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A new dynamic programming formulation for scheduling independent tasks with common due date on parallel machines

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  • Huynh Tuong, Nguyen
  • Soukhal, Ameur
  • Billaut, Jean-Charles

Abstract

This paper deals with a scheduling problem of independent tasks with common due date where the objective is to minimize the total weighted tardiness. The problem is known to be ordinary NP-hard in the case of a single machine and a dynamic programming algorithm was presented in the seminal work of Lawler and Moore [E.L. Lawler, J.M. Moore, A functional equation and its application to resource allocation and sequencing problems, Management Science 16 (1969) 77-84]. In this paper, this algorithm is described and discussed. Then, a new dynamic programming algorithm is proposed for solving the single machine case. These methods are extended for solving the identical and uniform parallel-machine scheduling problems.

Suggested Citation

  • Huynh Tuong, Nguyen & Soukhal, Ameur & Billaut, Jean-Charles, 2010. "A new dynamic programming formulation for scheduling independent tasks with common due date on parallel machines," European Journal of Operational Research, Elsevier, vol. 202(3), pages 646-653, May.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:3:p:646-653
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    References listed on IDEAS

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    1. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    2. Sen, Tapan & Sulek, Joanne M. & Dileepan, Parthasarati, 2003. "Static scheduling research to minimize weighted and unweighted tardiness: A state-of-the-art survey," International Journal of Production Economics, Elsevier, vol. 83(1), pages 1-12, January.
    3. Gordon, Valery & Proth, Jean-Marie & Chu, Chengbin, 2002. "A survey of the state-of-the-art of common due date assignment and scheduling research," European Journal of Operational Research, Elsevier, vol. 139(1), pages 1-25, May.
    4. Cheng, T. C. E. & Ng, C. T. & Yuan, J. J. & Liu, Z. H., 2005. "Single machine scheduling to minimize total weighted tardiness," European Journal of Operational Research, Elsevier, vol. 165(2), pages 423-443, September.
    5. Michael H. Rothkopf, 1966. "Scheduling Independent Tasks on Parallel Processors," Management Science, INFORMS, vol. 12(5), pages 437-447, January.
    6. Kenneth R. Baker & Gary D. Scudder, 1990. "Sequencing with Earliness and Tardiness Penalties: A Review," Operations Research, INFORMS, vol. 38(1), pages 22-36, February.
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