Marketplace confidence 158380 148941 138614 127269 114748 100855 85695 74755 68988 49782 27313 1119864 minus 04

Table 7 Varying marketplace fairness weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 763739 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441Marketplace fairness 42 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 10459 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755

8 Mathematical Problems in Engineering

Table 8 Varying marketplace confidence weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 911812 141246 139581 137823 135860 133686 131261 129441 128466 125278 121454 116649Marketplace fairness 38 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 1119864 minus 04 7986 16752 26517 37424 49783 64046 74755 80572 100855 126351 158380

The solutions of Table 6 can be compared directly toTable 3 as can be Tables 7 and 4 as well as Tables 8 and 5respectively Generally when the weights for the cost objec-tive are reduced on a 005 step decrease from 1 to 0 the costvalue steadily increases for the CPM This trend is also truefor marketplace confidence However the WOM model isinsensitive to weight changes when the cost weights are in[05 1] The same pattern is found for marketplace fairnessand shipperrsquos confidence where varying weights between[0 015] and [005 025] for the respective objectives didnot change the values of those objectives (Tables 4 and5) The CPM quickly reaches a minimum for marketplacefairness with a slight change in weights from the maximum1 Choosing a different 119875 value will alter marketplace fairnessThus theWOMcan provide solutions quickly for eachweightvariation However the CPM can provide many solutionsfor the same weight variations albeit having to vary theparameter 119901

5 Conclusions

While research on transportation procurement has benefitedfrom the use of CA the literature does not explicitly providemodel solutions and formulation for the multiobjective con-textThismay be due to the difficulty in operationalising con-cepts such as marketplace fairness and shipperrsquos confidenceThis paper treating the MODM problem in the context asa multiobjective optimization model allows the shipper toinclude nonfinancial carrier selection measures Future workcan consider a service index that can be incorporated andupdated from one auction to another to allow carriers tobe tracked on performance Our results suggest that there isno dominant MODM technique However this is good forthe shipper as shipper now has at its disposal a variety oftechniques to compare against when making a final decisionon the winner for the auction Alternatively the shipper canuse the results for a further bargaining process with thecarriers There may be a situation where the shipper intendsto use a particular carrier who has a high quality service levelbut has a higher service cost too The shipper may then askthe carrier whether it could provide the service at the nextlower price For incorporating a bargaining phase into a CAmechanism readers may be interested in the work of Huanget al [19] Another alternative would be to introduce trust-based mechanism by observing the discrepancy between theresults and the services offered One step further would be

to use this as a means to validate the sensitivity resultsTrust mechanisms have been used in agent-based researchto support decisions made on economic exchange (see [20])Future workmay also include soft computing approaches thatallow the shipper to automate and filter the solutions based onother criteria such as the business relationships

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y Sheffi ldquoCombinatorial auctions in the procurement of trans-portation servicesrdquo Interfaces vol 34 no 4 pp 245ndash252 2004

[2] Y Guo A Lim B Rodrigues and Y Zhu ldquoCarrier assignmentmodels in transportation procurementrdquo Journal of the Opera-tional Research Society vol 57 no 12 pp 1472ndash1481 2006

[3] S M H Motlagh M M Sepehri J Ignatius and A MustafaldquoOptimizing trade in transportation procurement is combi-natorial double auction approach truly betterrdquo InternationalJournal of Innovative Computing Information and Control vol6 no 6 pp 2537ndash2550 2010

[4] J R Forster and S Strasser ldquoCarrier modal selection factorsthe shipper carrier paradoxrdquo Transportation Research Forumvol 31 no 1 pp 206ndash212 1991

[5] W Elmaghraby and P Keskinocak ldquoCombinatorial auctionsin procurementrdquo Tech Rep School of Industrial and SystemsEngineering Georgia Institute of Technology 2002

[6] A Nair ldquoEmerging internet-enabled auction mechanisms insupply chainrdquo Supply ChainManagement vol 10 no 3 pp 162ndash168 2005

[7] O Ergun G Kuyzu and M Savelsbergh ldquoShipper collabora-tionrdquo Computers and Operations Research vol 34 no 6 pp1551ndash1560 2007

[8] C Caplice Optimization-based bidding a new framework forshipper-carrier relationships [PhD dissertation] MIT Cam-bridge Mass USA 1996

[9] C Caplice and Y Sheffi ldquoOptimization based procurement fortransportation servicesrdquo Journal of Business Logistics vol 24 no2 pp 109ndash128 2004

[10] J Ignatius Y-J Lai SMHosseini-MotlaghMM Sepehri andA Mustafa ldquoModeling fuzzy combinatorial auctionrdquo ExpertSystems with Applications vol 38 pp 11482ndash11488 2011

Mathematical Problems in Engineering 9

[11] N Remli and M Rekik ldquoA robust winner determination prob-lem for combinatorial transportation auctions under uncertainshipment volumesrdquo Transportation Research C vol 35 no 10pp 204ndash217 2013

[12] M Tamiz D Jones and C Romero ldquoGoal programming fordecision making an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 111 no 3 pp569ndash581 1998

[13] A M Geoffrion ldquoProper efficiency and the theory of vectormaximizationrdquo Journal of Mathematical Analysis and Applica-tions vol 22 no 3 pp 618ndash630 1968

[14] A Charnes andW W CooperManagement Models and Indus-trial Applications of Linear Programming John Wiley amp SonsNew York NY USA 1961

[15] VWadhwa andA R Ravindran ldquoVendor selection in outsourc-ingrdquo Computers and Operations Research vol 34 no 12 pp3725ndash3737 2007

[16] A Imai E Nishimura and S Papadimitriou ldquoBerth allocationwith service priorityrdquo Transportation Research B vol 37 no 5pp 437ndash457 2003

[17] D F Jones S K Mirrazavi and M Tamiz ldquoMulti-objectivemeta-heuristics an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 137 no 1 pp 1ndash92002

[18] A Charnes and W W Cooper ldquoGoal programming and multi-objective optimization Part 1rdquo European Journal of OperationalResearch vol 1 no 1 pp 39ndash54 1977

[19] HHuang R J KauffmanH Xu and L Zhao ldquoA hybridmecha-nism for heterogeneous e-procurement involving a combinato-rial auction and bargainingrdquo Electronic Commerce Research andApplications vol 12 no 3 pp 181ndash194 2013

