Abstract
Permutation flow shop problems (PFSPs) with makespan minimization that model production lines working in industry often have some special features: they are typically large-scale and the jobs can be sorted into types so that jobs of the same type have equal processing time values at each machine. We define the related R-PFSP, the Permutation with Repetition Flow Shop Problem, which is of less complexity if the number of types is bounded. Moreover, a subproblem set of R-PFSPs, the RL-PFSP is considered too, where only those permutations are in the design space in which subsequent tuples of a certain size contain jobs of the same type. We construct adequate new MILP models for R-PFSPs and RL-PFSPs and investigate their effectiveness experimentally. We demonstrate that via our new MILP models significantly larger problems can be solved than via the classical MILP models.
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Hajba, T., Horváth, Z. New effective MILP models for PFSPs arising from real applications. Cent Eur J Oper Res 21, 729–744 (2013). https://doi.org/10.1007/s10100-012-0263-6
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DOI: https://doi.org/10.1007/s10100-012-0263-6
Keywords
- Flow shop scheduling
- Minimizing makespan
- Mixed integer programming formulations
- Computational comparisons