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Approximation algorithms for minimizing the maximum lateness and makespan on parallel machines

Author

Listed:
  • Gais Alhadi

    (Université de Lorraine
    University of Gezira)

  • Imed Kacem

    (Université de Lorraine)

  • Pierre Laroche

    (Université de Lorraine)

  • Izzeldin M. Osman

    (Sudan University of Science and Technology)

Abstract

We consider a multiobjective scheduling problem, with the aim of minimizing the maximum lateness and the makespan on two identical machines. In this problem, we are given a set J of n jobs to be scheduled on two identical machines. Each job $$j\in J$$j∈J has a processing time $$p_j$$pj and a delivery time $$q_j$$qj. The machines are available at time $$t=0$$t=0 and each of them can process at most one job at a given time. This paper proposes an exact algorithm (based on a dynamic programming) to generate the complete Pareto Frontier in a pseudo-polynomial time. Then, we present a polynomial time approximation scheme (PTAS) to generate an approximate Pareto Frontier. In this scheme, we use a simplification technique based on the merging of jobs. Furthermore, we present two fully polynomial time approximation scheme (FPTAS) to generate an approximate Pareto Frontier, the first one is based on the conversion of the dynamic programming, the second one is applied to the simplified instances given by the PTAS. The proposed FPTAS algorithms are strongly polynomial. Finally, some numerical experiments are provided in order to compare the four proposed approaches.

Suggested Citation

  • Gais Alhadi & Imed Kacem & Pierre Laroche & Izzeldin M. Osman, 2020. "Approximation algorithms for minimizing the maximum lateness and makespan on parallel machines," Annals of Operations Research, Springer, vol. 285(1), pages 369-395, February.
    • Handle: RePEc:spr:annopr:v:285:y:2020:i:1:d:10.1007_s10479-019-03250-x
    DOI: 10.1007/s10479-019-03250-x
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    References listed on IDEAS

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    1. Allahverdi, Ali & Aldowaisan, Tariq, 2004. "No-wait flowshops with bicriteria of makespan and maximum lateness," European Journal of Operational Research, Elsevier, vol. 152(1), pages 132-147, January.
    2. Demange, Marc & Paschos, Vangelis Th., 2005. "Polynomial approximation algorithms with performance guarantees: An introduction-by-example," European Journal of Operational Research, Elsevier, vol. 165(3), pages 555-568, September.
    3. Ben Amor, Sarah & Martel, Jean-Marc, 2014. "A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1165-1169.
    4. Cheng He & Hao Lin & Yixun Lin & Ji Tian, 2013. "Bicriteria scheduling on a series-batching machine to minimize maximum cost and makespan," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 177-186, January.
    5. Geng, Zhichao & Yuan, Jinjiang & Yuan, Junling, 2018. "Scheduling with or without precedence relations on a serial-batch machine to minimize makespan and maximum cost," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 1-18.
    6. Sarah Ben Amor & Kazimierz Zaras & Ernesto A. Aguayo, 2017. "The value of additional information in multicriteria decision making choice problems with information imperfections," Annals of Operations Research, Springer, vol. 253(1), pages 61-76, June.
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    Cited by:

    1. Ye Wang & Jiafu Tang, 2022. "Optimized skill configuration for the seru production system under an uncertain demand," Annals of Operations Research, Springer, vol. 316(1), pages 445-465, September.
    2. Anghinolfi, Davide & Paolucci, Massimo & Ronco, Roberto, 2021. "A bi-objective heuristic approach for green identical parallel machine scheduling," European Journal of Operational Research, Elsevier, vol. 289(2), pages 416-434.
    3. Adel Kacem & Abdelaziz Dammak, 2021. "Multi-objective scheduling on two dedicated processors," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 694-721, October.

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