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.

1. Introduction

2. Example

3. Main Menu

4. Printing

5. Graphs

6. Modules

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