A New Possibilistic Optimization Model for Multiple Criteria Assignment Problem

Abstract

This paper presents a new multiple criteria optimization model of an assignment problem with imprecise coefficients. Besides, minimizing the total cost, total time of finishing jobs, and maximization of the overall achieved quality, we introduce a new criterion that minimizes the number of workers employed to finish all jobs. It contributes significantly in multi-job assignment to adjust the number of workers assigned to at least one job for balancing work allocation among the workers. Furthermore, we employ new diversification constraints to obtain a reasonable tradeoff between the number of workers employed and number of jobs assigned. A new interactive possibilistic programming approach is developed for trapezoidal possibility distributions, which uses $\alpha$ -level sets to incorporate confidence levels of the decision maker in his fuzzy judgments leading to $\alpha$ -efficient solutions. Numerical experiments are conducted using data coming from a manpower planning problem to demonstrate working of the proposed multiple criteria assignment model and effectiveness of the fuzzy interactive approach.