research article the tractor and semitrailer routing...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 509160 12 pageshttpdxdoiorg1011552013509160

Research ArticleThe Tractor and Semitrailer Routing ConsideringCarbon Dioxide Emissions

Hongqi Li1 Yanran Li1 Qiuhong Zhao2 Yue Lu1 and Qiang Song3

1 School of Transportation Science and Engineering Beihang University No 37 Xueyuan Road Haidian District Beijing 100191 China2 School of Economics and Management Beihang University No 37 Xueyuan Road Haidian District Beijing 100191 China3 School of Humanities and Social Sciences Beihang University No 37 Xueyuan Road Haidian District Beijing 100191 China

Correspondence should be addressed to Qiuhong Zhao qhzhaobuaaeducn

Received 5 July 2013 Revised 10 November 2013 Accepted 10 November 2013

Academic Editor John Gunnar Carlsson

Copyright copy 2013 Hongqi Li et al This 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

The incorporation of the minimization of carbon dioxide (CO2) emissions in the VRP is important to logistics companies The

paper deals with the tractor and semitrailer routing problem with full truckload between any two depots of the network an integerprogramming model with the objective of minimizing CO

2emissions per ton-kilometer is proposed A two-stage approach with

the same core steps of the simulated annealing (SA) in both stages is designed The number of tractors is provided in the firststage and the CO

2emissions per ton-kilometer are then optimized in the second stage Computational experiments on small-scale

randomly generated instances supported the feasibility and validity of the heuristic algorithm To a practical-scale problem the SAalgorithm can provide advice on the number of tractors the routes and the location of the central depot to realize CO

2emissions

decrease

1 Introduction

Recent studies in freight transportation have focused notonly on cost minimization or profit maximization for afreight company but also on carbon reduction [1] Carbondioxide (CO

2) is emitted during the combustion of fossil

fuels to drive vehicles The efficient use of trucks and roadnetworks becomes more and more important to enhancethe corporate social responsibility for companies Optimizedvehicle routing can reduce the number of trucks and utilizebetter the network by reducing vehicle movements Theoptimization problem has been extensively studied in theliterature known as the vehicle routing problem (VRP)

The incorporation of the minimization of fuel consump-tion and CO

2emissions in the VRP is a relatively recent

topic addressed in the research work VRP-related researchthat aims to minimize total fuel consumption is rather rare[2] Kara et al [3] define an energy-minimizing VRP thatminimizes the weighted load instead of a distance basedobjective function Kuo [2] calculated total fuel consumption

for the time-dependent VRP Lin and Ng [1] formulated atwo-stage stochastic program to minimize the emission ofthe carriers to see the effects of backhaul collaboration Xiaoet al [4] extended the capacitated VRP taking into accounttravel distance and load impacts on fuel costs Kwon et al [5]used a mixed integer programming model to investigate theheterogeneous fixed fleet VRP with carbon emission

From the experimental results of Pradenas et al [6] thetype of vehicles and the use rate of vehicles are importantfactors affecting CO

2emissions of the vehicle routing We

distinguish the VRP and its extensions by considering bothvehicle types and service segment types (i) The constitutionmode of the autonomous part and the nonautonomouspart can classify vehicles into two types [7] trucks andcombination vehicles In some extensions of the VRP thecombination vehicles and especially the use of trailers areconsidered (ii) The road freight industry has basically twotypes of service segments full truckload (TL) shipping andless-than-truckload (LTL) shipping TL is more suitable forcustomers with large shipment sizes that require individual

2 Mathematical Problems in Engineering

tailored services such as direct transportation between twopoints LTL is more appropriate for clients that have to sharethe carrierrsquos transportation resources with other customers[8] Most VRP research concentrated on the optimization ofdelivery orand pickup of LTL service

Logistics companies use various types of vehicles andoperate from more than one distribution center Shipmentsoccur between depots and the pickupdelivery locations oforders and between depots In multilevel freight distributionsystems (eg city logistics multimodal freight transportationsystems parcels or public postal services) in which freightarrives at a depot and is transported further to anotherdepot by large vehicles and the freight is then brought to thefinal customers by small vehicles both TL and LTL appearThe problem how to efficiently route vehicles operating atboth levels is known in the literature as the two-echelonvehicle routing problem (2E-VRP) [9] the generalized vehiclerouting problem (GVRP) [10] or the single-sourcing two-echelon capacitated location-routing problem (2E-CLRP)[11]

Compared with most VRP research employing trucksto serve the delivery orand pickup of LTL we study avariant of the combination-vehicle routing problem wheretractor-semitrailer combinations are utilized A tractor canpull multiple and independent trailers The tractor cannotload goods and is only used for pulling the trailers Since thetime to attachdetach a semitrailer to a tractor at locationsis usually considerably less than the time to loadunload allcargoes in a semitrailer the tractor has a high use rateWe callthis variant of the VRP as the tractor and semitrailer routingproblem (TSRP) The tractor and semitrailer transportationis regarded to be more energy-efficient than single-unit trucktransportation [12] As Van Ierland et al [13] stated the CO

2

emission factor which is defined as CO2emissions per ton-

kilometer (unit g CO2t-km) is a typical index to describe

the CO2emission effects of the road freight transportation

Differing from other pieces of literature we aim to minimizeCO2emissions per ton-kilometer of the TSRP

We propose the TSRP on a loaded semitrailer flownetwork The loaded semitrailers are assumed to be TLThere are two types of terminals on the network one centraldepot and a number of satellite depots At the beginning alltractors locate in the central depot while the satellite depotshave loaded semitrailers waiting for sending All tractorsor vehicles (a vehicle is one tractor pulling one semitrailer)originate and terminate at the central depot A homogeneousfleet composed of tractors and semitrailers serves the loadedsemitrailer flow demand among depots A tractor can pullone loaded semitrailer and can also run alone The objectiveof the TSRP is to determine the number of tractors and theroute of each tractor so as to minimize CO

2emissions per

ton-kilometerOur interest in the TSRP arises from the full truckload

transporting of multilevel freight distribution systems Ouraim is to develop a solving method for the TSRP and toshow the effect of CO

2emission mitigation The paper is

organized as followsThe next section introduces the relevantliterature A mathematical model for the TSRP is developedin Section 3 Section 4 proposes the heuristic algorithm for

solving the TSRP Computational experiments are describedin Section 5 Finally conclusions and future work are given inSection 6

2 The Literature Review

The introduction reviewed briefly the limited literaturedirectly targeting the incorporation of CO

2emissions mini-

mization in the VRPWe turn to a brief overview of contribu-tions to the combination-vehicle routing problem the TSRPconcerns

Research on the VRP to date has considered especiallytrucks and truck and full trailer combinationsThe truck andtrailer routing problem (TTRP) has been brought forwardfor decades In the TTRP a heterogeneous fleet composedof trucks and trailers serves a set of customers Both thetruck and the trailer have hauling capacity and goods canbe transferred between the truck and the trailer en-route inthe parking places of the trailer Each customer has a certaindemand and the capacities of the trucks and trailers aredeterminate Some customers must be served only by a truckwhile other customers can be served either by a truck or bya combination vehicle The objective of the TTRP is to finda set of routes with minimum total distance or cost so thateach customer is visited Interested readers are referred toVillegas et al [14] in order to get an overview of recentlyrelated publications of the TTRP

Semet and Taillard [15] and Caramia and Guerriero [16]provided some real-world TTRP applications Gerdessen [17]extended the VRP to the VRP with trailers and investigatedthe optimal deployment of a fleet of truck-trailer combina-tions Chao [18] distinguished three types of routes in a TTRPsolution Subsequently Scheuerer [19] Tan et al [20] Lin etal [21] and Villegas et al [22] solved the TTRP by variousheuristics On the extensions of the TTRP Villegas et al[23] proposed two metaheuristics to solve the single truckand trailer routing problemwith satellite depots (STTRPSD)Considering the number of available trucks and trailers beinglimited in the TTRP Lin et al [24] relaxed the fleet sizeconstraint and developed a SA heuristic for solving therelaxed truck and trailer routing problem (RTTRP) Lin et al[25] proposed a SA heuristic for solving the truck and trailerrouting problem with time windows (TTRPTW) RecentlyDerigs et al [26] combined local search and large neighbor-hood search metaheuristic to solve the TTRP withwithoutload transfer and the TTRP withwithout time windowsVillegas et al [14] presented a two-phase matheuristic to theTTRP A pool of routes with the local optima was obtained bya hybridGRASPtimesILSmetaheuristic and these routes becomecolumns in a set-partitioning problem solved with a mixedinteger programming optimizer

