Fuzzy Assignment Method for Finding an Optimal Solution for Fuzzy Assignment Problem

Optimizing assignment problems using fuzzy assignment method

Abstract

The present paper describes the method called fuzzy assignment method for finding an optimal solution for fuzzy assignment problem where the assignment matrix is in a triangular fuzzy numbers. The optimal solution is also in a triangular fuzzy number. The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operation research in mathematics. It is a special case of transportation problem in which the objective is to assign a number of origins to the equal number of destinations at the minimum cost (or maximum profit). It involves assignment of people to projects, jobs to machines, workers to jobs and teachers to classes etc., while minimizing the total assignment costs. One of the important characteristics of assignment problem is that only one job (or worker) is assigned to one machine (or project). Hence the number of sources are equal to the number of destinations and each requirement and capacity value is exactly one unit.