8s-1 The Transportation Model

William J. Stevenson

Operations Management

8th edition

8s-2 The Transportation Model

CHAPTER8s

The Transportation Model

McGraw-Hill/IrwinOperations Management, Eighth Edition, by William J. StevensonCopyright © 2005 by The McGraw-Hill Companies, Inc. All rights

reserved.

8s-3 The Transportation ModelRequirements for Transportation Requirements for Transportation ModelModel

List of origins and each one’s capacity

List of destinations and each one’s demand

Unit cost of shipping

Note: The DVD that accompanies this bookcontains a module that provides detailedinstruction on the transportation model

8s-4 The Transportation Model

Transportation Model AssumptionsTransportation Model Assumptions

1. Items to be shipped are homogeneous

2. Shipping cost per unit is the same

3. Only one route between origin and destination

8s-5 The Transportation Model

The Transportation ProblemThe Transportation Problem

D(demand)

D(demand)

D(demand)

D(demand)

S(supply)

S(supply)

S(supply)

Figure 8S.1

8s-6 The Transportation Model

A Transportation TableA Transportation Table

Warehouse

4 7 7 1100

12 3 8 8200

8 10 16 5150

450

45080 90 120 160

A B C D

1

2

3

Factory Factory 1can supply 100units per period

Total supplycapacity perperiod

Total demandper period

Demand

Warehouse B can use 90 units per period

Table 8S.1

8s-7 The Transportation Model

Special ProblemsSpecial Problems

Unequal supply and demand

Dummy: Imaginary number added equal to the difference between supply and demand when these are unequal

Degeneracy: The condition of too few completed cells to allow all necessary paths to be constructed

8s-8 The Transportation Model

Summary of ProcedureSummary of Procedure

Make certain that supply and demand are equal

Develop an initial solution using intuitive, low-cost approach

Check that completed cells = R+C-1

Evaluate each empty cell

Repeat until all cells are zero or positive

8s-9 The Transportation Model

Excel TemplateExcel TemplateFigure 8S.2

8s-10 The Transportation Model

Additional PowerPoint slides contributed by Geoff Willis, University of Central Oklahoma.

CHAPTER8s

8s-11 The Transportation Model

ANALYSESANALYSES

Transportation ModelTransportation Model minimizes transportation costs using LPminimizes transportation costs using LP

Center of gravity & simple median modelsCenter of gravity & simple median models minimizes transportation costs using geometryminimizes transportation costs using geometry

8s-12 The Transportation Model

Determine the center of gravity for the destinations shown on the following map. Monthly shipments will be the quantities listed in the table.

Destination Quantity

D1 900

D2 300

D3 700

D4 600

D5 800

D1

D2

D3

D4

D5

Center of GravityCenter of Gravity