In the TTRP each trailer can be pulled by a unique associ-ated truck and only this truck is permitted to transfer the loadinto the trailer The amount of trucks is generally more thanthat of trailers Drexl [7] described the VRP with trailers andtransshipments (VRPTT) in which there is no fixed truck-trailer assignment The TTRP is evidently a special case ofthe VRPTT Besides Pureza et al [27] addressed the VRP

Mathematical Problems in Engineering 3

with time windows and multiple deliverymen (VRPTWMD)that allows a number of deliverymen to be assigned to eachroute Two solution approaches based on tabu search and antcolony optimization were proposed The impact of the use ofextra deliverymen in route planning was assessed by meansof computational experiments If regarding deliverymen astrucks the VRPTWMD becomes the TTRP when there isonly one deliveryman

There are several variants of the VRP which considertractor and semitrailer combinations These variants includethe rollon-rolloff vehicle routing problem (RRVRP) andothers In the literature the RRVRP arises when tractorsmove trailers between locations generating a high volumeof waste like construction sites and disposal facilities In thebasic RRVRP there is a single depot where all tractors arelocated at the beginning and there is a single disposal facilitywhere full trailers get dumped and empty trailers can beput on or pulled from inventory At the end of the day alltractors return to the depot while trailers may remain atcustomer locations or the disposal facility The problem isto assign trips to tractors and to find routes for the tractorswhich do not exceed a given maximal duration and whichaltogether minimize the nonproductive deadhead time oftractors between trips as well as the number of tractors used

Bodin et al [28] studied the RRVRP with a depot anda disposal site and classified customer demands of four triptypesHeuristicmethodswere proposed to solve somebench-mark problems on the RRVRP Wy and Kim [29] proposed ahybrid metaheuristic approach that consists of a large neigh-borhood search and various improvement methods to solvethe RRVRP The benchmark data of Bodin et al [28] wereused to test the effectiveness of the proposed method Derigset al [30] solved the RRVRP by combining local search andlarge neighborhood search controlled by two relatively simpleand parameter-free-poor metaheuristic control proceduresWy et al [31] introduced the RRVRP with time windows(RRVRPTW)The objective of the RRVRPTW is tominimizethe number of required tractors and their total route timeA LNS based iterative heuristic approach consisting of aconstruction algorithm and several improvement algorithmswas proposed Baldacci et al [32] modeled the multipledisposal facilities and multiple inventory locations RRVRP(M-RRVRP) as a time constrained VRP on a multigraph

There are other variants concerning the tractor andsemitrailer combination routing problem Hall and Sabnani[33] studied routes that consisted of two or more segmentsand two or more stops in the route for a tractor Controlrules based onpredicted route productivitywere developed todetermine when to release a tractor Francis et al [34] solvedthe multiresource routing problem (MRRP) with flexibletasks Two resources (tractors and trailers) performed tasksto transport loaded and empty equipment Cheng et al [35]proposed a model for a steel plant to find the tractor andsemitrailer running routes to minimize transport distanceDerigs et al [36] presented two approaches to solve theVRP with multiple uses of tractors and trailers With anassumption of exactly one semitrailer in each depot and anexplanation on the relationship between the assumption andany number of vehicles in a depot Li et al [37] studied

the tractor and semitrailer routing problem on a unit-flownetwork (TSRP-UF) and a heuristic algorithm was used todecide the number of tractors and the route of each tractor

Among all the work we have reviewed little work hasbeen done on the problemwe have described earlier in whichthe tractor and semitrailer combination vehicles are usedfor the TL of multilevel freight distribution systems Theobjective of our problem is to provide the number of tractorsused and reduce the disparity of routes of the tractors tominimize CO

2emissions per ton-kilometer We are going to

discuss this problem in detail in the next section

3 Model Formulation

The underlying assumptions of the TSRP model include thefollowing

(i) All loaded semitrailer flow demands are known in ad-vance Empty semitrailer exchanges are ignored

(ii) Loaded semitrailer flow demand can originate be-tween any two depots

(iii) A route must not exceed a given distance span Inorder to reduce the disparity of routes and to bal-ance tractors workload a route must exceed a givenminimization-distance

(iv) Routes start and end at the central depot If a satellitedepot is already present in a route it cannot bereinserted in the same route

(v) All tractors are assigned to the central depot wherethey must return to after each route Each tractorleaves from and returns to the depot once or more

(vi) The TSRP is a homogeneous vehicle routing

The TSRP can be formulated as followsLet 119866 = (119881 119860) be a directed graph where 119881 = 0 1 2

119899 is the vertex set and 119860 = (119894 119895) | 119894 119895 isin 119881 119894 = 119895 the arcset Vertex 0 (V

0) is the central depot and other vertices (V

119894)

in 119881 (ie 119881 0) correspond to satellite depots Denote thedistance between V

119894and V119895as 119889119894119895and the running time from V

119894

to V119895as 119905119894119895 Loaded semitrailer flows between any two depots

are 119877

119877 =

[[[[[[

[

0 1199030111990302sdot sdot sdot 119903

0119899

119903100 11990312sdot sdot sdot 119903

1119899

11990320119903210 sdot sdot sdot 119903

2119899

11990311989901199031198991sdot sdot sdot 119903119899119899minus1

0

]]]]]]

]

(1)

where 119903119894119895denotes that there are 119903

119894119895loaded semitrailer s needed

to be transported from V119894to V119895

119862119905

119894119895119896is the fuel consumption of the 119896th tractor running

from V119894to V119895 and 119862119897

119894119895119896is the fuel consumption of the 119896th

combination vehicle running from V119894to V119895 vel119905 is the average

velocity of the 119896th tractor running alone from V119894to V119895 vel119897 is

the average velocity of the kth combination vehicle runningfrom V

119894to V119895 Suppose that vel119905 = vel119897 = vel then 119889

119894119895=


vel sdot 119905119894119895 the total number of tractors used is119867 the minimum

distance and themaximum distance of a route are1198631and119863

2

respectively119883119905

119894119895119896and 119883119897

119894119895119896are the decision variables If the 119896th tractor

runs from V119894to V119895for120572 times119883119905

119894119895119896= 120572 if the 119896th combination

vehicle (ie the 119896th tractor pulling one loaded semitrailer)runs from V

119894to V119895for 120573 times119883119897

119894119895119896= 120573

The objective function is

Min120574 sdot (sum

119894sum119895sum119896119862119905

119894119895119896119883119905

119894119895119896+ sum119894sum119895sum119896119862119897

119894119895119896119883119897

119894119895119896)

119882 sdot sum119896sum119894sum119895119883119897

119894119895119896sdot 119889119894119895

(2)

The constraints are

sum

119896

119883119897

119894119895119896= 119903119894119895 (3)

sum

119894

119883119905

119895119894119896+sum

119894

119883119897

119895119894119896ge 1 (4)

sum

119894

119883119905

119894119895119896+sum

119894

119883119897

119894119895119896ge 1 (5)

sum

119894

119883119905

119895119894119896+sum

119894

119883119897

119895119894119896= sum

119894

119883119905

119894119895119896+sum

119894

119883119897

119894119895119896 (6)

sum

119894

sum

119895

(119889119894119895sdot 119883119905

119894119895119896+ 119889119894119895sdot 119883119897

119894119895119896) ge 119863

1 (7)

sum

119894

sum

119895

(119889119894119895sdot 119883119905

119894119895119896+ 119889119894119895sdot 119883119897

119894119895119896) le 119863

2 (8)

119883119905

119894119895119896and 119883119897

119894119895119896are integers 119894 119895 = 0 1 2 119899 119894 = 119895 119896 is an

integer and the maximum 119896 is the total of tractors used (119867)119867 ge (sum

119894sum119895119889119894119895sdot 119903119894119895)1198632

The objective function is the CO2emissions per ton-

kilometer where 120574 is the emission coefficient and 119882 thefreight weight on a loaded semitrailer Constraints (3) guar-antee that the freight flowdemand is satisfiedConstraints (4)(5) and (6) guarantee the assumption (V) and constraints (6)also guarantee vehicle balance of satellite depots Constraints(7) and (8) are the restriction of balancing the route lengths

Generally efficient exact algorithms to solve the modelwe presented here for realistic problem sizes do not existThus such model can only be solved by heuristics to attainsuboptimal solutions of a priori unknown quality