[20] Y Yang S Singhal and Y Xu ldquoAlternate strategies for a win-win seeking agent in agent-human negotiationsrdquo Journal ofManagement Information Systems vol 29 no 3 pp 223ndash2552012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

The number of carriers winning the right to haul at origin 119894

is denoted as 119871119894in (13) while 119878 is the system limit of winning

carriers for the entire auction

Simple Reload Bids Constraint This constraint denotes thatthe ratio of outbound volume to inbound volume must be atleast119888120573119895 Consider

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119895119894 119888119888119896

119895119894

ge119888120573119895lowast

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895 119888119909119896

119894119895forall119888 119896

(16)

Nonnegativity and Binary Constraints As the decision vari-ables are expressed as percentages we define

119888119909119896

119894119895in (17) as

real numbers Carrier 119888 is assigned package bid 119896when 119888119910119896 =

1 (or 0 otherwise) (18) Carrier 119888 is assigned to origin 119894 when119888119908119894= 1 (or 0 else) (19) Also carrier 119888 is assigned to a network

when119888119911119894= 1 (or 0 otherwise) (20) Consider

119888119909119896

119894119895isin 119877+ (17)

119888119910119896= 0 1 (18)

119888119908119894= 0 1 (19)

119888119911 = 0 1 (20)

We now present the three models for the CA transportprocurement problem WOM preemptive GP and CPWOM Consider

Min 1199081(

sellersum

119888=1

packag

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895)

minus 1199082(

sellersum

119888=1

package

sum

119896=1

119888119910119896)

+ 1199083(

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816)

st (9)ndash(20) (21)

Preemptive Goal Model (PGM) Consider

Min 1198751119889+

1+ 1198752119889minus

2+ 1198753119889+

3 1198751gt 1198752gt 119875119904(119909)

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895+ 119889minus

1minus 119889+

1

= Cost Goal

sellersum

119888=1

package

sum

119896=1

119888119910119896+119889minus

2minus 119889+

2

= Marketplace Reputation Goal

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816+ 119889minus

3minus 119889+

3

= Shipperrsquos Confidence Goal

st (9)ndash(20) (22)

where 119889minus119894and 119889

+

119894are the underachievement and overachieve-

ment deviations of the 119894th goal

CPM The combinatorial auction transportation procure-ment model in a CP is as follows

Min

1199081((

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119901119896

119894119895 119888119886119896

119894119895 119888119909119896

119894119895

minus 119888lowast

119894) times (119888

lowast

119894)minus1

)

119875

minus 1199082(

sumseller119888=1

sumpackage119896=1 119888

119910119896minus119903lowast

119894

119903lowast

119894

)

119875

+ 1199083((

sellersum

119888=1

package

sum

119896=1

destinationsum

119895=1

origin

sum

119894=1

119888119886119896

119894119895

100381610038161003816100381610038161003816 119888119910119896minus119888119909119896

119894119895

100381610038161003816100381610038161003816

minus119904lowast

119894) times (119904

lowast

119894)minus1

)

119875

1119875

st (9)ndash(20) (23)

where 119901 = 1 2 infin The ideal values of cost marketplacefairness and shipperrsquos confidence are gathered from 119888

lowast

119894=

min1198911(119909) 119903lowast

119894= max119891

2(119909) and 119904

lowast

119894= min119891

3(119909) respec-

tively (see (6)ndash(8)) The larger deviations receive greaterimportance as 119901 increases This is the penalizing effectplaced on larger deviations from their respective ideal solu-tions The compromise solutions satisfy 1 le 119901 le infin

6 Mathematical Problems in Engineering

Table 2 Results experimental runs

Test Model Cost ($) Marketplace fairness Shipperrsquos confidence1 Ideal cost 116650 4 158382 Ideal marketplace fairness 2589176 100 2724223 Ideal shipperrsquos confidence 673384 34 04 Preemptive GP 129611 4 737575 Equal weight 194505 12 2783

CP (equal weights)6 119901 = 1 441444 27 23087 119901 = 2 153932 5 20388 119901 = infin 129441 4 74755

The solution at 119901 = infin indicates that the largest deviationamong all objectives is the most dominant in the optimalsolutionrsquos distance function

4 Solution and Analysis

The following steps detail our dataset generation procedureand analysis

Step 1 (generate shipperrsquos lane offerings) The condition ofCA requires each shipper to put the amount of volume fora set of lanes on offer in separate auction markets We set[119878+]1times119899

as the shipperrsquos volume required in a CA of 119899 lanesThe maximum amount of loads available for carriers to bidon each 119894-119895 origin-destination (lane) or cell 0119886

119894119895isin [119878+]1times119899

is randomly generated from [1000 10000] using a uniformdistribution

Step 2 (generate carriersrsquo bids) We assume that the carriersare able to view the total available volumes for each lane andset their bids accordingly For our simulated carrierrsquos amountof loads we generate a seed number 120572 between [1 100] foreach lane A value of 120572 greater than 50 enforces the rule ofempty cells and signifies the refusal of a carrier to accepta particular lane If 120572 lt 50 another random number 120573 isgenerated between [06 1] where 120573 lowast

0119886119894119895=1119886119894119895and 1119888119886119894119895isin

[119862+]119898times119899

correspond to the amount of loads offered by the119898thcarrier of the 119899th lane

Step 3 (solving routines) The buy and sell prices of each laneare fixed at $3 and $1 per unit of load respectivelyThe datasetis solved by WOM PGM and CPM respectively on Lingoversion 8

Step 4 (results and sensitivity analysis) Table 2 shows theresults where a series of 8 tests were run The ideal valuesof each objective are obtained by analyzing each objectiveindependently while keeping all the constraints in themodelWe observe that the model that optimises the cost yieldsthe lowest cost ($11665) out of all models tested This trendcontinues with models that optimise marketplace fairnessand shipperrsquos confidence respectively yielding the best resultfor marketplace fairness (100) and shipperrsquos confidence (0)when compared with other models We define shipperrsquos

confidence to be the distance between the carriersrsquo bidvolume and the shipperrsquos request The value of 0 indicates nodistance and denotes that all requested volumes by shippercan be met

In the PGM the preemptive weights are specified in thefollowing order of importance cost marketplace fairnessand shipperrsquos confidence Here the cost value is close to theideal cost as this objective was stated to be infinitely moreimportant than the other objectivesThe value ofmarketplacefairness in Test 4 is the same as Test 1 However the differencein shipperrsquos confidence is expected as its inclusion as anobjective renders that cost will be sacrificed by 129611 minus

