The Transportation

Model

McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

You should be able to:1. Describe the nature of a transportation

problem2. Set up transportation problems in the general

linear programming format3. Interpret computer solutions

8S-2Student Slides

Involves finding the lowest-cost plan for distributing stocks of goods or supplies from multiple origins to multiple destinations that demand the goods.

8S-3Student Slides

The transportation model has numerous applications: Location decisions

Compare location alternatives in terms of their impact cost on the total distribution costs for the system

Involves working through a separate model for each location being considered

Production planning Capacity planning Transshipment

8S-4Student Slides

Shipping (supply) points Any place from which good are sent

Factories WarehousesDepartments

Destinations Any point that receives goods

FactoriesWarehousesDepartments

8S-5Student Slides

Information requirements1. A list of the origins and each one’s capacity or

supply quantity per period2. A list of the destinations and each one’s

demand per period3. The unit cost of shipping items from each

origin to each destination

Student Slides 8S-6

Transportation model assumptions1. The items to be shipped are homogeneous2. Shipping cost per unit is the same regardless

of the number of units shipped3. There is only one route or mode of

transportation being used between each origin and destination

Student Slides 8S-7

4 7 7 1

100

12

3 8 8

200

810

16

5

150

80 90 120 160

A B C D Supply

Demand

1

2

3

Warehouse

Factory

450

450

Factory 1 can supply 100 units per period

Total capacity per period

Cost to ship one unit from factory 1 to warehouse A

Total Demand per period

Warehouse B can use 90 units per period

Student Slides 8S-8

4 710

790

1100

12

903

1108 8

200

808

10

16

705

150

80 90 120 160

A B C D Supply

Demand

1

2

3

WarehouseFactory

450

450

8S-9Student Slides

jix

xxx

xxx

xxx

xxx

xxxx

xxxx

xxxx

xxxxx

xxxxxxx

jix

ij

DDD

CCC

BBB

AAA

DCBA

DCBA

DCBA

DCBAD

CBADCBA

ij

and allfor 0

160

120

90

80 (columns) Demand

150

200

100 (rows)Supply

Subject to

5161088

83121774 Minimize

D and C, B, A, j and 3 and 2, ,1i

where

warehouse tofactory from ship tounits ofnumber the

VariablesDecision

321

321

321

321

3333

2222

1111

33332

2221111

Student Slides 8S-10

Transportation problems can be solved manually in a straightforward manner Except for very small problems, solving the problem

manually can be very time consuming For medium to large problems, computer solution

techniques are more practical

A variety of software packages are available for solving the transportation model Some require formulating the problem as a general LP

model Others allow data entry in a more simple, tabular format

Student Slides 8S-11

8S-12Student Slides