Synchronous flow shop scheduling with pliable jobs

Matthias Bultmann, Sigrid Knust and Stefan Waldherr

European Journal of Operational Research, 2018, vol. 270, issue 3, 943-956

Abstract: In this paper, we consider synchronous flow shop scheduling problems where the processing times of the operations are not fixed in advance. Instead, for each job a total processing time is given which can be distributed freely among the machines, respecting some lower and/or upper bounds on the processing times of the operations. We prove that even if no additional bounds are given, minimizing the makespan is NP-hard already for two machines. On the other hand, we can draw on a more general result to show that for a fixed job permutation optimal corresponding processing times can be determined via a linear program in polynomial time. However, for larger problem instances, this leads to large run times. As a more efficient alternative, we propose direct combinatorial algorithms to determine the processing times. We embed these algorithms in a two-stage approach using the set of all job permutations as search space and calculating corresponding processing times in a second step. Computational results are presented for randomly generated data with varying degrees of allowed flexibility.

Keywords: Scheduling; Flow shop; Synchronous movement; Pliability (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:270:y:2018:i:3:p:943-956

DOI: 10.1016/j.ejor.2018.04.024

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