## 5

## Assignment Problem

##### 5.1 INTRODUCTION AND FORMULATION

The assignment problem is a particular case of transportation problem in which the number of jobs (or origins or sources) are equal to the number of facilities (or destinations or machines or persons and so on). The objective is to maximise total profit of allocation or to minimise the total cost. An assignment problem is a completely degenerate form of a transportation problem. The units available at each origin and the units demanded at each destination are all equal to one.

#### Mathematical Formulation of an Assignment Problem

Given *n* jobs (or activities) and *n* persons (or facilities) and effectiveness (in terms of cost, profit, time and others) of each person for each job, the problem lies ...