116650 = $12961 Thus in considering the 3 objectiveshierarchically the feasible solution sacrificed in cost waspassed onto satisfying shipperrsquos confidence This can be seenfrom the reduced unawarded volume of 73757 (Test 4) from15838 (Test 1)

InTest 5 we formulated aweighted-objectivesmodelwith1199081

= 1199082

= 1199083

= 13 to optimize a set of objectivessimultaneously with the same priority for all objectives

A sensitivity analysis is conducted on the WOM byvarying the weights of each objective while the other 2objectives are restricted to sharing the remainder weightsequally (Tables 3ndash5) The results of the WOMmodel are alsocompared directly against the CP model since the weights ofthe three objectives are standardized to be equal across thetwo techniques It is observed that the CPmethod dominateson cost and shipperrsquos confidence The CPM solution isobtained when 119901 is set to infin Further as 119901 rarr infin the costand shipperrsquos confidence objectives improve at the expenseof marketplace fairness (Table 2 Tests 6 to 8) However theWOM results are not necessarily inferior to the CPM asthe shipper now can now choose between the solutions ofTest 5 or Test 8 Test 5 produces 12 winning bids whileTest 8 produces 4 winning bids If all 12 winning bidsare won by a single carrier in Test 5 but the 4 winningbids of Test 8 are won by different carriers the shippermay strategically select the CPM solution On the otherhand if some of the winning bids in Test 5 are won by aprominent carrier that is not part of the winning carrier inTest 8 the shipper may opt for the Test 5 WOM solutioninstead to keep the service relationship intact as much aspossible

Mathematical Problems in Engineering 7

Table 3 Varying cost objective weights WOMmethod

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 1166496 1166496 1166496 1166496 1166496 1166496 123742 194505 265986 758231 3052837 3052837Marketplace fairness 4 4 4 4 4 4 5 12 18 39 100 100Marketplace confidence 15838 15838 15838 15838 15838 15838 16924 2783 38234 109119864 minus 04 0 0

Table 4 Varying marketplace fairness weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 2589176 244227 244227 244227 1752309 7371432 3894 1945048 14262 1166496 1166496 1166496Marketplace fairness 100 100 100 100 82 45 27 12 7 4 4 4Marketplace confidence 272422 358248 358248 358248 256872 108082 55576 2783 19708 15838 15838 15838

Table 5 Varying marketplace confidence weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 673384 200191 200191 200191 200191 200191 1950118 1945048 217084 2408288 2532848 3047688Marketplace fairness 34 100 100 100 100 100 11 12 14 16 17 21Marketplace confidence 0 0 0 0 0 0 18462 2783 31358 3474 3647 43678

Table 6 Varying cost objective weights CP method

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 116650 118066 119614 121316 123194 125278 127647 129441 130421 133686 137680 911812Marketplace fairness 4 4 4 4 4 4 4 4 4 4 4 38Marketplace confidence 158380 148941 138614 127269 114748 100855 85695 74755 68988 49782 27313 1119864 minus 04

Table 7 Varying marketplace fairness weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 763739 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441Marketplace fairness 42 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 10459 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755

8 Mathematical Problems in Engineering

Table 8 Varying marketplace confidence weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 911812 141246 139581 137823 135860 133686 131261 129441 128466 125278 121454 116649Marketplace fairness 38 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 1119864 minus 04 7986 16752 26517 37424 49783 64046 74755 80572 100855 126351 158380

The solutions of Table 6 can be compared directly toTable 3 as can be Tables 7 and 4 as well as Tables 8 and 5respectively Generally when the weights for the cost objec-tive are reduced on a 005 step decrease from 1 to 0 the costvalue steadily increases for the CPM This trend is also truefor marketplace confidence However the WOM model isinsensitive to weight changes when the cost weights are in[05 1] The same pattern is found for marketplace fairnessand shipperrsquos confidence where varying weights between[0 015] and [005 025] for the respective objectives didnot change the values of those objectives (Tables 4 and5) The CPM quickly reaches a minimum for marketplacefairness with a slight change in weights from the maximum1 Choosing a different 119875 value will alter marketplace fairnessThus theWOMcan provide solutions quickly for eachweightvariation However the CPM can provide many solutionsfor the same weight variations albeit having to vary theparameter 119901

5 Conclusions

While research on transportation procurement has benefitedfrom the use of CA the literature does not explicitly providemodel solutions and formulation for the multiobjective con-textThismay be due to the difficulty in operationalising con-cepts such as marketplace fairness and shipperrsquos confidenceThis paper treating the MODM problem in the context asa multiobjective optimization model allows the shipper toinclude nonfinancial carrier selection measures Future workcan consider a service index that can be incorporated andupdated from one auction to another to allow carriers tobe tracked on performance Our results suggest that there isno dominant MODM technique However this is good forthe shipper as shipper now has at its disposal a variety oftechniques to compare against when making a final decisionon the winner for the auction Alternatively the shipper canuse the results for a further bargaining process with thecarriers There may be a situation where the shipper intendsto use a particular carrier who has a high quality service levelbut has a higher service cost too The shipper may then askthe carrier whether it could provide the service at the nextlower price For incorporating a bargaining phase into a CAmechanism readers may be interested in the work of Huanget al [19] Another alternative would be to introduce trust-based mechanism by observing the discrepancy between theresults and the services offered One step further would be

to use this as a means to validate the sensitivity resultsTrust mechanisms have been used in agent-based researchto support decisions made on economic exchange (see [20])Future workmay also include soft computing approaches thatallow the shipper to automate and filter the solutions based onother criteria such as the business relationships

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y Sheffi ldquoCombinatorial auctions in the procurement of trans-portation servicesrdquo Interfaces vol 34 no 4 pp 245ndash252 2004

[2] Y Guo A Lim B Rodrigues and Y Zhu ldquoCarrier assignmentmodels in transportation procurementrdquo Journal of the Opera-tional Research Society vol 57 no 12 pp 1472ndash1481 2006

[3] S M H Motlagh M M Sepehri J Ignatius and A MustafaldquoOptimizing trade in transportation procurement is combi-natorial double auction approach truly betterrdquo InternationalJournal of Innovative Computing Information and Control vol6 no 6 pp 2537ndash2550 2010

