The Assignment Model

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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 :

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