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A two-machine no-wait flow shop problem with two competing agents

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Abstract

In this paper, we study the two-machine no-wait flow shop scheduling problem with two competing agents. The objective is to minimize the overall completion time of one agent subject to an upper bound on the makespan of the second agent. We proved the \(\mathcal {NP}\)-hardness for three special cases: (1) each agent has exactly two operations. (2) the jobs of one agent require processing only on one machine, (3) the no-wait constraint is only required for the jobs of one agent. We exhibited polynomial time algorithms for other restricted cases. We also proposed a mathematical programming model and a branch and bound scheme as solving approaches for small-scale problems. For large instances, we present a tabu search meta-heuristic algorithm. An intensive experimental study is conducted to illustrate the effectiveness of the proposed exact and approximation algorithms.

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Authors and Affiliations

  1. Laboratoire RECITS, Faculté de mathématiques, Université des Sciences et de la Technologie Houari Boumedienne, Alger, Algérie

    Abdennour Azerine & Mourad Boudhar

  2. Département d’informatique et de mathématique, Université du Québec à Chicoutimi, Québec, Canada

    Djamal Rebaine

Authors
  1. Abdennour Azerine
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  2. Mourad Boudhar
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  3. Djamal Rebaine
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Correspondence to Abdennour Azerine.

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Azerine, A., Boudhar, M. & Rebaine, D. A two-machine no-wait flow shop problem with two competing agents. J Comb Optim 43, 168–199 (2022). https://doi.org/10.1007/s10878-021-00755-9

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