4 A Two-Stage Heuristic AlgorithmBased on the SA

Three types of algorithms are used to solve the VRP [38]The first type consists of exact algorithms that are time-consuming The second type consists of classical heuristicssuch as greedy local search and relaxation based The thirdtype consists of heuristics that are based on somemetaheuris-tic rules Such metaheuristics or framework for buildingheuristics are the SA tabu search genetic algorithms variableneighborhood search and so forth The high computationalcost of exact methods and their poor performance in large

problems have involved that the current research concen-trates on stochastic algorithms that are capable of producingfeasible but not necessarily optimal solutions in limited time[39]

The SA algorithm is one of the commonly used meta-heuristics and has been successfully applied to solve severaltypes of the VRP Motivated by the success of the SA forthe TTRP (eg [24 25]) we have therefore opted a heuristicalgorithm based on the SA to solve the TSRP

The SA uses a stochastic approach to search for andmoveto neighborhood solutions If a better neighborhood solutionis identified in the search starting from the current solutionthen the move will be accepted and the current solution willbe replaced by the better neighborhood solution The searchfor a better neighborhood solution then continues Besidesthe SA will accept the moving to a worse neighborhoodsolution with a certain probability so as to escape from alocal optimum The accepted probability is based on twoparameters the temperature which gradually reduces and theobjective function difference between the two solutions Inthe beginning of the search the accepted probability of themove is high When nearing the end of the search processthe accepted probability of the move is small The initialtemperature the cooling function and the final temperatureaffect the results of the SA

41 Neighborhood and Initial Solution Local search playsa very important role in the design of metaheuristics forthe VRP [40] A local search operator iteratively improvesa solution by exploring its neighborhood The TSRP modelin Section 3 suggests that the route is made up of sequentialarcs We regard constraints (7) and (8) as the most importantfactors to decide the solutionrsquos neighborhood

Regulations related to long-distance transportationimpose complex rules for driving time and driver breaksCombining the VRP with break scheduling leads tocomplicated route feasibility checks The distance span (ortime-span when the velocity is constant) constraint is usuallyan important consideration in the VRP Almoustafa et al [38]investigated distance constrained VRP (DVRP) where thetotal travelled distance by each vehicle in the solution is lessthan or equal to the maximum possible travelled distanceLetchford and Salazar-Gonzalez [41] took DVRP as a specialcase of VRP with time windows constraints Through theminimization-distance and the maximization-distanceincluded in constraints the workload of divers and tractorsis balanced

The distance span constraints decide that the routesinclude finite inserted satellite depots We can enumerate thenumber of satellite depots in a route to search entirely to findall routes that satisfy distance span constraints When theroutes include at least 1 and at most 119891

1198961015840 satellite depots there

are 119874(1198991198911198961015840 ) potential routes for selection The neighborhoodis made up of routes

Referring to the traditional destroy and repair frameworkwe take a whole route as the operator unit There are threetypes of operators (i) A route is removed from the currentsolution by a destroy operator (ii) A route is removed fromthe current solution by a destroy operator and another route is


Simulated Annealing for finding the number of tractors119873best (1198790119879119865120591119872119890)Step 1 Let 119873 = lfloor(sum

119894sum119895119903119894119895)4rfloor

Step 2 Generate the initial solution119883 randomlyStep 3 Let 119879 = 119879

119900 119908 = 0 119902 = 0 119877best = 119877(119883)

Step 4 119908 = 119908 + 1 119902 = 119902 + 1Step 5 Generate a solution 119884 based on119883 by the three types of operators in Section 41Step 6 If Δ = 119877(119884) minus 119877(119883) ge 0 Let119883 = 119884 Else

Generate 120574 = 119903119886119899119889119900119898(0 1)If exp(Δ sdot 1199082119879) gt 120574 Let 119883 = 119884

Step 7119883best = 119883 119877best = 119877(119883)Step 8 If 119902 = 119872

119890119879 = 120591 sdot 119879 119902 = 0

Else Go to Step 3Step 9 If 119879 minus 119879

119865gt 0 Go to Step 3

Else Terminate the SA heuristicsStep 10 If 119877best lt 100 119873 = 119873 + 1 Go to Step 2

If 119877best = 100 119873 = 119873 minus 1 Go to Step 2Else 119873best = 119873

Pseudocode 1 Pseudocode of the proposed SA heuristics for finding the number of tractors

reinserted by a repair operatorThe removed route is recordedby the neighborhood and is still a candidate route of the repairoperator (iii) A route may clone itself several times and thetimes are decided by themaximumdemand of satellite depotsincluded in the route The clone operator is a special type ofrepair operators

For the generation of the initial solution our computa-tional tests showed a similar conclusion as that of Coelho etal [42]The initial solution does not have a significant impacton the overall solution cost or the running timeWe thereforegenerate randomly the initial solution

42 The SA Heuristics Research dealing with the VRP isgenerally based on a two-stage approach where the numberof routes is minimized in the first stage and the otherobjective is then optimized in the second oneMinimizing thenumber of vehicles is often considered the primary objectiveMeanwhile several practical situations directly consideredthe other objective (eg total transporting distance) as theprimary objective [43] We deal with the TSRP based on SAheuristics in the paper to find firstly the number of tractorsused and then the routes so as to minimize CO

2emissions

per ton-kilometerThe number of tractors (or the number of routes in the

solution) is an essential parameter at the beginning of theSA heuristics It is certain that a tractor pulls more than oneindependent semitrailer on the route Denoting the averagenumber of transported loaded semitrailer s on a route as 120585then (sum

119894sum119895119903119894119895)120585 is an important bound of the number of

tractors needed The computational tests showed that it isfeasible for 120585 = 4 The SA procedure is started by selectingrandomly 119873 = lfloor(sum

119894sum119895119903119894119895)4rfloor routes as the initial solution

where lfloor∙rfloor denotes the largest integer which is smaller than orequal to the enclosed number

In the beginning of the SA heuristics the current temper-ature 119879 is set to be the same as 119879

0 Then an initial solution 119883

is generated randomly from the neighborhood described inSection 41The current best solution and the best percentageof satisfied freight demand obtained so far are set to be 119883and 119877(119883) respectively At each iteration the next solution119884 is generated from the neighborhood and its percentageof satisfied freight demand is evaluated Let Δ denote thedifference between 119877(119883) and 119877(119884) that is Δ = 119877(119884) minus 119877(119883)The probability of replacing 119883 with 119884 given that Δ lt 0 isexp(Δ sdot1199082119879) gt 120574where119908 is an integerThis is accomplishedby generating a random number 120574 isin [0 1] and replacingsolution 119883 with 119884 if 120574 lt exp(Δ sdot 1199082119879) Meanwhile if Δ ge0 the probability of replacing 119883 with 119884 is 1 119872

119890iterations

are run during the course of temperature 119879 decreasing totemperature 120591119879where 0 lt 120591 lt 1The algorithm is terminatedwhen the current temperature 119879 is lower than 119879

119865 Following

the termination of the SA procedure the number of tractors1198730is adjusted according to the percentage of satisfied freight

demand of the solutionThe SA approach to find the numberof tractors is summarized in Pseudocode 1

In the second phase successive CO2emissions per ton-

kilometer are minimized for the current number of tractorsuntil a predefined stopping criterion is met (eg the CO

2

emissions per ton-kilometer stop decrease or the numberof iterations) The core steps (steps 2sim8 in Pseudocode 1) ofthe SA heuristics of both phases are the same Let 119862

0the

CO2emissions per ton-kilometer attained by the SA heuristic

that has found the number of tractors Let 119862(119883) the CO2

emissions per ton-kilometer of solution 119883 The SA heuristicfor routes is summarized in Pseudocode 2

5 Computational Study

Since we are not aware of any prior test instance for the TSRPminimizing CO

2emissions per ton-kilometer the proposed


Simulated Annealing for routesStep 1 Let119873 = 119873bestStep 2sim8 (As Step 2sim8 in Pseudocode 1 )Step 9 If 119862(119883) le 119862

0and 119877(119883) = 100 and 119879 minus 119879

119865gt 0 119862

0= 119862(119883) Go to Step 3

Else 119862best = 1198620 Terminate the SA heuristics

Pseudocode 2 Pseudocode of the proposed SA heuristics for routes

model and algorithm were tested on a range of randomlygenerated small-scale instances and a realistic instance TheSA heuristic algorithm was coded in MATLAB and run ona computer with an AMD Athlon (tm) X2 Dual-Core QL-65running at 210GHz underWindows 7 ultimate (32 bits) with2GB of RAM Our computational experiments were carriedout in two parts First we calibrated the solution methodson a set of small-scale instances as explained in Section 51Second we run the SA heuristics on a realistic instance asexplained in Section 52

