# The Assignment Model

The assignment model is used to solve the traditional one to one assignment problem of assigning employees to jobs, employees to machines, machines to jobs, etc. The model is a special case of the transportation method. In order to generate an assignment problem it is necessary to provide the number of jobs and machines and indicate whether the problem is a minimization or maximization problem. The number of jobs and machines do not have to be equal but usually they are.

Objective function. The objective can be to minimize or to maximize. This is set at the creation screen but can be changed in the data screen.

## Example

The table below shows data for a 7 by 7 assignment problem. Our goal is to assign each salesperson to a territory at minimum total cost. There must be exactly one salesperson per territory and exactly one territory per salesperson.
 Mort Chorine Bruce Beth Lauren Eddie Brian Pennsylvania 12 54 34 87 54 89 98 New Jersey 33 45 87 27 34 76 65 New York 12 54 76 23 87 44 62 Florida 15 37 37 65 26 96 23 Canada 42 32 18 77 23 55 87 Mexico 40 71 78 76 82 90 44 Europe 12 34 65 23 44 23 12

The data structure is nearly identical to the structure for the transportation model. The basic difference is that the assignment model does not display supplies and demands since they are all equal to one.

## The Solution

The results are very straightforward.

Assignments. The 'Assigns's in the main body of the table are the assignments which are to be made. For example, Mort is to be assigned to Pennsylvania, Chorine is to be assigned to Florida, Bruce is to be sent to Canada, Beth is to work the streets of New York, Lauren is across the river in New Jersey, Eddie works Europe and Brian will work in Mexico.

Total cost. The total cost appears in the upper left cell. In this example the total cost is given by \$191.

The assignments can also be given in list form as shown below.

The marginal costs can be displayed also. For example, if we want to assign Chorine to Pennsylvania then the total will increase by \$6 to \$197.

NOTE: To preclude an assignment from being made (in a minimization problem) you should enter a very large cost. If you enter an 'x' then the program will place a high cost in that cell.