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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.
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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:
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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.pdf8/4/2019 03 Designing Logistics Network
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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.
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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.pdf8/4/2019 03 Designing Logistics Network
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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.xls8/4/2019 03 Designing Logistics Network
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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)
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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.
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Ghiani, p. 77
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Designing the Logistics Network (Henry C. Co) 10
Ghiani, p. 77
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11
KosterExpress
Ghiani, p. 8111
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Ghiani, p. 81-8212
KosterExpress
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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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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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Designing the Logistics Network (Henry C. Co) 16
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.xls8/4/2019 03 Designing Logistics Network
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Ghiani, p. 93-94
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Designing the Logistics Network (Henry C. Co) 19
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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Designing the Logistics Network (Henry C. Co) 20
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.pdf8/4/2019 03 Designing Logistics Network
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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.pdf8/4/2019 03 Designing Logistics Network
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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