51 Small-Scale Instances The lack of publicly availabletest instances for the considered problem prevented fromcomparing our results to similar results from the literatureTherefore our test examples were randomly generated insuch a way that the number of satellite depots 119899 was variedfrom 4 to 7 with increment 1 Moreover for each value of119899 10 instances were produced with different flow networkcharacteristics (depot locations distances and loaded semi-trailer flows) which are summarized in Table 1 Columns 1ndash9 indicate the test problem the rectangle region the totalnumber of loaded semitrailer the average loaded semitrailernumber of all satellite facilities the variance of loaded semi-trailer number of all satellite facilities the minimum distancebetween central depot and satellite facility the maximumdistance between central depot and satellite facility theaverage distance between any two terminals and the varianceof distances between any two terminals respectively

The tractor-semitrailer combination which can loadmaximally 30 tons and satisfies the fuel-efficiency require-ments of ldquoRegulation of Supervising Vehicle Fuel Con-sumptionrdquo (no 112009 Decree of Ministry of Transportof the Peoplersquos Republic of China (MOTPRC)) is used inthe small-scale instances The type codes of the selectedcombinations are ldquoCQ4254HTVG324Vrdquo and ldquoND4251B32J7rdquoWhen the velocity is 50 kmh the fuel consumption is 18litres diesels per 100 kilometers for tractor running alone and32 litres diesels per 100 kilometers for combination runningSupposing that the loading factor of loaded semitrailer is 50the distance span is from 500 km to 700 km

The integer programming model presented in Section 3has been implemented and solved using CPLEX 124 Thecomputational results are presented in Table 2

As shown in Table 2 we can find that the solutionCO2emissions per ton-kilometer obtained by the proposed

SA heuristics are close to the integer programming modelsolution For some instances such as RAND5-7 RAND5-8 RAND6-7 RAND6-9 and RAND7-8 the gaps between

the heuristic solution and the integer programming modelsolution are less than 1 For all 40 test instances the largestpercentage gap is 179 and the average percentage gap is70 Out of 40 test instances the gap is less than 10 in22 cases A phenomenon worth to notice is that the locationof a central depot likely affects the percentage gap Instanceswith percentage gaps of over 10 generally have their centraldepots located alongside the boundary of the regions

Although we can solve the TSRP using the sequentialformulation it is still computationally challenging It canbe observed that even for a 10-node problem CPLEX MIPsolver failed to prove the near optimality of the solutiondue to being time-consuming or the insufficient memoryresources Thus a heuristic algorithm is essential for theproblem to improve the computational effectiveness

52 A Realistic Instance The main purpose of the realisticinstance study is to evaluate the applicability of the developedSA heuristics for realistic-size problems A LTL truckingcompany in Shandong province of China simply namedSDEXP is the object of our computational study SDEXPcomprises 17 depots distributed in 17 cities in Shandongprovince We abbreviate the 17 city names to JNA (Jinan)DZH (Dezhou) LCH (Liaocheng) TA (Tairsquoan) LW (Laiwu)HZ (Heze) JNI (Jining) ZZH (Zaozhuang) LY (Linyi) RZH(Rizhao) QD (Qingdao) YT (Yantai) WH (Weihai) WF(Weifang) ZB (Zibo) BZH (Binzhou) and DY (Dongying)respectively SDEXP employed hundreds of single-unit trucksto transport cargoes before 2007 and had a road freightmarket share of about 12 in Shandong province Alongwith the policy on encouraging and popularizing tractor andsemitrailer combinations inChina SDEXPplans to substitutetractor and semitrailer combinations for single-unit trucks

We abstract the transportation network of SDEXP on agraph where the nodes denote the cities The arcs denotehighway infrastructure connecting every two cities SDEXPplans to rebuild a central depot by selecting one of the depotslocated in the following 6 cities JNA QD ZB WF TA andLW Suppose that any one of the 6 city depots can be regardedas a central depot and all other city nodes as satellite depotsTable 3 gives the distances between every two cities SDEXPrsquosexpected freight flows between any two cities per day aregiven in Table 4

The tractor-semitrailer combination adopted in thesmall-scale instances is used in the realistic instance Theloading factor of loaded semitrailer is 50 the velocity is80 kmh The distance span is affected by driversrsquo on-duty


Table 1 Basic characteristics of the 40 test problems

Problem Region (km times km) Freight flow demand (loaded-semitrailer) Distance between centraldepot and satellite depot

Distance between any twodepots

Total Average Variance Min Max Average VarianceRAND5-1 200 times 150 49 25 10 50 200 1267 27126RAND5-2 200 times 200 51 26 10 50 200 1333 22989RAND5-3 250 times 200 60 24 11 50 200 1633 49885RAND5-4 200 times 200 58 29 08 50 200 1333 22989RAND5-5 200 times 250 46 23 11 50 250 1767 71954RAND5-6 200 times 200 66 26 09 50 150 1433 30575RAND5-7 250 times 250 57 23 10 50 300 1867 74023RAND5-8 200 times 250 74 25 10 50 300 1733 61609RAND5-9 200 times 250 70 23 10 200 350 1833 67816RAND5-10 250 times 150 81 23 12 50 200 1238 38095RAND6-1 200 times 250 74 25 10 50 300 1733 61609RAND6-2 200 times 200 99 28 13 50 250 1476 49942RAND6-3 200 times 250 91 25 12 50 200 1619 53426RAND6-4 200 times 250 72 24 09 50 200 1381 48548RAND6-5 250 times 150 73 24 09 50 250 1429 49477RAND6-6 250 times 250 97 27 09 100 200 1857 61324RAND6-7 200 times 200 99 28 13 50 250 1476 49942RAND6-8 250 times 200 80 27 10 50 250 1619 68060RAND6-9 250 times 200 98 27 11 50 300 1429 47038RAND6-10 150 times 250 106 29 07 50 250 1381 48548RAND7-1 200 times 200 102 24 11 50 200 1321 36753RAND7-2 250 times 250 74 21 08 100 250 1768 66331RAND7-3 250 times 250 109 26 09 100 300 1625 50227RAND7-4 250 times 200 88 25 13 100 200 1554 51526RAND7-5 250 times 250 74 21 08 100 300 1768 66331RAND7-6 250 times 250 74 21 08 100 300 1768 66331RAND7-7 250 times 250 74 21 08 100 200 1768 66331RAND7-8 250 times 250 74 21 08 100 300 1768 66331RAND7-9 250 times 250 74 21 08 150 250 1768 66331RAND7-10 250 times 250 74 21 08 100 400 1768 66331RAND8-1 200 times 250 126 26 12 50 300 1417 44366RAND8-2 200 times 250 126 26 12 50 250 1417 44366RAND8-3 200 times 250 126 26 12 50 150 1417 44366RAND8-4 200 times 250 126 26 12 50 150 1417 44366RAND8-5 200 times 250 126 26 12 50 200 1417 44366RAND8-6 200 times 250 126 26 12 150 300 1417 44366RAND8-7 200 times 250 126 26 12 50 200 1417 44366RAND8-8 200 times 250 126 26 12 50 250 1417 44366RAND8-9 200 times 250 150 31 08 100 350 1639 54382RAND8-10 200 times 250 150 31 08 100 350 1639 54382Note the problem is denoted by RAND (number 1)-(number 2) where number 1 is the number of satellite depots and ranges from 4 to 7 and number 2 is theinstance sequence in a similar set


Table 2 Computational results for the 40 test problems

Problem CPLEX SA Gap ()Tractor quantity CO2 emissions per

ton-kilometer (gtm) Tractor quantity CO2 emissions perton-kilometer (gtm)

