8s-1

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

The Transportation Model

Chapter 8 Supplement

The Transportation Model

8s-2

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

The Transportation Model

Requirements for Transportation Model

• List of origins and each one’s capacity

• List of destinations and each one’s demand

• Unit cost of shipping

8s-3

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

The Transportation Model

Transportation Model Assumptions

• Items to be shipped are homogeneous

• Shipping cost per unit is the same

• Only one route between origin and destination

8s-4

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

The Transportation Model

The Transportation Problem

D(demand)

D(demand)

D(demand)

D(demand)

S(supply)

S(supply)

S(supply)

Figure 8S-1

8s-5

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

The Transportation Model

A 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-6

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

The Transportation Model

Special 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-7

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

The Transportation Model

Summary 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-8

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

The Transportation Model

Excel TemplateFigure 8S-2