Scheduling hybrid flow shops with time windows

  • Fan Yang
  • Roel LeusEmail author


Hybrid flow shops can be encountered in various industrial settings. In this paper we develop methods for scheduling hybrid flow shops with hard time windows. Specifically, we study a two-stage hybrid flow shop scheduling problem with time windows to minimize the total weighted completion times. Each stage consists of one or more identical parallel machines, and each job visits two processing stages in series. Finding a feasible schedule with hard time windows is a challenging task in this setting, because it is NP-complete in the strong sense even for a single machine in a single stage. We propose two matheuristics to find an initial feasible solution by local branching. We also develop two schedule improvement procedures, one based on stage-by-stage decomposition, and one using adapted local branching. The performance of our methods is validated via extensive computational experiments.


Hybrid flow shop Scheduling Time windows Matheuristic Local branching 



Adapted local branching


Job ordering in average starting time of the linear relaxation


Earliest-deadline-first rule


Feasible schedule search by artificial variables


Infeasible schedule repair


Job window heuristic and adapted local branching


Job window heuristic and stage-by-stage decomposition


Job window heuristic


Random priority rule


Stage-by-stage decomposition

\(\triangle _r^{AL}\)

Radius decrement in AL

\(\triangle _r^{ISR}\)

Radius increment in ISR

\(\triangle _t\)

Time increment in AL


threshold on the gap in a node in AL


Predetermined number of rounds for AL


Initialization time


Time limit for bottleneck stage in SD


Time limit for non-bottleneck stage in SD


Time limit for AL


Time limit for each node in AL



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.ORSTAT, Faculty of Economics and BusinessKU LeuvenLeuvenBelgium

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