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Minimizing weighted earliness–tardiness on a single machine with a common due date using quadratic models

Author

Listed:
  • Ramon Alvarez-Valdes

    ()

  • Enric Crespo
  • Jose Tamarit
  • Fulgencia Villa

Abstract

In this paper we study the problem of minimizing weighted earliness and tardiness on a single machine when all the jobs share the same due date. We propose two quadratic integer programming models for solving both cases of unrestricted and restricted due dates, an auxiliary model based on unconstrained quadratic integer programming and an algorithmic scheme for solving each instance, according to its size and characteristics, in the most efficient way. The scheme is tested on a set of well-known test problems. By combining the solutions of the three models we prove the optimality of the solutions obtained for most of the problems. For large instances, although optimality cannot be proved, we actually obtain optimal solutions for all the tested instances. Copyright Sociedad de Estadística e Investigación Operativa 2012

Suggested Citation

  • Ramon Alvarez-Valdes & Enric Crespo & Jose Tamarit & Fulgencia Villa, 2012. "Minimizing weighted earliness–tardiness on a single machine with a common due date using quadratic models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 754-767, October.
  • Handle: RePEc:spr:topjnl:v:20:y:2012:i:3:p:754-767
    DOI: 10.1007/s11750-010-0163-7
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    References listed on IDEAS

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    1. Hoogeveen, J. A. & van de Velde, S. L., 1991. "Scheduling around a small common due date," European Journal of Operational Research, Elsevier, vol. 55(2), pages 237-242, November.
    2. Plateau, M.-C. & Rios-Solis, Y.A., 2010. "Optimal solutions for unrelated parallel machines scheduling problems using convex quadratic reformulations," European Journal of Operational Research, Elsevier, vol. 201(3), pages 729-736, March.
    3. Hino, Celso M. & Ronconi, Debora P. & Mendes, Andre B., 2005. "Minimizing earliness and tardiness penalties in a single-machine problem with a common due date," European Journal of Operational Research, Elsevier, vol. 160(1), pages 190-201, January.
    4. Lin, Shih-Wei & Chou, Shuo-Yan & Ying, Kuo-Ching, 2007. "A sequential exchange approach for minimizing earliness-tardiness penalties of single-machine scheduling with a common due date," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1294-1301, March.
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