RAND5-1 11 6521 14 6882 55RAND5-2 11 6135 15 7091 156RAND5-3 16 6214 14 6792 93RAND5-4 12 6173 16 6872 113RAND5-5 12 6422 12 7283 134RAND5-6 16 6234 14 6677 71RAND5-7 19 6417 13 6448 05RAND5-8 21 6578 17 6633 08RAND5-9 31 7970 17 6590 173RAND5-10 17 6297 17 6981 109RAND6-1 21 6578 17 6688 17RAND6-2 25 6172 19 6256 14RAND6-3 24 6423 19 6256 26RAND6-4 16 6358 17 7391 162RAND6-5 15 6112 16 7012 147RAND6-6 32 6421 20 6150 42RAND6-7 27 6214 19 6277 10RAND6-8 23 6340 17 6460 19RAND6-9 22 6053 18 6099 08RAND6-10 24 6195 21 6479 46RAND7-1 21 6129 21 6762 103RAND7-2 21 6418 17 6861 69RAND7-3 30 6449 21 6300 23RAND7-4 21 6256 21 7373 179RAND7-5 23 6944 18 7165 32RAND7-6 22 6750 17 6999 37RAND7-7 22 6805 17 6888 12RAND7-8 24 6944 17 6999 08RAND7-9 22 7386 17 7082 41RAND7-10 20 6805 18 7275 69RAND8-1 28 6069 33 6741 111RAND8-2 31 6414 27 6995 91RAND8-3 29 6214 27 6886 108RAND8-4 29 6232 27 6995 122RAND8-5 29 6214 27 6995 126RAND8-6 38 7376 26 7049 44RAND8-7 30 6287 25 6704 66RAND8-8 30 6323 25 6704 60RAND8-9 46 6509 30 6285 34RAND8-10 53 6883 32 6546 49Note with the total number of tractors (H) enumerated the computation time for CPLEX124 was limited to one hour The solutions obtained by CPLEX arenot absolutely theoretically optimal ones


Table 3 The distances between any two cities (km)

JNA QD ZB ZZH DY YT WF JNI TA WH RZH LW LY DZH LCH BZH HZJNA 0 361 111 245 225 457 209 202 75 517 332 86 250 131 125 159 251QD 361 0 263 429 275 251 157 448 363 272 175 308 300 469 464 330 557ZB 111 263 0 313 128 360 112 270 146 419 323 91 240 222 216 83 357ZZH 245 429 313 0 439 589 424 137 172 649 267 222 116 329 324 372 247DY 225 275 128 439 0 350 141 398 274 410 359 219 368 335 329 75 470YT 457 251 360 589 350 0 252 606 504 65 333 449 458 565 559 426 700WF 209 157 112 424 141 252 0 382 257 314 226 202 249 318 313 179 454JNI 202 448 270 137 398 606 382 0 130 667 285 180 203 287 156 331 126TA 75 363 146 172 274 504 257 130 0 566 277 58 195 169 163 207 240WH 517 272 419 649 410 65 314 667 566 0 395 510 519 626 621 487 762RZH 332 175 323 267 359 333 226 285 277 395 0 247 137 443 437 383 395LW 86 308 91 222 219 449 202 180 58 510 247 0 165 225 220 152 290LY 250 300 240 116 368 458 249 203 195 519 137 165 0 361 355 301 313DZH 131 469 222 329 335 565 318 287 169 626 443 225 361 0 180 271 338LCH 125 464 216 324 329 559 313 156 163 621 437 220 355 180 0 263 225BZH 159 330 83 372 75 426 179 331 207 487 383 152 301 271 263 0 404HZ 251 557 357 247 470 700 454 126 240 762 395 290 313 338 225 404 0

Table 4 The freight flows between any two cities (unit loaded semitrailer)

To FromJNA QD ZB ZZH DY YT WF JNI TA WH RZH LW LY DZH LCH BZH HZ

JNA 0 1 2 1 2 1 3 1 0 0 0 0 1 0 1 2 1QD 1 0 6 0 4 7 18 0 1 3 3 1 2 1 1 1 0ZB 1 4 0 1 2 2 3 1 1 1 0 0 3 3 3 0 1ZZH 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0DY 2 3 2 0 0 1 1 0 1 0 0 0 1 1 1 0 0YT 1 6 2 0 2 0 5 0 0 1 1 0 1 0 0 0 0WF 3 15 3 0 1 4 0 1 2 1 1 1 2 1 1 4 0JNI 1 0 1 0 0 0 1 0 0 0 0 0 1 1 2 0 0TA 0 1 1 1 1 0 2 0 0 0 0 0 2 2 3 1 1WH 0 2 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0RZH 0 3 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0LW 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0LY 1 2 3 0 1 1 2 1 2 0 0 1 0 0 1 1 0DZH 0 0 3 0 1 0 1 1 2 0 0 0 0 0 2 1 0LCH 1 1 4 0 1 0 1 2 3 0 0 1 0 2 0 1 1BZH 2 1 0 0 0 0 4 0 1 0 0 1 1 1 1 0 0HZ 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0

time According to SDEXP experience a driverrsquos average on-duty time is 85 hours per day A tractor with two driverscan work consecutively for no more than 170 hours in a 24-consecutive-hour period The attachdetach time at satellitedepots is 23 hour and the residence time in the central depotis 2 hours

In the computational study we assume any one of the6 cities the candidate central depot city for SDEXP Thereare 6 scenarios classified by the candidate central depotcities The satisfactory solutions of the 6 scenarios are in

Table 5The SA heuristic was run for 5 times for any scenarioand the average was showed When the depot located ina different spatial zone and having various freight flows isrespectively regarded as the central depot the performanceof the satisfactory solution varies obviously We use ldquotractorquantityrdquo ldquopercentage of fuel consumption for tractor run-ning alonerdquo and ldquoCO

2emissions per ton-kilometerrdquo to show

the performance of the solutionSince the loaded semitrailer needing transport and its

transported distance are certain the total ton-kilometer is


Table 5 The results of the 6 scenarios of the realistic instance

The centraldepot city

Tractorquantity

Average number of loadedsemitrailer on a route

Average distancespan (km)

Percentage of fuel consumptionfor tractor running alone ()

CO2 emissions perton-kilometer (gtm)

JNA 84 30 10678 202 729QD 89 28 10966 245 771ZB 79 32 10505 161 694WF 74 34 10669 134 673TA 94 27 10707 262 793LW 89 28 10542 225 751

certain When the distance span is decided the more thetractor number themore the percentage of fuel consumptionfor tractor running alone Less number of tractors leadsto more loaded semitrailer on a route There exists anobvious relationship between ldquopercentage of fuel consump-tion for tractor running alonerdquo and ldquoCO

2emissions per ton-

kilometerrdquo More ldquopercentage of fuel consumption for tractorrunning alonerdquo likely leads to more ldquoCO

2emissions per ton-

kilometerrdquoEscobar et al [44] and Hashemi et al [45] pointed that

the transportation costs are often influenced by the decisionof locating a depot and vice versa Our results showeda similar conclusion According to the methodology andfactors developed by the Intergovernmental Panel on ClimateChange (IPCC) CO

2emissions are in direct proportion to

fuel consumption so CO2emissions of the solutions can

express the variable cost of transportation The solutions forvarious central depot cities have different CO

2emissions per

ton-kilometer Central depot cities located near the centerof the research spatial scope (eg WF ZB and JNA) haverelatively good solutions Besides central depot cities locatedalong Jinan-Qingdao Highway (JNA-ZB-WF-QD line) havegood solutions that include more loaded semitrailer on aroute and a low level of CO

2emissions per ton-kilometer It

is implied that the CO2emissions per ton-kilometer of the

solutions for different central depot cities are affected not onlyby central depot locations but also by transportation flowsfrom economic relations

There are estimation results of CO2emissions per ton-

kilometer for various countries For example Van Ierland etal [13] noted that the CO

2emission factor for trucks was

155 gCO2t-km in The Netherlands European Environment

Agency [46] noted that the average CO2emissions were 62sim

110 g CO2t-km for road transportation in the EU Member

States Li et al [47] noted that the average CO2emissions

fluctuated between 100 gCO2t-km and 132 gCO

2t-km from

1985 to 2007 in China We have investigated some point-to-point haulages of SDEXP in 2009 and found that the CO

2

emission factor ranged from 100 gCO2t-km to 180 gCO

2t-

km and the average was 135 gCO2t-km Our computational

realistic-instance study showed that the vehicle schedulingprovided by the TSRP is promising to reduce road freighttransportation CO

2emissions

The results suggested that SDEXP can locate the centraldepot in cityWF ZB or JNA About 80 tractors are needed to

serve routes of around 1000 km distance With the help of theTSRP satisfactory solution SDEXP is likely to reduce around30 of the CO

2emissions per ton-kilometer

6 Conclusions

This paper discussed the tractor and semitrailer routingproblem with the objective of minimizing the CO

