A Comparative Study of Scalarization Techniques on the Multi-Objective Single Machine-Scheduling Problem Under Sequence-Dependent Setup Time, Release Date and Due Date Constraints

Abstract

In this paper, we considered a two-objective machine-scheduling problem under sequence-dependent setup time, release date and due date constraints. The problem is formulated as a multi-objective mixed-integer programming model. Two conflicting objectives are considered as minimization of maximum completion time (makespan) and total tardiness. Despite the most use of metaheuristics in this kind of multi-objective problems, here, we try to solve the problem by transforming the two-objectives as a single objective using scalarization techniques. Test instances are generated as proposed in the scheduling literature. The solutions are obtained using Weighted Sum Scalarization, Benson's Method and Pascoletti-Serafini Method. In addition, a comparison of scalarization techniques using. performance metric is given on the considered problem instances. The obtained results are evaluated and. values, which were obtained for Benson's method, are mostly better than other techniques for the generated test problems.