Pixelation of time matrices for solving permutation flowshop scheduling problem

Abstract

Over the last decades, scheduling theory has been put into practice so as to tackle production process as a combinatorial optimisation problem and specifically as a PFSP (Permutation Flowshop Scheduling Problem). Often, NP-completeness of PFSP leads numerous research towards suggesting heuristic algorithms. The objective is to propose an optimal or near-to-optimal order of n jobs processing on m machines with a minimum completion time of all jobs. In this paper, a two-phase heuristic algorithm will be presented, named IFRS (Improved FRS). FRS, within the first phase, is going to be used to find a superior order of jobs out of Taillard’s instances; then the order of jobs will be improved again in phase 2. While running IFRS, a completely new idea, named Pixelation of time matrices, will be used for the very first time and provide a final pattern, which can be used in any heuristic algorithm with makespan criterion. After using the hard benchmark instances of Taillard, the superiority of IFRS over 20 algorithms is going to be shown by tables and statistical graphics. Due to its low makespan values, IFRS benefits flow production, as does NEH.