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Minimizing Total Costs in One-Machine Scheduling

Author

Listed:
  • A. H. G. Rinnooy Kan

    (Graduate School of Management, Delft, The Netherlands)

  • B. J. Lageweg

    (Mathematisch Centrum, Amsterdam, The Netherlands)

  • J. K. Lenstra

    (Mathematisch Centrum, Amsterdam, The Netherlands)

Abstract

Suppose we have n jobs that arrive simultaneously to be processed on a continuously available machine that can handle only one job at a time. Each job has a fixed processing time and a cost function that is nondecreasing in its finishing time. We want to find a schedule that minimizes total costs. After reviewing the relevant work on this problem, we present a new algorithm for a general cost function. The algorithm is tested for the well known case of a weighted tardiness criterion.

Suggested Citation

  • A. H. G. Rinnooy Kan & B. J. Lageweg & J. K. Lenstra, 1975. "Minimizing Total Costs in One-Machine Scheduling," Operations Research, INFORMS, vol. 23(5), pages 908-927, October.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:5:p:908-927
    DOI: 10.1287/opre.23.5.908
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    Citations

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    Cited by:

    1. J. J. Kanet, 2007. "New Precedence Theorems for One-Machine Weighted Tardiness," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 579-588, August.
    2. Rostami, Salim & Creemers, Stefan & Leus, Roel, 2019. "Precedence theorems and dynamic programming for the single-machine weighted tardiness problem," European Journal of Operational Research, Elsevier, vol. 272(1), pages 43-49.
    3. Valente, Jorge M.S., 2007. "Improving the performance of the ATC dispatch rule by using workload data to determine the lookahead parameter value," International Journal of Production Economics, Elsevier, vol. 106(2), pages 563-573, April.
    4. Janiak, Adam & Krysiak, Tomasz, 2012. "Scheduling jobs with values dependent on their completion times," International Journal of Production Economics, Elsevier, vol. 135(1), pages 231-241.
    5. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1980. "A Recursive Approach To The Implementation Of Enumerative Methods," Econometric Institute Archives 272202, Erasmus University Rotterdam.
    6. John J. Kanet, 2014. "One-Machine Sequencing to Minimize Total Tardiness: A Fourth Theorem for Emmons," Operations Research, INFORMS, vol. 62(2), pages 345-347, April.
    7. N Madhushini & C Rajendran & Y Deepa, 2009. "Branch-and-bound algorithms for scheduling in permutation flowshops to minimize the sum of weighted flowtime/sum of weighted tardiness/sum of weighted flowtime and weighted tardiness/sum of weighted f," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(7), pages 991-1004, July.
    8. George Li, 1997. "Single machine earliness and tardiness scheduling," European Journal of Operational Research, Elsevier, vol. 96(3), pages 546-558, February.
    9. Louis-Philippe Bigras & Michel Gamache & Gilles Savard, 2008. "Time-Indexed Formulations and the Total Weighted Tardiness Problem," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 133-142, February.
    10. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    11. Su, Ling-Huey & Chen, Chung-Jung, 2008. "Minimizing total tardiness on a single machine with unequal release dates," European Journal of Operational Research, Elsevier, vol. 186(2), pages 496-503, April.
    12. Koltai, Tamás, 2009. "Robustness of a production schedule to inventory cost calculations," International Journal of Production Economics, Elsevier, vol. 121(2), pages 494-504, October.
    13. Somaye Geramipour & Ghasem Moslehi & Mohammad Reisi-Nafchi, 2017. "Maximizing the profit in customer’s order acceptance and scheduling problem with weighted tardiness penalty," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(1), pages 89-101, January.
    14. Holsenback, J. E. & Russell, R. M. & Markland, R. E. & Philipoom, P. R., 1999. "An improved heuristic for the single-machine, weighted-tardiness problem," Omega, Elsevier, vol. 27(4), pages 485-495, August.
    15. 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.
    16. Akturk, M. Selim & Ozdemir, Deniz, 2001. "A new dominance rule to minimize total weighted tardiness with unequal release dates," European Journal of Operational Research, Elsevier, vol. 135(2), pages 394-412, December.
    17. Tan, Keah-Choon & Narasimhan, Ram & Rubin, Paul A. & Ragatz, Gary L., 2000. "A comparison of four methods for minimizing total tardiness on a single processor with sequence dependent setup times," Omega, Elsevier, vol. 28(3), pages 313-326, June.
    18. Silva, Marco & Poss, Michael & Maculan, Nelson, 2020. "Solution algorithms for minimizing the total tardiness with budgeted processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 283(1), pages 70-82.
    19. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    20. John J. Kanet & Federico Della Croce & Christos Koulamas & Vincent T’kindt, 2015. "Erratum—One Machine Sequencing to Minimize Total Tardiness: A Fourth Theorem for Emmons," Operations Research, INFORMS, vol. 63(2), pages 351-352, April.
    21. Tan, K. C. & Narasimhan, R., 1997. "Minimizing tardiness on a single processor with sequence-dependent setup times: a simulated annealing approach," Omega, Elsevier, vol. 25(6), pages 619-634, December.
    22. Huo, Yumei & Leung, Joseph Y.-T. & Zhao, Hairong, 2007. "Bi-criteria scheduling problems: Number of tardy jobs and maximum weighted tardiness," European Journal of Operational Research, Elsevier, vol. 177(1), pages 116-134, February.

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