03 designing logistics network

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Designing the LogisticsNetwork

Henry C. CoTechnology and Operations Management,

California Polytechnic and State University


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Classification of Location Models

Time horizon.l Single-period problems decisions made at the beginning of the planning

horizon on the basis of the forecasted logistics requirements.

l Multi-period problems at the beginning of the planning horizon, decide asequence of changes to be made at given time instants within the planning

horizon.Facility typology.

l Single-type location problems a single type of facility (e.g. only RDCs) arelocated.

l Multi-type problems several kinds of facility (e.g. both CDCs and RDCs)

are located.Material flows.

l Single-commodity problems a single homogeneous flow of materialsexists in the logistics system

l Multi-commodity problems there are several items, each with different

characteristics; each commodity is associated with a specific flow pattern.Interaction among facilities.

l In complex logistics systems there can be material flows among facilities ofthe same kind (e.g. component flows among plants). Facility locationsdepend not only on the spatial distribution of product demand but also on

the mutual position of the facilities (location problems with interaction).

Designing the Logistics Network (Henry C. Co) 2

Ghiani, p. 74


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Dominant material flows.l Single-echelon location problems either the material flow coming out or the material

flow entering the facilities to be located is negligible.

l Multiple-echelon problems both inbound and outbound commodities are relevant (e.g.,when DCs have to be located taking into account both the transportation cost fromplants to DCs and the transportation cost from DCs to customers); Constraints aiming at

balancing inbound and outbound flows have to be considered.


Ghiani, p. 75


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Classification of Location Problems

Demand divisibility.l Divisible For administrative or book-keeping reasons, that each facility or

customer may have to be supplied by a single center

l Indivisible Facility or customer may be served by two or more centers.

Influence of transportation on location decisions.

l Direct route Transportation cost = transportation rate x freight volume xdistance; appropriate

l Consolidation (pdf) (Excel)

l Vehicle makes collections or deliveries to several points the routesfollowed by the vehicles should be taken explicitly into account when

locating the facilities (location-routing models). See Figure 3.2:


A warehouse serves three sales districtslocated at the vertices of triangle ABC:

1. If each customer requires a full-loadsupply, then the optimal location of theDC is equal to the Steiner pointO.

2. If a single vehicle can service all threepoints, then the DC may be located atany point of the triangle ABC perimeter.

Ghiani, p. 75-76
http://linked/Pool_Distribution.pdfhttp://excel/Pool_Distribution.xlshttp://excel/Pool_Distribution.xlshttp://linked/Pool_Distribution.pdf


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Retail location.l Main issue is to optimally locate a set of retail outlets

that compete with other stores for customers.

l

Predicting the expected revenues of a new site isdifficult since it depends on a number of factors suchas location, sales area and level of competition.

l Retail location problems can be modeled as

competitive location models, the analysis of which isalso beyond the scope of this course.


Ghiani, p. 76


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The Transportation Problem

The Hot Mexican Restaurant problem is an exampleof a transportation problem by linear programming.

Students who have not taken TOM 315 will find this exercise very helpful.The Excel worksheet for the problem is available here.
http://linked/Hot_Mexican_Restaurant.pdfhttp://excel/Hot_Mexican_Restaurant.xlshttp://excel/Hot_Mexican_Restaurant.xlshttp://linked/Hot_Mexican_Restaurant.pdf


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Single-Echelon Single-CommodityLocation Models

The Excel worksheet for the Koster Express examplein Gianni, p. 81 can be found here.
http://excel/Koster_Express.xlshttp://excel/Koster_Express.xlshttp://excel/Koster_Express.xls


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Assumptions

Facilities to be located are homogeneous (e.g.they are all regional warehouses);

Either the material flow coming out or the

material flow entering such facilities isnegligible (i.e., Single-echelon problems).All material flows are homogeneous and can

therefore be considered as a single commodity;Transportation cost is linear or piecewiselinear and concave;

Facility operating cost is piecewise linear andconcave (or, in particular, constant)


Ghiani, p. 77


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A Bipartite Complete Directed Graph

G(V1 V2, A), where the vertices in V1 stand for thepotential facilities, the vertices in V2 represent thecustomers, and the arcs in A = V1V2 are associatedwith the material flows between the potential facilities

and the demand points.Assume demand is divisible (each facility/customer mayhave to be supplied by a single center). Let:l dj = the demand of customer j; jV2l Qi = the capacity of the potential facility i; iV1l Ui = a decision variable that accounts for operations in potential

facility i; iV1l sij = a decision variable representing the amount of product sent

from site i to demand point j; iV1, jV2l Cij (sij ) = the cost of transporting sij units of product from site i to

customer j; iV1, jV2l Fi(ui ) = the cost for operating potential facility i at level ui; iV1.


