B-22
Module B
1/9/09
8:19 AM
Page B-22
Transportation and Assignment Solution Methods
Solution of the Assignment Model
An assignment model is a special form of the transportation model in which all supply and demand values equal one.
Table B-34
The Travel Distances to Each
Game for Each Team of
Officials
An opportunity cost table is developed by first substracting the minimum value in each row from all other row values and then repeating this process for each column.
Table B-35
The Assignment Tableau with
Row Reductions
The assignment model is a special form of a linear programming model that is similar to the transportation model. There are differences, however. In the assignment model, the supply at each source and the demand at each destination are limited to one unit each.
The following example from the text will be used to demonstrate the assignment model and its special solution method. The Atlantic Coast Conference has four basketball games on a particular night. The conference office wants to assign four teams of officials to the four games in a way that will minimize the total distance traveled by the officials. The distances in miles for each team of officials to each game location are shown in Table B-34.
Game Sites
Officials
RALEIGH
ATLANTA
DURHAM
CLEMSON
A
B
C
D
210
100
175
80
90
70
105
65
180
130
140
105
160
200
170
120
The supply is always one team of officials, and the demand is for only one team of officials at each game. Table B-34 is already in the proper form for the assignment.
The first step in the assignment method of solution is to develop an opportunity cost table. We accomplish this by first subtracting the minimum value in each row from every value in the row. These computations are referred to as row reductions. We applied a similar principle in the VAM method when we determined penalty costs. In other