Bi-criteria Fuzzy Assignment Problem

Abstract

The objective of the ordinary assignment problem is maximizing the total efficiency when each worker is assigned to exactly one job and each job receives exactly one worker. In some situation, however, it is not so easy to determine every efficiency rigidly. In this paper, we accordingly consider the assignment problem as a "decision making in fuzzy environment". That is, the weights of jobs are presented by membership functions and introduce fuzzy efficiencies characterized by fuzzy numbers. In this case, we can formulate and solve the problem by making use of the agreement index. Further, in order to consider more flexible situation, we characterize each worker's satisfaction degree for each job by the corresponding membership functions and formulate the problem with two objectives, i. e., (1)the total efficiency to be maximized and (2)the minimum among all satisfaction degrees to be maximized. In other words, the bi-criteria problem is formulated from the viewpoint of not only (1) DM (Decision Maker) but also (2) workers. To solve the bi-criteria problem, we propose an efficient algorithm which is the interactive system with the concept of non-dominated solution.