[4] J R Forster and S Strasser ldquoCarrier modal selection factorsthe shipper carrier paradoxrdquo Transportation Research Forumvol 31 no 1 pp 206ndash212 1991

[5] W Elmaghraby and P Keskinocak ldquoCombinatorial auctionsin procurementrdquo Tech Rep School of Industrial and SystemsEngineering Georgia Institute of Technology 2002

[6] A Nair ldquoEmerging internet-enabled auction mechanisms insupply chainrdquo Supply ChainManagement vol 10 no 3 pp 162ndash168 2005

[7] O Ergun G Kuyzu and M Savelsbergh ldquoShipper collabora-tionrdquo Computers and Operations Research vol 34 no 6 pp1551ndash1560 2007

[8] C Caplice Optimization-based bidding a new framework forshipper-carrier relationships [PhD dissertation] MIT Cam-bridge Mass USA 1996

[9] C Caplice and Y Sheffi ldquoOptimization based procurement fortransportation servicesrdquo Journal of Business Logistics vol 24 no2 pp 109ndash128 2004

[10] J Ignatius Y-J Lai SMHosseini-MotlaghMM Sepehri andA Mustafa ldquoModeling fuzzy combinatorial auctionrdquo ExpertSystems with Applications vol 38 pp 11482ndash11488 2011

Mathematical Problems in Engineering 9

[11] N Remli and M Rekik ldquoA robust winner determination prob-lem for combinatorial transportation auctions under uncertainshipment volumesrdquo Transportation Research C vol 35 no 10pp 204ndash217 2013

[12] M Tamiz D Jones and C Romero ldquoGoal programming fordecision making an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 111 no 3 pp569ndash581 1998

[13] A M Geoffrion ldquoProper efficiency and the theory of vectormaximizationrdquo Journal of Mathematical Analysis and Applica-tions vol 22 no 3 pp 618ndash630 1968

[14] A Charnes andW W CooperManagement Models and Indus-trial Applications of Linear Programming John Wiley amp SonsNew York NY USA 1961

[15] VWadhwa andA R Ravindran ldquoVendor selection in outsourc-ingrdquo Computers and Operations Research vol 34 no 12 pp3725ndash3737 2007

[16] A Imai E Nishimura and S Papadimitriou ldquoBerth allocationwith service priorityrdquo Transportation Research B vol 37 no 5pp 437ndash457 2003

[17] D F Jones S K Mirrazavi and M Tamiz ldquoMulti-objectivemeta-heuristics an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 137 no 1 pp 1ndash92002

[18] A Charnes and W W Cooper ldquoGoal programming and multi-objective optimization Part 1rdquo European Journal of OperationalResearch vol 1 no 1 pp 39ndash54 1977

[19] HHuang R J KauffmanH Xu and L Zhao ldquoA hybridmecha-nism for heterogeneous e-procurement involving a combinato-rial auction and bargainingrdquo Electronic Commerce Research andApplications vol 12 no 3 pp 181ndash194 2013

[20] Y Yang S Singhal and Y Xu ldquoAlternate strategies for a win-win seeking agent in agent-human negotiationsrdquo Journal ofManagement Information Systems vol 29 no 3 pp 223ndash2552012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

Table 2 Results experimental runs

Test Model Cost ($) Marketplace fairness Shipperrsquos confidence1 Ideal cost 116650 4 158382 Ideal marketplace fairness 2589176 100 2724223 Ideal shipperrsquos confidence 673384 34 04 Preemptive GP 129611 4 737575 Equal weight 194505 12 2783

CP (equal weights)6 119901 = 1 441444 27 23087 119901 = 2 153932 5 20388 119901 = infin 129441 4 74755

The solution at 119901 = infin indicates that the largest deviationamong all objectives is the most dominant in the optimalsolutionrsquos distance function

4 Solution and Analysis

The following steps detail our dataset generation procedureand analysis

Step 1 (generate shipperrsquos lane offerings) The condition ofCA requires each shipper to put the amount of volume fora set of lanes on offer in separate auction markets We set[119878+]1times119899

as the shipperrsquos volume required in a CA of 119899 lanesThe maximum amount of loads available for carriers to bidon each 119894-119895 origin-destination (lane) or cell 0119886

119894119895isin [119878+]1times119899

is randomly generated from [1000 10000] using a uniformdistribution

Step 2 (generate carriersrsquo bids) We assume that the carriersare able to view the total available volumes for each lane andset their bids accordingly For our simulated carrierrsquos amountof loads we generate a seed number 120572 between [1 100] foreach lane A value of 120572 greater than 50 enforces the rule ofempty cells and signifies the refusal of a carrier to accepta particular lane If 120572 lt 50 another random number 120573 isgenerated between [06 1] where 120573 lowast

0119886119894119895=1119886119894119895and 1119888119886119894119895isin

[119862+]119898times119899

correspond to the amount of loads offered by the119898thcarrier of the 119899th lane

Step 3 (solving routines) The buy and sell prices of each laneare fixed at $3 and $1 per unit of load respectivelyThe datasetis solved by WOM PGM and CPM respectively on Lingoversion 8

Step 4 (results and sensitivity analysis) Table 2 shows theresults where a series of 8 tests were run The ideal valuesof each objective are obtained by analyzing each objectiveindependently while keeping all the constraints in themodelWe observe that the model that optimises the cost yieldsthe lowest cost ($11665) out of all models tested This trendcontinues with models that optimise marketplace fairnessand shipperrsquos confidence respectively yielding the best resultfor marketplace fairness (100) and shipperrsquos confidence (0)when compared with other models We define shipperrsquos

confidence to be the distance between the carriersrsquo bidvolume and the shipperrsquos request The value of 0 indicates nodistance and denotes that all requested volumes by shippercan be met

In the PGM the preemptive weights are specified in thefollowing order of importance cost marketplace fairnessand shipperrsquos confidence Here the cost value is close to theideal cost as this objective was stated to be infinitely moreimportant than the other objectivesThe value ofmarketplacefairness in Test 4 is the same as Test 1 However the differencein shipperrsquos confidence is expected as its inclusion as anobjective renders that cost will be sacrificed by 129611 minus

116650 = $12961 Thus in considering the 3 objectiveshierarchically the feasible solution sacrificed in cost waspassed onto satisfying shipperrsquos confidence This can be seenfrom the reduced unawarded volume of 73757 (Test 4) from15838 (Test 1)

