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Mixed graph colouring for unit-time scheduling

Author

Listed:
  • Ahmed Kouider
  • Hacène Ait Haddadène
  • Samia Ourari
  • Ammar Oulamara

Abstract

We consider the job shop scheduling problem with unit-time operations and the makespan criterion. This problem is reduced to finding an optimal colouring of a special class of mixed graph, where its partial graph without edges represents the union of maximal directed paths and its partial graph without arcs represents the union of maximal cliques. As the problem is known to be NP-hard, both exact and heuristic methods are proposed to solve it. This study is carried out in three steps. First, a new lower and upper bounds for the mixed chromatic number are proposed. Afterwards, a colour-indexed mathematical model using the proposed bounds is developed. Then, a tabu search using a dynamic neighbourhood structure is adapted for solving large instances. Computational experiments conducted on several modified benchmarks show the efficiency and effectiveness of the proposed resolution methods.

Suggested Citation

  • Ahmed Kouider & Hacène Ait Haddadène & Samia Ourari & Ammar Oulamara, 2017. "Mixed graph colouring for unit-time scheduling," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1720-1729, March.
    • Handle: RePEc:taf:tprsxx:v:55:y:2017:i:6:p:1720-1729
    DOI: 10.1080/00207543.2016.1224950
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    References listed on IDEAS

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