A Novel Approach to Solving the Fuzzy Assignment Problems

Abstract

The most successful and practical approach to solving an optimization problem is linear programming. A prime scenario of a problem is a situation where all the constraints are linear and either the function is inequalities or equivalent. Here, the problem of maximizing or minimizing an objective function was the key thing. Due to these factors, numerous types of optimization problems developed. Such as the problems with scheduling, transportation, and engineering. In the fields of logistics and business operations, for example, assignment problems are quite important. To optimally allocate a set of resources to a set of tasks is the main goal of the classical assignment problem in mathematical optimization. Here, resources should be distributed among each other so that costs are minimized. In solving such problems, the Hungarian method can be pointed out as one of the most successful and widely used methods. However, problems are created with some uncertainty or ambiguity in solving them in the real world.When the cost values related to the assignment problem cannot be expressed precisely, fuzzy theory is used for a range of values. It has created fuzzy assignment problems. The main purpose of these problems is to develop ways to minimize the total cost of resource distribution. There are many techniques for fuzzy set theory and fuzzy optimization in linear programming. Also, to solve the problem, researchers have proposed different methods to obtain an optimal or near optimal solution. Thus, the purpose of this research paper is to address the above mentioned point. For that, a new alternative method was proposed in this research paper, and its efficiency and correctness have been shown by solving numerical problems using MATLAB software.