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Original Articles

Scheduling problems on a new setting of flexible flowshops: ℓ-Machine proportionate flowshops

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Pages 1499-1516 | Received 09 Feb 2020, Accepted 04 Apr 2021, Published online: 21 Jun 2021
 

Abstract

The classical flexible flowshop (FFc) environment consists of c-stages in series with m-machines in parallel at each stage, where each job has to undergo a particular series of actions. In this paper we consider a similar, yet different, and still a challenging real-life setting, that, to the best of our knowledge, has not been studied to date. We assume that there are -sets in parallel in which each of the sets is an m-machine proportionate flowshop. In this new setting, each job can be processed on each one of the sets, but once a set is chosen, the job must be processed on all of its machines, in first-in-first-out method. We study several fundamental scheduling measures such as makespan, maximum tardiness with common due-date, total tardiness with common due-date, and total load. Moreover, we consider optional job-rejection and focus on minimising the total completion time. All problems are shown to be NP-hard, and pseudo-polynomial dynamic programming (DP) solution algorithms and Simulated Annealing (SA) metaheuristics are provided. The efficiency of all our proposed algorithms is validated through an extensive numerical study.

Disclosure statement

No potential conflict of interest was reported by the authors.

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