InTest 5 we formulated aweighted-objectivesmodelwith1199081

= 1199082

= 1199083

= 13 to optimize a set of objectivessimultaneously with the same priority for all objectives

A sensitivity analysis is conducted on the WOM byvarying the weights of each objective while the other 2objectives are restricted to sharing the remainder weightsequally (Tables 3ndash5) The results of the WOMmodel are alsocompared directly against the CP model since the weights ofthe three objectives are standardized to be equal across thetwo techniques It is observed that the CPmethod dominateson cost and shipperrsquos confidence The CPM solution isobtained when 119901 is set to infin Further as 119901 rarr infin the costand shipperrsquos confidence objectives improve at the expenseof marketplace fairness (Table 2 Tests 6 to 8) However theWOM results are not necessarily inferior to the CPM asthe shipper now can now choose between the solutions ofTest 5 or Test 8 Test 5 produces 12 winning bids whileTest 8 produces 4 winning bids If all 12 winning bidsare won by a single carrier in Test 5 but the 4 winningbids of Test 8 are won by different carriers the shippermay strategically select the CPM solution On the otherhand if some of the winning bids in Test 5 are won by aprominent carrier that is not part of the winning carrier inTest 8 the shipper may opt for the Test 5 WOM solutioninstead to keep the service relationship intact as much aspossible

Mathematical Problems in Engineering 7

Table 3 Varying cost objective weights WOMmethod

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 1166496 1166496 1166496 1166496 1166496 1166496 123742 194505 265986 758231 3052837 3052837Marketplace fairness 4 4 4 4 4 4 5 12 18 39 100 100Marketplace confidence 15838 15838 15838 15838 15838 15838 16924 2783 38234 109119864 minus 04 0 0

Table 4 Varying marketplace fairness weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 2589176 244227 244227 244227 1752309 7371432 3894 1945048 14262 1166496 1166496 1166496Marketplace fairness 100 100 100 100 82 45 27 12 7 4 4 4Marketplace confidence 272422 358248 358248 358248 256872 108082 55576 2783 19708 15838 15838 15838

Table 5 Varying marketplace confidence weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 673384 200191 200191 200191 200191 200191 1950118 1945048 217084 2408288 2532848 3047688Marketplace fairness 34 100 100 100 100 100 11 12 14 16 17 21Marketplace confidence 0 0 0 0 0 0 18462 2783 31358 3474 3647 43678

Table 6 Varying cost objective weights CP method

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 116650 118066 119614 121316 123194 125278 127647 129441 130421 133686 137680 911812Marketplace fairness 4 4 4 4 4 4 4 4 4 4 4 38Marketplace confidence 158380 148941 138614 127269 114748 100855 85695 74755 68988 49782 27313 1119864 minus 04

Table 7 Varying marketplace fairness weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 763739 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441Marketplace fairness 42 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 10459 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755

8 Mathematical Problems in Engineering

Table 8 Varying marketplace confidence weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 911812 141246 139581 137823 135860 133686 131261 129441 128466 125278 121454 116649Marketplace fairness 38 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 1119864 minus 04 7986 16752 26517 37424 49783 64046 74755 80572 100855 126351 158380

The solutions of Table 6 can be compared directly toTable 3 as can be Tables 7 and 4 as well as Tables 8 and 5respectively Generally when the weights for the cost objec-tive are reduced on a 005 step decrease from 1 to 0 the costvalue steadily increases for the CPM This trend is also truefor marketplace confidence However the WOM model isinsensitive to weight changes when the cost weights are in[05 1] The same pattern is found for marketplace fairnessand shipperrsquos confidence where varying weights between[0 015] and [005 025] for the respective objectives didnot change the values of those objectives (Tables 4 and5) The CPM quickly reaches a minimum for marketplacefairness with a slight change in weights from the maximum1 Choosing a different 119875 value will alter marketplace fairnessThus theWOMcan provide solutions quickly for eachweightvariation However the CPM can provide many solutionsfor the same weight variations albeit having to vary theparameter 119901

5 Conclusions

While research on transportation procurement has benefitedfrom the use of CA the literature does not explicitly providemodel solutions and formulation for the multiobjective con-textThismay be due to the difficulty in operationalising con-cepts such as marketplace fairness and shipperrsquos confidenceThis paper treating the MODM problem in the context asa multiobjective optimization model allows the shipper toinclude nonfinancial carrier selection measures Future workcan consider a service index that can be incorporated andupdated from one auction to another to allow carriers tobe tracked on performance Our results suggest that there isno dominant MODM technique However this is good forthe shipper as shipper now has at its disposal a variety oftechniques to compare against when making a final decisionon the winner for the auction Alternatively the shipper canuse the results for a further bargaining process with thecarriers There may be a situation where the shipper intendsto use a particular carrier who has a high quality service levelbut has a higher service cost too The shipper may then askthe carrier whether it could provide the service at the nextlower price For incorporating a bargaining phase into a CAmechanism readers may be interested in the work of Huanget al [19] Another alternative would be to introduce trust-based mechanism by observing the discrepancy between theresults and the services offered One step further would be

to use this as a means to validate the sensitivity resultsTrust mechanisms have been used in agent-based researchto support decisions made on economic exchange (see [20])Future workmay also include soft computing approaches thatallow the shipper to automate and filter the solutions based onother criteria such as the business relationships

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y Sheffi ldquoCombinatorial auctions in the procurement of trans-portation servicesrdquo Interfaces vol 34 no 4 pp 245ndash252 2004

[2] Y Guo A Lim B Rodrigues and Y Zhu ldquoCarrier assignmentmodels in transportation procurementrdquo Journal of the Opera-tional Research Society vol 57 no 12 pp 1472ndash1481 2006

[3] S M H Motlagh M M Sepehri J Ignatius and A MustafaldquoOptimizing trade in transportation procurement is combi-natorial double auction approach truly betterrdquo InternationalJournal of Innovative Computing Information and Control vol6 no 6 pp 2537ndash2550 2010

[4] J R Forster and S Strasser ldquoCarrier modal selection factorsthe shipper carrier paradoxrdquo Transportation Research Forumvol 31 no 1 pp 206ndash212 1991

[5] W Elmaghraby and P Keskinocak ldquoCombinatorial auctionsin procurementrdquo Tech Rep School of Industrial and SystemsEngineering Georgia Institute of Technology 2002

[6] A Nair ldquoEmerging internet-enabled auction mechanisms insupply chainrdquo Supply ChainManagement vol 10 no 3 pp 162ndash168 2005

