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On the m-clique free interval subgraphs polytope: polyhedral analysis and applications

Author

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  • Mohammed-Albarra Hassan

    (Université de Lorraine)

  • Imed Kacem

    (Université de Lorraine)

  • Sébastien Martin

    (Université de Lorraine)

  • Izzeldin M. Osman

    (Sudan University of Science and Technology)

Abstract

In this paper we study the m-clique free interval subgraphs. We investigate the facial structure of the polytope defined as the convex hull of the incidence vectors associated with these subgraphs. We also present some facet-defining inequalities to strengthen the associated linear relaxation. As an application, the generalized open-shop problem with disjunctive constraints (GOSDC) is considered. Indeed, by a projection on a set of variables, the m-clique free interval subgraphs represent the solution of an integer linear program solving the GOSDC presented in this paper. Moreover, we propose exact and heuristic separation algorithms, which are exploited into a Branch-and-cut algorithm for solving the GOSDC. Finally, we present and discuss some computational results.

Suggested Citation

  • Mohammed-Albarra Hassan & Imed Kacem & Sébastien Martin & Izzeldin M. Osman, 2018. "On the m-clique free interval subgraphs polytope: polyhedral analysis and applications," Journal of Combinatorial Optimization, Springer, vol. 36(3), pages 1074-1101, October.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:3:d:10.1007_s10878-018-0291-9
    DOI: 10.1007/s10878-018-0291-9
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    References listed on IDEAS

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    1. Eva Vallada & Rubén Ruiz, 2012. "Scheduling Unrelated Parallel Machines with Sequence Dependent Setup Times and Weighted Earliness–Tardiness Minimization," Springer Optimization and Its Applications, in: Roger Z. Ríos-Mercado & Yasmín A. Ríos-Solís (ed.), Just-in-Time Systems, chapter 0, pages 67-90, Springer.
    2. K. Aardal & C. P. M. Van Hoesel, 1999. "Polyhedral techniques in combinatorial optimization II: applications and computations," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 53(2), pages 131-177, July.
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    4. Mokotoff, E. & Chretienne, P., 2002. "A cutting plane algorithm for the unrelated parallel machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 141(3), pages 515-525, September.
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    Cited by:

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    2. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.

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