2emissions

per ton-kilometer which are promising with applications inmultilevel freight distribution systems and full truckloadAn exact formulation was presented The SA heuristic wasput forward to solve this problem of a realistic size TheSA heuristics algorithm was tested on different types ofproblemsThe experimental results showed that the proposedheuristics provide satisfactory-quality solutions in a reason-able computing time The impact of central depot locationsand freight flow distributions on the solution quality is alsoexplored In conclusion the proposed algorithms can providerobust solutions

For future research it would be interesting to test theeffectiveness and efficiency of the proposed TSRP model andits solution approach on large-scale instances Some efficientheuristics for the TSRP may also be proposed Besidesattention can be focused on the extension of the TSRP forexample TSRP with time windows and TSRP with vehiclerouting of other levels of freight distribution system

Acknowledgment

Thisworkwas supported by researchGrant from theNationalNatural Science Foundation of China (nos 71202016 and71071007) This support is gratefully acknowledged

References

[1] D Y Lin and K H Ng ldquoThe impact of collaborative backhaulrouting on carbon reduction in the freight industryrdquo Trans-portation Research Part D vol 17 pp 626ndash628 2012

[2] Y Kuo ldquoUsing simulated annealing to minimize fuel con-sumption for the time-dependent vehicle routing problemrdquoComputers and Industrial Engineering vol 59 no 1 pp 157ndash1652010

[3] I Kara B Y Kara and M K Yetis ldquoEnergy minimizingvehicle routing problemrdquo in Combinatorial Optimization andApplications vol 4616 of Lecture Notes in Computer Science pp62ndash71 Springer Berlin Germany 2007


[4] Y Xiao Q Zhao I Kaku and Y Xu ldquoDevelopment of a fuelconsumption optimization model for the capacitated vehiclerouting problemrdquoComputers ampOperations Research vol 39 no7 pp 1419ndash1431 2012

[5] Y J Kwon Y J Choi and D H Lee ldquoHeterogeneous fixed fleetvehicle routing considering carbon emissionrdquo TransportationResearch Part D vol 23 pp 81ndash89 2013

[6] L Pradenas B Oportus and V Parada ldquoMitigation of green-house gas emissions in vehicle routing problems with backhaul-ingrdquo Expert Systems with Applications vol 40 pp 2985ndash29912013

[7] M Drexl ldquoApplications of the vehicle routing problem withtrailers and transshipmentsrdquo European Journal of OperationalResearch vol 227 pp 275ndash283 2013

[8] R S de Camargo G de Miranda and A Loslashkketangen ldquoA newformulation and an exact approach for the many-to-many hublocation-routing problemrdquo Applied Mathematical Modellingvol 37 no 12-13 pp 7465ndash7480 2013

[9] V C Hemmelmayr J-F Cordeau and T G Crainic ldquoAnadaptive large neighborhood search heuristic for two-echelonvehicle routing problems arising in city logisticsrdquo Computers ampOperations Research vol 39 no 12 pp 3215ndash3228 2012

[10] P C Pop I Kara and A Horvat Marc ldquoNew mathematicalmodels of the generalized vehicle routing problem and exten-sionsrdquoAppliedMathematicalModelling vol 36 no 1 pp 97ndash1072012

[11] C Contardo V Hemmelmayr and T G Crainic ldquoLower andupper bounds for the two-echelon capacitated location-routingproblemrdquo Computers amp Operations Research vol 39 no 12 pp3185ndash3199 2012

[12] H Q Li and Y Lu ldquoTractor and semi-trailer transportationrsquoseffect on the reduction of CO

2emission in Chinardquo in Systems

Science and Transportation Development B H Mao S J Yangand L L Yang Eds pp 232ndash237The Institution of Engineeringand Technology Beijing China 2011

[13] E Van Ierland CGraveland andRHuiberts ldquoAn environmen-tal economic analysis of the new rail link to Europeanmain portRotterdamrdquo Transportation Research Part D vol 5 no 3 pp197ndash209 2000

[14] J G Villegas C Prins C Prodhon A L Medaglia andN Velasco ldquoA matheuristic for the truck and trailer routingproblemrdquo European Journal of Operational Research vol 230no 2 pp 231ndash244 2013

[15] F Semet and E Taillard ldquoSolving real-life vehicle routingproblems efficiently using tabu searchrdquo Annals of OperationsResearch vol 41 no 4 pp 469ndash488 1993

[16] M Caramia and F Guerriero ldquoA milk collection problem withincompatibility constraintsrdquo Interfaces vol 40 no 2 pp 130ndash143 2010

[17] J C Gerdessen ldquoVehicle routing problem with trailersrdquo Euro-pean Journal of Operational Research vol 93 no 1 pp 135ndash1471996

[18] I-M Chao ldquoA tabu search method for the truck and trailerrouting problemrdquo Computers and Operations Research vol 29no 1 pp 33ndash51 2002

[19] S Scheuerer ldquoA tabu search heuristic for the truck and trailerrouting problemrdquo Computers and Operations Research vol 33no 4 pp 894ndash909 2006

[20] K C Tan Y H Chew and L H Lee ldquoA hybrid multi-objectiveevolutionary algorithm for solving truck and trailer vehiclerouting problemsrdquo European Journal of Operational Researchvol 172 no 3 pp 855ndash885 2006

[21] S-W Lin V F Yu and S-Y Chou ldquoSolving the truck and trailerrouting problem based on a simulated annealing heuristicrdquoComputers and Operations Research vol 36 no 5 pp 1683ndash1692 2009

[22] J G Villegas C Prins C Prodhon A L Medaglia and NVelasco ldquoA GRASP with evolutionary path relinking for thetruck and trailer routing problemrdquo Computers and OperationsResearch vol 38 no 9 pp 1319ndash1334 2011

[23] J G Villegas C Prins C Prodhon A L Medaglia andN Velasco ldquoGRASPVND and multi-start evolutionary localsearch for the single truck and trailer routing problem withsatellite depotsrdquo Engineering Applications of Artificial Intelli-gence vol 23 no 5 pp 780ndash794 2010

[24] S-W Lin V F Yu and S-Y Chou ldquoA note on the truck andtrailer routing problemrdquo Expert Systems with Applications vol37 no 1 pp 899ndash903 2010

[25] S-W Lin V F Yu and C-C Lu ldquoA simulated annealingheuristic for the truck and trailer routing problem with timewindowsrdquo Expert Systems with Applications vol 38 no 12 pp15244ndash15252 2011

[26] U Derigs M Pullmann and U Vogel ldquoTruck and trailerroutingmdashproblems heuristics and computational experiencerdquoComputers amp Operations Research vol 40 pp 536ndash546 2013

[27] V Pureza R Morabito and M Reimann ldquoVehicle routing withmultiple deliverymen modeling and heuristic approaches fortheVRPTWrdquoEuropean Journal ofOperational Research vol 218no 3 pp 636ndash647 2012

[28] L Bodin AMingozzi R Baldacci andM Ball ldquoRollon-Rolloffvehicle routing problemrdquo Transportation Science vol 34 no 3pp 271ndash288 2000

[29] J Wy and B I Kim ldquoA hybrid metaheuristic approach for therollon-rolloff vehicle routing problemrdquo Computers amp Opera-tions Research vol 40 pp 1947ndash1952 2013

[30] UDerigsM Pullmann andUVogel ldquoA short note on applyinga simple LSLNS-based metaheuristic to the rollon-rolloffvehicle routing problemrdquo Computers amp Operations Researchvol 40 pp 867ndash872 2013

[31] J Wy B I Kim and S Kim ldquoThe rollon-rolloff waste collectionvehicle routing problem with time windowsrdquo European Journalof Operational Research vol 224 pp 466ndash476 2013

[32] R Baldacci L Bodin and A Mingozzi ldquoThe multiple disposalfacilities and multiple inventory locations rollon-rolloff vehiclerouting problemrdquo Computers and Operations Research vol 33no 9 pp 2667ndash2702 2006

[33] R W Hall and V C Sabnani ldquoControl of vehicle dispatchingon a cyclic route serving trucking terminalsrdquo TransportationResearch Part A vol 36 no 3 pp 257ndash276 2002

[34] P Francis G Zhang and K Smilowitz ldquoImproved modelingand solution methods for the multi-resource routing problemrdquoEuropean Journal of Operational Research vol 180 no 3 pp1045ndash1059 2007

[35] Y-R Cheng B Liang and M-H Zhou ldquoOptimization forvehicle scheduling in iron and steel works based on semi-trailer swap transportrdquo Journal of Central South University ofTechnology vol 17 no 4 pp 873ndash879 2010

