Contributions to the study on assignment problems in fuzzy environment

Abstract

In real life, we are encountered with problems of allocating different personnel/workers to different jobs. It is to be kept in consideration that not everyone has the same ability to perform a given job. Different persons have different abilities to execute the same task and these different capabilities are expressed in terms of various parameters like cost/profit/time involved in executing a given job. Hence, it is to be decided that we need to assign different workers to different jobs so that, the cost of performing such job gets reduced to a considerable extent. Thus this specific thesis is devoted to analyze and find the optimum value of the assignment problem using different approaches so as to get the minimum cost or maximum profit either way. In all these approaches, it is to be remembered that costs/profits are considered as imprecise numbers. These approaches are surely easily understandable and applicable in real life assignment problems for decision makers and problem solvers as well. Assignment problem is a combinatorial optimization problem in the field of operations research. In real world situation, the objectives, constraints or parameters are imprecise, because a decision is often made on the basis of vague or ambiguous information. As a result of this in recent years, fuzzy approach plays a vital role. Fourier elimination method is proposed to find the optimal solution. Here the costs are taken as triangular fuzzy numbers and are converted into crisp or precise number using Graded mean integration representation. The illustrated numerical example shows the efficiency of the proposed method. newline