A Possibility Linear Programming Approach to Solve a Fuzzy Single Machine Scheduling Problem

This paper employs an interactive possibility linear programming approach to solve a single machine scheduling problem with imprecise processing times, due dates, as well as earliness and tardiness penalties of jobs. The proposed approach is based on a strategy of minimizing the most possible value of the imprecise total costs, maximizing the possibility of obtaining a lower total costs, and minimizing the risk of obtaining higher total costs simultaneously. This approach is applicable to just-in-time systems, in which many firms face the need to complete jobs as close as possible to their due dates. The objective of the model is to minimize the total costs of earliness/tardiness penalties. In this paper, the proposed possibility linear programming approach is applied to a fuzzy single machine scheduling problem with respect to the overall degree of decision maker satisfaction. Due to the proposed model’s complexity, conventional optimization methods cannot be utilized in reasonable time. Hence, the particle swarm optimization method is applied toward its solution.