[36] U Derigs R Kurowsky and U Vogel ldquoSolving a real-worldvehicle routing problem with multiple use of tractors andtrailers and EU-regulations for drivers arising in air cargo roadfeeder servicesrdquo European Journal of Operational Research vol213 no 1 pp 309ndash319 2011


[37] H Li Y Lu J Zhang and T Wang ldquoSolving the tractor andsemi-trailer routing problem based on a heuristic approachrdquoMathematical Problems in Engineering vol 2012 Article ID182584 12 pages 2012

[38] S Almoustafa S Hanafi and N Mladenovic ldquoNew exactmethod for large asymmetric distance-constrained vehicle rout-ing problemrdquo European Journal of Operational Research vol226 no 3 pp 386ndash394 2013

[39] R Banos J Ortega C Gil A Fernandez and F Toro ldquoASimulated Annealing-based parallel multi-objective approachto vehicle routing problemswith timewindowsrdquo Expert Systemswith Applications vol 40 pp 1696ndash1707 2013

[40] O Braysy and M Gendreau ldquoVehicle routing problem withtime windows Part I route construction and local searchalgorithmsrdquo Transportation Science vol 39 no 1 pp 104ndash1182005

[41] A N Letchford and J-J Salazar-Gonzalez ldquoProjection resultsfor vehicle routingrdquoMathematical Programming vol 105 no 2-3 pp 251ndash274 2006

[42] L C Coelho J-F Cordeau and G Laporte ldquoConsistency inmulti-vehicle inventory-routingrdquo Transportation Research PartC vol 24 pp 270ndash287 2012

[43] R Banos J Ortega C Gil A LMarquez and F Toro ldquoA hybridmeta-heuristic for multi-objective vehicle routing problemswith time windowsrdquo Computers amp Industrial Engineering vol65 pp 286ndash296 2013

[44] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[45] S H Hashemi Doulabi and A Seifi ldquoLower and upper boundsfor location-arc routing problems with vehicle capacity con-straintsrdquo European Journal of Operational Research vol 224 no1 pp 189ndash208 2013

[46] European Environment Agency Transport at a CrossroadsmdashTERM 2008 Indicators Tracking Transport and Environmentin the European Union Office for Official Publications of theEuropean Communities Esch-sur-Alzette Luxembourg 2009

[47] H Q Li Y Lu J Zhang and T YWang ldquoTrends in road freighttransportation carbon dioxide emissions and policies in ChinardquoEnergy Policy vol 57 pp 99ndash106 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

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Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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International Journal of


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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


tailored services such as direct transportation between twopoints LTL is more appropriate for clients that have to sharethe carrierrsquos transportation resources with other customers[8] Most VRP research concentrated on the optimization ofdelivery orand pickup of LTL service

Logistics companies use various types of vehicles andoperate from more than one distribution center Shipmentsoccur between depots and the pickupdelivery locations oforders and between depots In multilevel freight distributionsystems (eg city logistics multimodal freight transportationsystems parcels or public postal services) in which freightarrives at a depot and is transported further to anotherdepot by large vehicles and the freight is then brought to thefinal customers by small vehicles both TL and LTL appearThe problem how to efficiently route vehicles operating atboth levels is known in the literature as the two-echelonvehicle routing problem (2E-VRP) [9] the generalized vehiclerouting problem (GVRP) [10] or the single-sourcing two-echelon capacitated location-routing problem (2E-CLRP)[11]

Compared with most VRP research employing trucksto serve the delivery orand pickup of LTL we study avariant of the combination-vehicle routing problem wheretractor-semitrailer combinations are utilized A tractor canpull multiple and independent trailers The tractor cannotload goods and is only used for pulling the trailers Since thetime to attachdetach a semitrailer to a tractor at locationsis usually considerably less than the time to loadunload allcargoes in a semitrailer the tractor has a high use rateWe callthis variant of the VRP as the tractor and semitrailer routingproblem (TSRP) The tractor and semitrailer transportationis regarded to be more energy-efficient than single-unit trucktransportation [12] As Van Ierland et al [13] stated the CO

2

emission factor which is defined as CO2emissions per ton-

kilometer (unit g CO2t-km) is a typical index to describe

the CO2emission effects of the road freight transportation

Differing from other pieces of literature we aim to minimizeCO2emissions per ton-kilometer of the TSRP

We propose the TSRP on a loaded semitrailer flownetwork The loaded semitrailers are assumed to be TLThere are two types of terminals on the network one centraldepot and a number of satellite depots At the beginning alltractors locate in the central depot while the satellite depotshave loaded semitrailers waiting for sending All tractorsor vehicles (a vehicle is one tractor pulling one semitrailer)originate and terminate at the central depot A homogeneousfleet composed of tractors and semitrailers serves the loadedsemitrailer flow demand among depots A tractor can pullone loaded semitrailer and can also run alone The objectiveof the TSRP is to determine the number of tractors and theroute of each tractor so as to minimize CO

2emissions per

ton-kilometerOur interest in the TSRP arises from the full truckload

transporting of multilevel freight distribution systems Ouraim is to develop a solving method for the TSRP and toshow the effect of CO

2emission mitigation The paper is

organized as followsThe next section introduces the relevantliterature A mathematical model for the TSRP is developedin Section 3 Section 4 proposes the heuristic algorithm for

solving the TSRP Computational experiments are describedin Section 5 Finally conclusions and future work are given inSection 6

2 The Literature Review

The introduction reviewed briefly the limited literaturedirectly targeting the incorporation of CO

2emissions mini-

mization in the VRPWe turn to a brief overview of contribu-tions to the combination-vehicle routing problem the TSRPconcerns

Research on the VRP to date has considered especiallytrucks and truck and full trailer combinationsThe truck andtrailer routing problem (TTRP) has been brought forwardfor decades In the TTRP a heterogeneous fleet composedof trucks and trailers serves a set of customers Both thetruck and the trailer have hauling capacity and goods canbe transferred between the truck and the trailer en-route inthe parking places of the trailer Each customer has a certaindemand and the capacities of the trucks and trailers aredeterminate Some customers must be served only by a truckwhile other customers can be served either by a truck or bya combination vehicle The objective of the TTRP is to finda set of routes with minimum total distance or cost so thateach customer is visited Interested readers are referred toVillegas et al [14] in order to get an overview of recentlyrelated publications of the TTRP

Semet and Taillard [15] and Caramia and Guerriero [16]provided some real-world TTRP applications Gerdessen [17]extended the VRP to the VRP with trailers and investigatedthe optimal deployment of a fleet of truck-trailer combina-tions Chao [18] distinguished three types of routes in a TTRPsolution Subsequently Scheuerer [19] Tan et al [20] Lin etal [21] and Villegas et al [22] solved the TTRP by variousheuristics On the extensions of the TTRP Villegas et al[23] proposed two metaheuristics to solve the single truckand trailer routing problemwith satellite depots (STTRPSD)Considering the number of available trucks and trailers beinglimited in the TTRP Lin et al [24] relaxed the fleet sizeconstraint and developed a SA heuristic for solving therelaxed truck and trailer routing problem (RTTRP) Lin et al[25] proposed a SA heuristic for solving the truck and trailerrouting problem with time windows (TTRPTW) RecentlyDerigs et al [26] combined local search and large neighbor-hood search metaheuristic to solve the TTRP withwithoutload transfer and the TTRP withwithout time windowsVillegas et al [14] presented a two-phase matheuristic to theTTRP A pool of routes with the local optima was obtained bya hybridGRASPtimesILSmetaheuristic and these routes becomecolumns in a set-partitioning problem solved with a mixedinteger programming optimizer

In the TTRP each trailer can be pulled by a unique associ-ated truck and only this truck is permitted to transfer the loadinto the trailer The amount of trucks is generally more thanthat of trailers Drexl [7] described the VRP with trailers andtransshipments (VRPTT) in which there is no fixed truck-trailer assignment The TTRP is evidently a special case ofthe VRPTT Besides Pureza et al [27] addressed the VRP










3 Model Formulation











119894)



119894


are 119877

119877 =

[[[[[[

[

0 1199030111990302sdot sdot sdot 119903

0119899

119903100 11990312sdot sdot sdot 119903

1119899

11990320119903210 sdot sdot sdot 119903

2119899


0

]]]]]]

]

(1)




