Intelligent Valid Inequalities for No-Wait Permutation Flowshop Scheduling Problems

Abstract

The no-wait permutation flowshop scheduling problem is a well-recognized scheduling problem. Examples can be encountered in several industries such as hot metal rolling, painting, chemical, steel industries, etc. In this flowshop setting, the jobs are not allowed to wait between consecutive machines. Owing to the NP-hardness identity of the problem, the developed mathematical models to solve this problem cannot reach optimal solutions for large instances in polynomial time. However, the quality of the objective functions and the gap values obtained by the mathematical models in a specific time window can be improved by valid inequalities. This study generates intelligent valid inequalities to improve a mathematical model’s performance in optimizing the no-wait permutation flow shop scheduling problems. Valid inequalities’ performance is tested for three significant objective functions: (i) makespan, (ii) total flow time, and (iii) total tardiness. According to the computational experiments, the new valid inequalities improve the outcomes of the mathematical models mostly in the way of the gap values for makespan, total flow time, and total tardiness objective criteria.