Operation Research of Mathematical Formulation Hungarian Method Algorithm
Operations Research
Unit 6
Unit 6
Structure
Assignment Problem
6.1. 6.2. 6.3. 6.4.
Introduction Mathematical formulation of the problem Hungarian method algorithm Routing problem 6.4.1. Unbalanced A.P 6.4.2 Infeasible Assignments 6.4.3 Maximization in A.P
6.5. 6.6.
Traveling salesmen problem Summary Terminal Questions Answers to SAQs and TQs
6.1 Introduction The assignment problem is a special case of the transportation problem, where the objective is to minimize the cost or time of completing a number of jobs by a number of persons and Maximize efficiently Revenue, sales etc In other words, when the problem involves the allocation of n different facilities to n different tasks, it is often termed as an assignment problem. This model is mostly used for planning. The assignment model is also useful in solving problems such as, assignment of machines to jobs, assignment of salesman to sales territories, traveling salesman problem etc. It may be noted that with n facilities and n jobs, there are n! possible assignments. One way of finding an optimal assignment is to write all the n! possible arrangement ,evaluate their total cost and select the assignment with minimum cost. But because of many computational procedures this method is not possible. In this unit we study an efficient method for solving assignment problems. There are n jobs for a factory and factory has n machines to process the jobs. A job i(=1,…,n) , when processed by machine j(=1,…,n) is assumed to incur a cost Cij. The assignment is to be made in such a way that each job can associate with one and only one machine Determine an assignment of jobs to machines so as to minimize the overall cost.
Sikkim Manipal University
98
Operations Research
Unit 6
Learning Objectives After studying this unit, you should be able to understand the following
1. At the end of this
Unit 6
Unit 6
Structure
Assignment Problem
6.1. 6.2. 6.3. 6.4.
Introduction Mathematical formulation of the problem Hungarian method algorithm Routing problem 6.4.1. Unbalanced A.P 6.4.2 Infeasible Assignments 6.4.3 Maximization in A.P
6.5. 6.6.
Traveling salesmen problem Summary Terminal Questions Answers to SAQs and TQs
6.1 Introduction The assignment problem is a special case of the transportation problem, where the objective is to minimize the cost or time of completing a number of jobs by a number of persons and Maximize efficiently Revenue, sales etc In other words, when the problem involves the allocation of n different facilities to n different tasks, it is often termed as an assignment problem. This model is mostly used for planning. The assignment model is also useful in solving problems such as, assignment of machines to jobs, assignment of salesman to sales territories, traveling salesman problem etc. It may be noted that with n facilities and n jobs, there are n! possible assignments. One way of finding an optimal assignment is to write all the n! possible arrangement ,evaluate their total cost and select the assignment with minimum cost. But because of many computational procedures this method is not possible. In this unit we study an efficient method for solving assignment problems. There are n jobs for a factory and factory has n machines to process the jobs. A job i(=1,…,n) , when processed by machine j(=1,…,n) is assumed to incur a cost Cij. The assignment is to be made in such a way that each job can associate with one and only one machine Determine an assignment of jobs to machines so as to minimize the overall cost.
Sikkim Manipal University
98
Operations Research
Unit 6
Learning Objectives After studying this unit, you should be able to understand the following
1. At the end of this