[7] O Ergun G Kuyzu and M Savelsbergh ldquoShipper collabora-tionrdquo Computers and Operations Research vol 34 no 6 pp1551ndash1560 2007

[8] C Caplice Optimization-based bidding a new framework forshipper-carrier relationships [PhD dissertation] MIT Cam-bridge Mass USA 1996

[9] C Caplice and Y Sheffi ldquoOptimization based procurement fortransportation servicesrdquo Journal of Business Logistics vol 24 no2 pp 109ndash128 2004

[10] J Ignatius Y-J Lai SMHosseini-MotlaghMM Sepehri andA Mustafa ldquoModeling fuzzy combinatorial auctionrdquo ExpertSystems with Applications vol 38 pp 11482ndash11488 2011

Mathematical Problems in Engineering 9

[11] N Remli and M Rekik ldquoA robust winner determination prob-lem for combinatorial transportation auctions under uncertainshipment volumesrdquo Transportation Research C vol 35 no 10pp 204ndash217 2013

[12] M Tamiz D Jones and C Romero ldquoGoal programming fordecision making an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 111 no 3 pp569ndash581 1998

[13] A M Geoffrion ldquoProper efficiency and the theory of vectormaximizationrdquo Journal of Mathematical Analysis and Applica-tions vol 22 no 3 pp 618ndash630 1968

[14] A Charnes andW W CooperManagement Models and Indus-trial Applications of Linear Programming John Wiley amp SonsNew York NY USA 1961

[15] VWadhwa andA R Ravindran ldquoVendor selection in outsourc-ingrdquo Computers and Operations Research vol 34 no 12 pp3725ndash3737 2007

[16] A Imai E Nishimura and S Papadimitriou ldquoBerth allocationwith service priorityrdquo Transportation Research B vol 37 no 5pp 437ndash457 2003

[17] D F Jones S K Mirrazavi and M Tamiz ldquoMulti-objectivemeta-heuristics an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 137 no 1 pp 1ndash92002

[18] A Charnes and W W Cooper ldquoGoal programming and multi-objective optimization Part 1rdquo European Journal of OperationalResearch vol 1 no 1 pp 39ndash54 1977

[19] HHuang R J KauffmanH Xu and L Zhao ldquoA hybridmecha-nism for heterogeneous e-procurement involving a combinato-rial auction and bargainingrdquo Electronic Commerce Research andApplications vol 12 no 3 pp 181ndash194 2013

[20] Y Yang S Singhal and Y Xu ldquoAlternate strategies for a win-win seeking agent in agent-human negotiationsrdquo Journal ofManagement Information Systems vol 29 no 3 pp 223ndash2552012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

Table 3 Varying cost objective weights WOMmethod

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 1166496 1166496 1166496 1166496 1166496 1166496 123742 194505 265986 758231 3052837 3052837Marketplace fairness 4 4 4 4 4 4 5 12 18 39 100 100Marketplace confidence 15838 15838 15838 15838 15838 15838 16924 2783 38234 109119864 minus 04 0 0

Table 4 Varying marketplace fairness weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 2589176 244227 244227 244227 1752309 7371432 3894 1945048 14262 1166496 1166496 1166496Marketplace fairness 100 100 100 100 82 45 27 12 7 4 4 4Marketplace confidence 272422 358248 358248 358248 256872 108082 55576 2783 19708 15838 15838 15838

Table 5 Varying marketplace confidence weights WOMmethod

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 673384 200191 200191 200191 200191 200191 1950118 1945048 217084 2408288 2532848 3047688Marketplace fairness 34 100 100 100 100 100 11 12 14 16 17 21Marketplace confidence 0 0 0 0 0 0 18462 2783 31358 3474 3647 43678

Table 6 Varying cost objective weights CP method

WeightsCost 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 116650 118066 119614 121316 123194 125278 127647 129441 130421 133686 137680 911812Marketplace fairness 4 4 4 4 4 4 4 4 4 4 4 38Marketplace confidence 158380 148941 138614 127269 114748 100855 85695 74755 68988 49782 27313 1119864 minus 04

Table 7 Varying marketplace fairness weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 1 09 08 07 06 05 04 0333 03 02 01 0Marketplace confidence 0 005 01 015 02 025 03 0333 035 04 045 05

ValuesCost 763739 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441 129441Marketplace fairness 42 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 10459 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755 74755

8 Mathematical Problems in Engineering

Table 8 Varying marketplace confidence weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 911812 141246 139581 137823 135860 133686 131261 129441 128466 125278 121454 116649Marketplace fairness 38 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 1119864 minus 04 7986 16752 26517 37424 49783 64046 74755 80572 100855 126351 158380

The solutions of Table 6 can be compared directly toTable 3 as can be Tables 7 and 4 as well as Tables 8 and 5respectively Generally when the weights for the cost objec-tive are reduced on a 005 step decrease from 1 to 0 the costvalue steadily increases for the CPM This trend is also truefor marketplace confidence However the WOM model isinsensitive to weight changes when the cost weights are in[05 1] The same pattern is found for marketplace fairnessand shipperrsquos confidence where varying weights between[0 015] and [005 025] for the respective objectives didnot change the values of those objectives (Tables 4 and5) The CPM quickly reaches a minimum for marketplacefairness with a slight change in weights from the maximum1 Choosing a different 119875 value will alter marketplace fairnessThus theWOMcan provide solutions quickly for eachweightvariation However the CPM can provide many solutionsfor the same weight variations albeit having to vary theparameter 119901

5 Conclusions

While research on transportation procurement has benefitedfrom the use of CA the literature does not explicitly providemodel solutions and formulation for the multiobjective con-textThismay be due to the difficulty in operationalising con-cepts such as marketplace fairness and shipperrsquos confidenceThis paper treating the MODM problem in the context asa multiobjective optimization model allows the shipper toinclude nonfinancial carrier selection measures Future workcan consider a service index that can be incorporated andupdated from one auction to another to allow carriers tobe tracked on performance Our results suggest that there isno dominant MODM technique However this is good forthe shipper as shipper now has at its disposal a variety oftechniques to compare against when making a final decisionon the winner for the auction Alternatively the shipper canuse the results for a further bargaining process with thecarriers There may be a situation where the shipper intendsto use a particular carrier who has a high quality service levelbut has a higher service cost too The shipper may then askthe carrier whether it could provide the service at the nextlower price For incorporating a bargaining phase into a CAmechanism readers may be interested in the work of Huanget al [19] Another alternative would be to introduce trust-based mechanism by observing the discrepancy between theresults and the services offered One step further would be

to use this as a means to validate the sensitivity resultsTrust mechanisms have been used in agent-based researchto support decisions made on economic exchange (see [20])Future workmay also include soft computing approaches thatallow the shipper to automate and filter the solutions based onother criteria such as the business relationships

