MILP models and valid inequalities for the two-machine permutation flowshop scheduling problem with minimal time lags

Journal of Industrial Engineering International

مقاله 3، دوره 16، شماره 2، شهریور 2020، صفحه 223-229   

نویسندگان

Imen Hamdi^{* 1، 2}؛ Saïd Toumi^{1، 2، 3}

¹MODILS Lab, Faculty of Economics and Management, University of Sfax, Sfax, Tunisia

²High Institute of Transport and Logistics, University of Sousse, Sousse, Tunisia

³Department of Business Administration, College of Business Administartion, Majmaah University, Al Majmaah, Saudi Arabia

چکیده

In this paper, we consider the problem of scheduling on two-machine permutation flowshop with minimal time lags between consecutive operations of each job. The aim is to find a feasible schedule that minimizes the total tardiness. This problem is known to be NP-hard in the strong sense. We propose two mixed-integer linear programming (MILP) models and two types of valid inequalities which aim to tighten the models’ representations. One of them is based on dominance rules from the literature. Then, we provide the results of extensive computational experiments used to measure the performance of the proposed MILP models. They are shown to be able to solve optimally instances until the size 40-job and even several larger problem classes, with up to 60 jobs. Furthermore, we can distinguish the effect of the minimal time lags and the inclusion of the valid inequalities in the basic MILP model on the results.

کلیدواژه‌ها

Flow shop؛ Total tardiness؛ Time lags؛ MILP models؛ Valid inequalities

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