Ghiani, p. 77


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Ghiani, p. 77


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11

KosterExpress

Ghiani, p. 8111


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Ghiani, p. 81-8212

KosterExpress

Designing the Logistics Network (Henry C. Co)


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Notation: i location of a hub; j location ofa terminal. Good are transported from j to i.

V1 represent the set of hub locations, and V2

represent the set of terminals;The binary variables yi , i V1, is equal to 1 iflocation i is a hub; otherwise yi = 0.

The binary variables xij, iV1, jV2, is equal to1 if the hub located in i serves terminal j ,xij=0 otherwise; however, due to the

particular structure of the problem constraints,variables xij cannot be fractional and greaterthan 1, therefore xij{0,1}, iV1, jV2 can bereplaced with x

ij0, iV

1, jV

2.



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Ghiani, p. 82-8314

KosterExpress



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15

The table in row 17 through row 29 is cij = 20.74 lij , where 0.74 is thetransportation cost (in $/mile), and lij is the distance (in miles) between the terminals(see Tables 3.1 and 3.2).



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This is a difficult problem for Solver to solve. The Solver Parameters menu aboveassumes that Altus, Ardmore, and Bartlesville are not hubs.Problems like this (p-median) are generally not solved this way.


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Linear transportation costsand concave piecewise linearfacility operating costs

The Excel worksheet for the Logconsult example inGianni, p. 93-94 can be found here.
http://excel/Logconsult.xlshttp://excel/Logconsult.xlshttp://excel/Logconsult.xls


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Ghiani, p. 93-94


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This graph shows alinear cost curve.

These two graphs show a piece-wise linear cost

curve. Figure 3.8 shows the two graphs together.


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Ghiani, p. 92,96

(80,000+ 54,400) + $4.1/hundred kgs

Intercept = 54,400

Intercept = 2,252

(80,000+ 2,252) + $18.5/hundred kgs

IntersectAt 3,500

Facility fixed costs include rent, amortization of the machinery, insurance ofpremises and machinery, and staff wages. They add up to $80,000 per year.

In Equation (3.31), the intercept of the regression equation of the variablecost is added to the $80,000.


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D56=SUMPRODUCT(B27:E32,B37:E42)+SUMPRODUCT(F37:F42,G37:G42)

B44:E44 >= 1 F48:F53


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Two-Echelon MulticommodityLocation Models

Pool Distribution/Consolidation WarehouseExcel Worksheet
http://linked/Pool_Distribution.pdfhttp://linked/Pool_Distribution.pdf


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Cosmos Bottling Co. CasePowerPoint Presentation

Excel Worksheet

Merlion Golf Supplies Case

Excel Worksheet

Homework
http://pdf/Cosmos_Bottling_Case.pdfhttp://linked/Cosmos_Case.pdfhttp://excel/Cosmos_Bottling_Case.xlshttp://linked/Merlion_Golf_Supplies_Case.pdfhttp://excel/Merlion_Golf_Supplies_Case.xlshttp://excel/Merlion_Golf_Supplies_Case.xlshttp://linked/Merlion_Golf_Supplies_Case.pdfhttp://excel/Cosmos_Bottling_Case.xlshttp://linked/Cosmos_Case.pdfhttp://pdf/Cosmos_Bottling_Case.pdf


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Homework

Logistics Under Wraps CaseExcel file: Sales

Excel file: Distributor Zones
http://pdf/Stationery(Logistics_Under_Wraps).pdfhttp://excel/Stationery_Demand_Case_Sales.xlshttp://excel/Stationery_Demand_Case_Distributor_Zones.xlshttp://excel/Stationery_Demand_Case_Distributor_Zones.xlshttp://excel/Stationery_Demand_Case_Sales.xlshttp://pdf/Stationery(Logistics_Under_Wraps).pdf

03 designing logistics network

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