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 sequencedependent setup time, release date and due date constraints. The problem is formulated as amulti-objective mixed-integer programming model. Two conflicting objectives are consideredas minimization of maximum completion time (makespan) and total tardiness. Despite themost use of metaheuristics in this kind of multi-objective problems, here, we try to solve theproblem by transforming the two-objectives as a single objective using scalarizationtechniques. Test instances are generated as proposed in the scheduling literature. The solutionsare obtained using Weighted Sum Scalarization, Benson’s Method and Pascoletti−SerafiniMethod. In addition, a comparison of scalarization techniques using Δ performance metric isgiven on the considered problem instances. The obtained results are evaluated and Δ values,which were obtained for Benson’s method, are mostly better than other techniques for thegenerated test problems.