Abstract
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.
Highlights
The permutation flowshop scheduling problem (PFSP) is concerned with sequencing a set N of n jobs on a set M of m machines in a sequential manner
The last set of experiments reported are conducted to compare the algorithms we propose in this paper with a state-of-the-art heuristic described for the problem, namely the iterated greedy algorithm (IGA) of Pan and Ruiz (2014), in terms of the value of the solutions identified
This paper presented an enhancement to the traditional Benders decomposition by generating cuts using a local search algorithm for the mixed no-idle permutation flowshop scheduling problem
Summary
The permutation flowshop scheduling problem (PFSP) is concerned with sequencing a set N of n jobs on a set M of m machines in a sequential manner. One extension of the PFSP is the no-idle permutation flowshop scheduling problem (NPFSP), where machines should run continuously from the time that they start the first job until they complete the last job, i.e., idle times are not allowed at any machine in between the processing of consecutive jobs. In the remainder of the paper, we make use of the integer programming formulation below of the problem described in Pan and Ruiz (2014), provided here for the sake of completeness In this formulation, a binary variable x jk takes the value 1 if job j is in position k of the sequence, and 0 otherwise. We first describe an application of the traditional Benders decomposition followed by the proposed cut generation strategy using a local search algorithm
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