Page 158 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 8: Assignment Problem – Unbalanced

8.1 Variations of the Assignment Problem Notes

There can be many types of variations in a assignment problem. In this unit we will discuss in
detail about the various types of assignment problem you may encounter in the real life scenario.

In this unit, we will discuss on following four variations of the assignment problem:
1. Multiple Optimal Solutions
2. Maximization case in assignment problems

3. Unbalanced Assignment problem
4. Travelling Salesman Problem

8.2 Multiple Optimal Solutions

While making an assignment in the reduced assignment matrix, it is possible to have two or
more ways to strike off a certain number or zeroes. Such a situation indicates multiple optimal
solutions with the same optimal value of objective function. In such cases the more suitable
solution may be considered by the decision maker.

Notes If the assignment problem has only one solution then the solution is said to be
Unique solution.

8.3 Maximization Assignment Problems

In maximization problem, the objective is to maximize profit, revenue, etc. Such problems can
be solved by converting the given maximization problem into a minimization problem.
1. Change the signs of all values given in the table or another method is,
2. Select the highest element in the entire assignment table and subtract all the elements of
the table from the highest element.
Alpha Corporation has 4 plants, each of which can manufacture any one of the 4 products.
Production cost differs from one plant to another plant, so also the sales revenue. Given the
revenue and the cost data below, obtain which product each plant should produce to maximize
the profit.
Sales revenue (` in 000s)
Product 1 2 3 4
Plant A 50 68 49 62
B 60 70 51 74
C 55 67 53 70
D 58 65 54 69

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