Question

explain the conceptual justification that an assignment problem can be viewed as a linear programming problem

Answer 1

Assignment problem is a special type of linear programming problem that relates to the various resources allocation of different resources on one basis. It does this in such a way that the cost or time involved in the process is minimal and the profit or sale is maximum. Although the problems can be solved by a simple method or transportation method, the assignment model provides an easy approach to these problems.

In one factory, a supervisor can have six employees and six jobs can take fire. They have to decide which workers should be given a job. The problem makes one base one by one. This is an assignment problem.

1. Assignment model:

Let's say there are N facility and N jobs, it is clear that in this case, there will be n assignments. Every facilitator or employee who says can do each job at the same time. But there should be some process by which an assignment should be done so that the profit is maximized or the cost or time is low.

Cause is defined as cost when Jeth Job is assigned to the ith worker. It may have been mentioned here that this number of rows equals the number of columns when transport is a special case of problem.

Types of assignment problem in operational research

Assignment problem is classified into a balanced assignment problem and unbalanced assignment problem. If the number of rows is equal to the number of columns, then the problem is known as a balanced assignment problem;

Otherwise, an unbalanced assignment problem. If the problem is unbalanced, like the unbalanced transport problem, the dummy line (s) / column (s) is added in the required number as if the cost matrix is ​​a square matrix. Dummy row (s) / column considers the values ​​of entries zero. Under such a situation, when implementing the solution, there will be no assignment in the dummy line (or) dummy column.