Fuzzy Multi-objective Linear Programming Approach for Solving a Multi-objective Single-machine Scheduling Problem

This study develops a fuzzy multi-objective linear programming (FMOLP) model with piecewise linear membership function for solving a multi-objective single-machine scheduling problems (SMSP). In real-world situations, processing times and due dates is familiar with estimating the values of the upper bound (optimistic), lower bound (pessimistic), and modal value (most likely) parameters. This paper assumes that processing times and due dates have already adopted the triangular fuzzy number to represent all of the imprecise data in the original SMSP model. The proposed model attempts to simultaneously minimize the total weighted tardiness and number of tardy jobs by considering the levels α- cut of processing times and due dates. The proposed model yields a compromise solution and the decision maker’s overall levels of satisfaction with the determined objective values. The primary contribution of this paper is a fuzzy mathematical programming methodology for solving the SMSP in uncertain environments. A number of numerical examples are solved to show the effectiveness of the proposed approach.

Single-machine scheduling, Fuzzy multi-objective linear programming, Total weighted tardiness, Number of tardy job, Fuzzy set theory.