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 number of 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	Cippy	Bruce	Beth	Lauren	Eddie	Brian
Pennsylvania
New Jersey
New York
Florida
Canada
Mexico
Europe	12
33
12
15
42
40
12	54
45
54
37
32
71
34	34
87
76
37
18
78
65	87
27
23
65
77
76
23	54
34
87
26
23
82
44	89
76
44
96
55
90
23	98
65
62
23
87
44
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

Assignments. The 'Assigns' in the main body of the table are the assignments that are to be made. In the example, Mort is to be assigned to Pennsylvania, Cippy to Florida, Bruce to Canada, Beth to New York, Lauren to New Jersey, Eddie to Europe and Brian to Mexico.

Total cost. The total cost appears in the upper left cell, $191 in this example.

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

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

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