Page 139 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research Neha Tikoo, Lovely Professional University

Notes Unit 7: Assignment Problem – Balanced

CONTENTS
Objectives

Introduction
7.1 Application of Assignment Problem

7.2 Types of Assignment Problem
7.3 Mathematical Model of Assignment Problem
7.4 Hungarian Approach

7.5 Summary
7.6 Keywords
7.7 Review Questions

7.8 Further Readings

Objectives

After studying this unit, you will be able to:
 Understand the nature of assignment problem

 Analyze the mathematical formulation
 Learn the methods of solutions

Introduction

It is not uncommon to see Business Organisations confronting the conflicting need for optimal
utilization of their limited resources among competing activities. In recent years, Linear
Programming has received wider acclaim among the decision makers as a tool for achieving the
business objectives. Out of various Quantitative Techniques developed over the past three
decades, Linear Programming (LP) has found application in a wider screen. LP relates to the
problems concerning distribution of scarce resources (satisfying some constraints which can be
algebraically represented as Linear equations) so as to maximize profit or minimize cost. Under
LP, decisions are arrived at under certainty conditions i.e., the information available on resources
and relationship between variables are known. Hence, the course of action chosen will invariably
lead to optimal or nearly optimal results.
The prominent problems which gained much importance under the house of LP are:
(1) Assignment problems.
(2) Transportation problems.

L.P is used in solving problems faced in assigning the ‘equal number of jobs to equal number of
workers so as to maximise profit or minimize cost’. Hence it is called one-to-one assignment.
Say for instance, there are ‘n’ jobs to be performed and ‘n’ number of persons are available for
doing these jobs and each person can do one job at a time though with varying degree of
efficiency. Say let C be the total cost : here C=cost, I = individual and j = job. So, a problem arises
ij

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