A multi-objective production scheduling model and dynamic dispatching rules for unrelated parallel machines with sequence-dependent set-up times

Abstract

This study presents a production scheduling for unrelated parallel machines with machine and job sequence-dependent setup times. The system performance measures to minimize include makespan, total tardiness, and number of tardy jobs. The aim of the study is to develop a solution methodology that can solve the problem for the large scale. First, the problem is formulated as a mixed-integer linear programming model. The augmented $\varepsilon$-constraint method is applied to find Pareto solutions for small problem instances. The purpose is to demonstrate that Pareto solutions, which balance the trade-offs among three measures of performance, can be found for these instances. Dispatching rule-based heuristics is developed to solve large problem instances. The heuristics feature three dispatching rules that are designed to handle the dependent setup time. In addition, these rules are combined into six variants using a time-based rule-switching mechanism. The heuristics are tested with 18 problem instances, containing 244 to 298 jobs, in two demand scenarios derived from the monthly demand data from an industrial user. Under each demand scenario, a set of heuristics that provides the best performance with respect to the three measures is identified. The heuristics include combinations of the shortest completion time and due date-based rules. Finally, a multi-criteria decision-making analysis is performed to determine the conditions specified by the weight given to each measure, with which one heuristic is preferred over the others.