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y Sheffi ldquoCombinatorial auctions in the procurement of trans-portation servicesrdquo Interfaces vol 34 no 4 pp 245ndash252 2004

[2] Y Guo A Lim B Rodrigues and Y Zhu ldquoCarrier assignmentmodels in transportation procurementrdquo Journal of the Opera-tional Research Society vol 57 no 12 pp 1472ndash1481 2006

[3] S M H Motlagh M M Sepehri J Ignatius and A MustafaldquoOptimizing trade in transportation procurement is combi-natorial double auction approach truly betterrdquo InternationalJournal of Innovative Computing Information and Control vol6 no 6 pp 2537ndash2550 2010

[4] J R Forster and S Strasser ldquoCarrier modal selection factorsthe shipper carrier paradoxrdquo Transportation Research Forumvol 31 no 1 pp 206ndash212 1991

[5] W Elmaghraby and P Keskinocak ldquoCombinatorial auctionsin procurementrdquo Tech Rep School of Industrial and SystemsEngineering Georgia Institute of Technology 2002

[6] A Nair ldquoEmerging internet-enabled auction mechanisms insupply chainrdquo Supply ChainManagement vol 10 no 3 pp 162ndash168 2005

[7] O Ergun G Kuyzu and M Savelsbergh ldquoShipper collabora-tionrdquo Computers and Operations Research vol 34 no 6 pp1551ndash1560 2007

[8] C Caplice Optimization-based bidding a new framework forshipper-carrier relationships [PhD dissertation] MIT Cam-bridge Mass USA 1996

[9] C Caplice and Y Sheffi ldquoOptimization based procurement fortransportation servicesrdquo Journal of Business Logistics vol 24 no2 pp 109ndash128 2004

[10] J Ignatius Y-J Lai SMHosseini-MotlaghMM Sepehri andA Mustafa ldquoModeling fuzzy combinatorial auctionrdquo ExpertSystems with Applications vol 38 pp 11482ndash11488 2011

Mathematical Problems in Engineering 9

[11] N Remli and M Rekik ldquoA robust winner determination prob-lem for combinatorial transportation auctions under uncertainshipment volumesrdquo Transportation Research C vol 35 no 10pp 204ndash217 2013

[12] M Tamiz D Jones and C Romero ldquoGoal programming fordecision making an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 111 no 3 pp569ndash581 1998

[13] A M Geoffrion ldquoProper efficiency and the theory of vectormaximizationrdquo Journal of Mathematical Analysis and Applica-tions vol 22 no 3 pp 618ndash630 1968

[14] A Charnes andW W CooperManagement Models and Indus-trial Applications of Linear Programming John Wiley amp SonsNew York NY USA 1961

[15] VWadhwa andA R Ravindran ldquoVendor selection in outsourc-ingrdquo Computers and Operations Research vol 34 no 12 pp3725ndash3737 2007

[16] A Imai E Nishimura and S Papadimitriou ldquoBerth allocationwith service priorityrdquo Transportation Research B vol 37 no 5pp 437ndash457 2003

[17] D F Jones S K Mirrazavi and M Tamiz ldquoMulti-objectivemeta-heuristics an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 137 no 1 pp 1ndash92002

[18] A Charnes and W W Cooper ldquoGoal programming and multi-objective optimization Part 1rdquo European Journal of OperationalResearch vol 1 no 1 pp 39ndash54 1977

[19] HHuang R J KauffmanH Xu and L Zhao ldquoA hybridmecha-nism for heterogeneous e-procurement involving a combinato-rial auction and bargainingrdquo Electronic Commerce Research andApplications vol 12 no 3 pp 181ndash194 2013

[20] Y Yang S Singhal and Y Xu ldquoAlternate strategies for a win-win seeking agent in agent-human negotiationsrdquo Journal ofManagement Information Systems vol 29 no 3 pp 223ndash2552012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

Table 8 Varying marketplace confidence weights CP method

WeightsCost 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace fairness 0 005 01 015 02 025 03 0333 035 04 045 05Marketplace confidence 1 09 08 07 06 05 04 0333 03 02 01 0

ValuesCost 911812 141246 139581 137823 135860 133686 131261 129441 128466 125278 121454 116649Marketplace fairness 38 4 4 4 4 4 4 4 4 4 4 4Marketplace confidence 1119864 minus 04 7986 16752 26517 37424 49783 64046 74755 80572 100855 126351 158380

The solutions of Table 6 can be compared directly toTable 3 as can be Tables 7 and 4 as well as Tables 8 and 5respectively Generally when the weights for the cost objec-tive are reduced on a 005 step decrease from 1 to 0 the costvalue steadily increases for the CPM This trend is also truefor marketplace confidence However the WOM model isinsensitive to weight changes when the cost weights are in[05 1] The same pattern is found for marketplace fairnessand shipperrsquos confidence where varying weights between[0 015] and [005 025] for the respective objectives didnot change the values of those objectives (Tables 4 and5) The CPM quickly reaches a minimum for marketplacefairness with a slight change in weights from the maximum1 Choosing a different 119875 value will alter marketplace fairnessThus theWOMcan provide solutions quickly for eachweightvariation However the CPM can provide many solutionsfor the same weight variations albeit having to vary theparameter 119901

5 Conclusions

While research on transportation procurement has benefitedfrom the use of CA the literature does not explicitly providemodel solutions and formulation for the multiobjective con-textThismay be due to the difficulty in operationalising con-cepts such as marketplace fairness and shipperrsquos confidenceThis paper treating the MODM problem in the context asa multiobjective optimization model allows the shipper toinclude nonfinancial carrier selection measures Future workcan consider a service index that can be incorporated andupdated from one auction to another to allow carriers tobe tracked on performance Our results suggest that there isno dominant MODM technique However this is good forthe shipper as shipper now has at its disposal a variety oftechniques to compare against when making a final decisionon the winner for the auction Alternatively the shipper canuse the results for a further bargaining process with thecarriers There may be a situation where the shipper intendsto use a particular carrier who has a high quality service levelbut has a higher service cost too The shipper may then askthe carrier whether it could provide the service at the nextlower price For incorporating a bargaining phase into a CAmechanism readers may be interested in the work of Huanget al [19] Another alternative would be to introduce trust-based mechanism by observing the discrepancy between theresults and the services offered One step further would be

to use this as a means to validate the sensitivity resultsTrust mechanisms have been used in agent-based researchto support decisions made on economic exchange (see [20])Future workmay also include soft computing approaches thatallow the shipper to automate and filter the solutions based onother criteria such as the business relationships