119862119905


from V119894to V119895 and 119862119897






119894119895=




2


119894119895119896and 119883119897





119894to V119895for 120573 times119883119897

119894119895119896= 120573


Min120574 sdot (sum

119894sum119895sum119896119862119905

119894119895119896119883119905

119894119895119896+ sum119894sum119895sum119896119862119897

119894119895119896119883119897

119894119895119896)

119882 sdot sum119896sum119894sum119895119883119897

119894119895119896sdot 119889119894119895

(2)

The constraints are

sum

119896

119883119897

119894119895119896= 119903119894119895 (3)

sum

119894

119883119905

119895119894119896+sum

119894

119883119897

119895119894119896ge 1 (4)

sum

119894

119883119905

119894119895119896+sum

119894

119883119897

119894119895119896ge 1 (5)

sum

119894

119883119905

119895119894119896+sum

119894

119883119897

119895119894119896= sum

119894

119883119905

119894119895119896+sum

119894

119883119897

119894119895119896 (6)

sum

119894

sum

119895

(119889119894119895sdot 119883119905

119894119895119896+ 119889119894119895sdot 119883119897

119894119895119896) ge 119863

1 (7)

sum

119894

sum

119895

(119889119894119895sdot 119883119905

119894119895119896+ 119889119894119895sdot 119883119897

119894119895119896) le 119863

2 (8)

119883119905

119894119895119896and 119883119897



119894sum119895119889119894119895sdot 119903119894119895)1198632

















119894sum119895119903119894119895)4rfloor


119900 119908 = 0 119902 = 0 119877best = 119877(119883)




119890119879 = 120591 sdot 119879 119902 = 0









2emissions










119890iterations


119865 Following





2


0the









0and 119877(119883) = 100 and 119879 minus 119879

119865gt 0 119862

0= 119862(119883) Go to Step 3







































Tractorquantity





JNA 84 30 10678 202 729QD 89 28 10966 245 771ZB 79 32 10505 161 694WF 74 34 10669 134 673TA 94 27 10707 262 793LW 89 28 10542 225 751


2emissions per ton-


2emissions per ton-






2emissions per













2t-km from


2


2t-



2emissions




6 Conclusions


2emissions



Acknowledgment


References



























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















3 Model Formulation











119894)



119894


are 119877

119877 =

[[[[[[

[

0 1199030111990302sdot sdot sdot 119903

0119899

119903100 11990312sdot sdot sdot 119903

1119899

11990320119903210 sdot sdot sdot 119903

2119899


0

]]]]]]

]

(1)




119862119905


from V119894to V119895 and 119862119897






119894119895=




2


119894119895119896and 119883119897





119894to V119895for 120573 times119883119897

119894119895119896= 120573


Min120574 sdot (sum

119894sum119895sum119896119862119905

119894119895119896119883119905

119894119895119896+ sum119894sum119895sum119896119862119897

119894119895119896119883119897

119894119895119896)

119882 sdot sum119896sum119894sum119895119883119897

119894119895119896sdot 119889119894119895

(2)

The constraints are

sum

119896

119883119897

119894119895119896= 119903119894119895 (3)

sum

119894

119883119905

119895119894119896+sum

119894

119883119897

119895119894119896ge 1 (4)

sum

119894

119883119905

119894119895119896+sum

119894

119883119897

119894119895119896ge 1 (5)

sum

119894

119883119905

119895119894119896+sum

119894

119883119897

119895119894119896= sum

119894

119883119905

119894119895119896+sum

119894

119883119897

119894119895119896 (6)

sum

119894

sum

119895

(119889119894119895sdot 119883119905

119894119895119896+ 119889119894119895sdot 119883119897

119894119895119896) ge 119863

1 (7)

sum

119894

sum

119895

(119889119894119895sdot 119883119905

119894119895119896+ 119889119894119895sdot 119883119897

119894119895119896) le 119863

2 (8)

119883119905

119894119895119896and 119883119897



119894sum119895119889119894119895sdot 119903119894119895)1198632

















119894sum119895119903119894119895)4rfloor


119900 119908 = 0 119902 = 0 119877best = 119877(119883)




119890119879 = 120591 sdot 119879 119902 = 0









2emissions










119890iterations


119865 Following





2


0the









0and 119877(119883) = 100 and 119879 minus 119879

119865gt 0 119862

0= 119862(119883) Go to Step 3







































Tractorquantity





JNA 84 30 10678 202 729QD 89 28 10966 245 771ZB 79 32 10505 161 694WF 74 34 10669 134 673TA 94 27 10707 262 793LW 89 28 10542 225 751


2emissions per ton-


2emissions per ton-






2emissions per













2t-km from


2


2t-



2emissions




6 Conclusions


2emissions



Acknowledgment


References



























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












2


119894119895119896and 119883119897





119894to V119895for 120573 times119883119897

119894119895119896= 120573


Min120574 sdot (sum

119894sum119895sum119896119862119905

119894119895119896119883119905

119894119895119896+ sum119894sum119895sum119896119862119897

119894119895119896119883119897

119894119895119896)

119882 sdot sum119896sum119894sum119895119883119897

119894119895119896sdot 119889119894119895

(2)

The constraints are

sum

119896

119883119897

119894119895119896= 119903119894119895 (3)

sum

119894

119883119905

119895119894119896+sum

119894

119883119897

119895119894119896ge 1 (4)

sum

119894

119883119905

119894119895119896+sum

119894

119883119897

119894119895119896ge 1 (5)

sum

119894

119883119905

119895119894119896+sum

119894

119883119897

119895119894119896= sum

119894

119883119905

119894119895119896+sum

119894

119883119897

119894119895119896 (6)

sum

119894

sum

119895

(119889119894119895sdot 119883119905

119894119895119896+ 119889119894119895sdot 119883119897

119894119895119896) ge 119863

1 (7)

sum

119894

sum

119895

(119889119894119895sdot 119883119905

119894119895119896+ 119889119894119895sdot 119883119897

119894119895119896) le 119863

2 (8)

119883119905

119894119895119896and 119883119897



119894sum119895119889119894119895sdot 119903119894119895)1198632

















119894sum119895119903119894119895)4rfloor


119900 119908 = 0 119902 = 0 119877best = 119877(119883)




119890119879 = 120591 sdot 119879 119902 = 0









2emissions










119890iterations


119865 Following





2


0the









0and 119877(119883) = 100 and 119879 minus 119879

119865gt 0 119862

0= 119862(119883) Go to Step 3







































Tractorquantity





JNA 84 30 10678 202 729QD 89 28 10966 245 771ZB 79 32 10505 161 694WF 74 34 10669 134 673TA 94 27 10707 262 793LW 89 28 10542 225 751


2emissions per ton-


2emissions per ton-






2emissions per













2t-km from


2


2t-



2emissions




6 Conclusions


2emissions



Acknowledgment


References



























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119894sum119895119903119894119895)4rfloor


119900 119908 = 0 119902 = 0 119877best = 119877(119883)




119890119879 = 120591 sdot 119879 119902 = 0









2emissions










119890iterations


119865 Following





2


0the









0and 119877(119883) = 100 and 119879 minus 119879

119865gt 0 119862

0= 119862(119883) Go to Step 3







































Tractorquantity





JNA 84 30 10678 202 729QD 89 28 10966 245 771ZB 79 32 10505 161 694WF 74 34 10669 134 673TA 94 27 10707 262 793LW 89 28 10542 225 751


2emissions per ton-


2emissions per ton-






2emissions per













2t-km from


2


2t-



2emissions




6 Conclusions


2emissions



Acknowledgment


References



























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











0and 119877(119883) = 100 and 119879 minus 119879

119865gt 0 119862

0= 119862(119883) Go to Step 3







































Tractorquantity





JNA 84 30 10678 202 729QD 89 28 10966 245 771ZB 79 32 10505 161 694WF 74 34 10669 134 673TA 94 27 10707 262 793LW 89 28 10542 225 751


2emissions per ton-


2emissions per ton-






2emissions per













2t-km from


2


2t-



2emissions




6 Conclusions


2emissions



Acknowledgment


References



























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


































Tractorquantity





JNA 84 30 10678 202 729QD 89 28 10966 245 771ZB 79 32 10505 161 694WF 74 34 10669 134 673TA 94 27 10707 262 793LW 89 28 10542 225 751


2emissions per ton-


2emissions per ton-






2emissions per













2t-km from


2


2t-



2emissions




6 Conclusions


2emissions



Acknowledgment


References



























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article the tractor and semitrailer routing...

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