Title: The permutation flowshop scheduling problem with exact time lags to minimise the total earliness and tardiness

Authors: Imen Hamdi; Taïcir Loukil

Addresses: Research Unit LOGIQ, High Institute of Industrial Management, University of Sfax, Sfax 3018, Tunisia ' Research Unit LOGIQ, High Institute of Industrial Management, University of Sfax, Sfax 3018, Tunisia

Abstract: In this paper, we investigate the problem of n-jobs scheduling in an m-machine permutation flowshop with exact time lags between consecutive operations of each job. The exact time lag is defined as the time elapsed between every couple of successive operations of the same job which is equal to a prescribed value. The aim is to find a feasible schedule that minimises the total tardiness and earliness. We propose three mathematical formulations, which are then solved by running the commercial software CPLEX to provide an optimal solution for small size problems. As the problem is shown to be strongly NP-hard, we propose new improved upper and lower bounds useful for large size problems. We then evaluate their effectiveness through an extensive computational experiment.

Keywords: permutation flowshops; flowshop scheduling; exact time lags; tardiness; earliness; mathematical formulations; lower bounds; upper bounds.

DOI: 10.1504/IJOR.2017.080596

International Journal of Operational Research, 2017 Vol.28 No.1, pp.70 - 86

Received: 21 Jun 2014
Accepted: 19 Jul 2014
Published online: 01 Dec 2016 *

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