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y Sheffi ldquoCombinatorial auctions in the procurement of trans-portation servicesrdquo Interfaces vol 34 no 4 pp 245ndash252 2004

[2] Y Guo A Lim B Rodrigues and Y Zhu ldquoCarrier assignmentmodels in transportation procurementrdquo Journal of the Opera-tional Research Society vol 57 no 12 pp 1472ndash1481 2006

[3] S M H Motlagh M M Sepehri J Ignatius and A MustafaldquoOptimizing trade in transportation procurement is combi-natorial double auction approach truly betterrdquo InternationalJournal of Innovative Computing Information and Control vol6 no 6 pp 2537ndash2550 2010

[4] J R Forster and S Strasser ldquoCarrier modal selection factorsthe shipper carrier paradoxrdquo Transportation Research Forumvol 31 no 1 pp 206ndash212 1991

[5] W Elmaghraby and P Keskinocak ldquoCombinatorial auctionsin procurementrdquo Tech Rep School of Industrial and SystemsEngineering Georgia Institute of Technology 2002

[6] A Nair ldquoEmerging internet-enabled auction mechanisms insupply chainrdquo Supply ChainManagement vol 10 no 3 pp 162ndash168 2005

[7] O Ergun G Kuyzu and M Savelsbergh ldquoShipper collabora-tionrdquo Computers and Operations Research vol 34 no 6 pp1551ndash1560 2007

[8] C Caplice Optimization-based bidding a new framework forshipper-carrier relationships [PhD dissertation] MIT Cam-bridge Mass USA 1996

[9] C Caplice and Y Sheffi ldquoOptimization based procurement fortransportation servicesrdquo Journal of Business Logistics vol 24 no2 pp 109ndash128 2004

[10] J Ignatius Y-J Lai SMHosseini-MotlaghMM Sepehri andA Mustafa ldquoModeling fuzzy combinatorial auctionrdquo ExpertSystems with Applications vol 38 pp 11482ndash11488 2011

Mathematical Problems in Engineering 9

[11] N Remli and M Rekik ldquoA robust winner determination prob-lem for combinatorial transportation auctions under uncertainshipment volumesrdquo Transportation Research C vol 35 no 10pp 204ndash217 2013

[12] M Tamiz D Jones and C Romero ldquoGoal programming fordecision making an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 111 no 3 pp569ndash581 1998

[13] A M Geoffrion ldquoProper efficiency and the theory of vectormaximizationrdquo Journal of Mathematical Analysis and Applica-tions vol 22 no 3 pp 618ndash630 1968

[14] A Charnes andW W CooperManagement Models and Indus-trial Applications of Linear Programming John Wiley amp SonsNew York NY USA 1961

[15] VWadhwa andA R Ravindran ldquoVendor selection in outsourc-ingrdquo Computers and Operations Research vol 34 no 12 pp3725ndash3737 2007

[16] A Imai E Nishimura and S Papadimitriou ldquoBerth allocationwith service priorityrdquo Transportation Research B vol 37 no 5pp 437ndash457 2003

[17] D F Jones S K Mirrazavi and M Tamiz ldquoMulti-objectivemeta-heuristics an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 137 no 1 pp 1ndash92002

[18] A Charnes and W W Cooper ldquoGoal programming and multi-objective optimization Part 1rdquo European Journal of OperationalResearch vol 1 no 1 pp 39ndash54 1977

[19] HHuang R J KauffmanH Xu and L Zhao ldquoA hybridmecha-nism for heterogeneous e-procurement involving a combinato-rial auction and bargainingrdquo Electronic Commerce Research andApplications vol 12 no 3 pp 181ndash194 2013

[20] Y Yang S Singhal and Y Xu ldquoAlternate strategies for a win-win seeking agent in agent-human negotiationsrdquo Journal ofManagement Information Systems vol 29 no 3 pp 223ndash2552012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

[11] N Remli and M Rekik ldquoA robust winner determination prob-lem for combinatorial transportation auctions under uncertainshipment volumesrdquo Transportation Research C vol 35 no 10pp 204ndash217 2013

[12] M Tamiz D Jones and C Romero ldquoGoal programming fordecision making an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 111 no 3 pp569ndash581 1998

[13] A M Geoffrion ldquoProper efficiency and the theory of vectormaximizationrdquo Journal of Mathematical Analysis and Applica-tions vol 22 no 3 pp 618ndash630 1968

[14] A Charnes andW W CooperManagement Models and Indus-trial Applications of Linear Programming John Wiley amp SonsNew York NY USA 1961

[15] VWadhwa andA R Ravindran ldquoVendor selection in outsourc-ingrdquo Computers and Operations Research vol 34 no 12 pp3725ndash3737 2007

[16] A Imai E Nishimura and S Papadimitriou ldquoBerth allocationwith service priorityrdquo Transportation Research B vol 37 no 5pp 437ndash457 2003

[17] D F Jones S K Mirrazavi and M Tamiz ldquoMulti-objectivemeta-heuristics an overview of the current state-of-the-artrdquoEuropean Journal of Operational Research vol 137 no 1 pp 1ndash92002

[18] A Charnes and W W Cooper ldquoGoal programming and multi-objective optimization Part 1rdquo European Journal of OperationalResearch vol 1 no 1 pp 39ndash54 1977

[19] HHuang R J KauffmanH Xu and L Zhao ldquoA hybridmecha-nism for heterogeneous e-procurement involving a combinato-rial auction and bargainingrdquo Electronic Commerce Research andApplications vol 12 no 3 pp 181ndash194 2013

[20] Y Yang S Singhal and Y Xu ldquoAlternate strategies for a win-win seeking agent in agent-human negotiationsrdquo Journal ofManagement Information Systems vol 29 no 3 pp 223ndash2552012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of