Benders decomposition for the mixed no-idle permutation flowshop scheduling problem

[EN] The mixed no-idle flowshop scheduling problem arises in modern industries including integrated circuits, ceramic frit and steel production, among others, and where some machines are not allowed to remain idle between jobs. This paper describes an exact algorithm that uses Benders decomposition with a simple yet effective enhancement mechanism that entails the generation of additional cuts by using a referenced local search to help speed up convergence. Using only a single additional optimality cut at each iteration, and combined with combinatorial cuts, the algorithm can optimally solve instances with up to 500 jobs and 15 machines that are otherwise not within the reach of off-the-shelf optimization software, and can easily surpass ad-hoc existing metaheuristics. To the best of the authors' knowledge, the algorithm described here is the only exact method for solving the mixed no-idle permutation flowshop scheduling problem.
This research project was partially supported by the Scientific and Technological Research Council of Turkey (TuBITAK) under Grant 1059B191600107. While writing this paper, Dr Hamzaday was a visiting researcher at the Southampton Business School at the University of Southampton. Ruben Ruiz is supported by the Spanish Ministry of Science, Innovation and Universities, under the Project 'OPTEP-Port Terminal Operations Optimization' (No. RTI2018-094940-B-I00) financed with FEDER funds. Thanks are due to two anonymous reviewers for their careful reading of the paper and helpful suggestions.