The Assignment Model


[Page 234 ( continued )]

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 each limited to one unit.

An assignment model is for a special form of transportation problem in which all supply and demand values equal one .


The following example will demonstrate the assignment model. The Atlantic Coast Conference (ACC) 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 supply is always one team of officials, and the demand is for only one team of officials at each game. The distances in miles for each team of officials to each game location are shown in the following table:

The travel distances to each game for each team of officials

 

Game Sites

Officials

R ALEIGH

A TLANTA

D URHAM

C LEMSON

A

210

90

180

160

B

100

70

130

200

C

175

105

140

170

D

80

65

105

120


The linear programming formulation of the assignment model is similar to the formulation of the transportation model, except all the supply values for each source equal one, and all the demand values at each destination equal one. Thus, our example is formulated as follows :


[Page 235]

This is a balanced assignment model. An unbalanced model exists when supply exceeds demand or demand exceeds supply.




Introduction to Management Science
Introduction to Management Science (10th Edition)
ISBN: 0136064361
EAN: 2147483647
Year: 2006
Pages: 358

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