8S
The
Transportation
Model
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Objective
 Describe the nature of a transportation
problem
 Set up transportation problems in the general
linear programming format
 Interpret computer solutions
8S-2
Requirements for Transportation
Model
 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 book
contains a module that provides detailed
instruction on the transportation model
8S-3
Transportation 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-4
The Transportation Problem
Figure 8S.1
D
(demand)
D
(demand)
S
(supply)
S
(supply)
D
(demand)
S
(supply)
D
(demand)
8S-5
A Transportation Table
Table 8S.1
A
Factory
Warehouse
C
B
4
D
7
7
1
100
1
3
12
8
8
200
2
10
8
16
5
150
3
Demand
Factory 1
can
supply
100
units per
period
80
90
120
Warehouse B can use 90
units per period
160
Total
supply
450 capacity
per
450
period
Total demand
per period
8S-6
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
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
Excel Template
Figure 8S.2
8S-9