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A Branch-and-Bound Algorithm for Minimizing the Total Tardiness of Multiple Developers

Author

Listed:
  • Chung-Ho Su

    (Department of Animation and Game Design, Shu-Te University, Kaohsiung 824, Taiwan)

  • Jen-Ya Wang

    (Department of Multimedia Game Development and Application, Hungkuang University, Taichung 433, Taiwan)

Abstract

In the game industry, tardiness is an important issue. Unlike a unifunctional machine, a developer may excel in programming but be mediocre in scene modeling. His/her processing speed varies with job type. To minimize tardiness, we need to schedule these developers carefully. Clearly, traditional scheduling algorithms for unifunctional machines are not suitable for such versatile developers. On the other hand, in an unrelated machine scheduling problem, n jobs can be processed by m machines at n × m different speeds, i.e., its solution space is too wide to be simplified. Therefore, a tardiness minimization problem considering three job types and versatile developers is presented. In this study, a branch-and-bound algorithm and a lower bound based on harmonic mean are proposed for minimizing the total tardiness. Theoretical analyses ensure the correctness of the proposed method. Computational experiments also show that the proposed method can ensure the optimality and efficiency for n ≤ 18. With the exact algorithm, we can fairly evaluate other approximate algorithms in the future.

Suggested Citation

  • Chung-Ho Su & Jen-Ya Wang, 2022. "A Branch-and-Bound Algorithm for Minimizing the Total Tardiness of Multiple Developers," Mathematics, MDPI, vol. 10(7), pages 1-24, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1200-:d:788300
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    References listed on IDEAS

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    1. Wen-Chiung Lee & Jen-Ya Wang & Lin-Yo Lee, 2015. "A hybrid genetic algorithm for an identical parallel-machine problem with maintenance activity," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(11), pages 1906-1918, November.
    2. Nobuyuki Harada, 2007. "Video game demand in Japan: a household data analysis," Applied Economics, Taylor & Francis Journals, vol. 39(13), pages 1705-1710.
    3. Fuh-Der Chou, 2013. "Minimising the total weighted tardiness for non-identical parallel batch processing machines with job release times and non-identical job sizes," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 7(5), pages 529-557.
    4. Ju-Yong Lee & Yeong-Dae Kim, 2015. "A branch and bound algorithm to minimize total tardiness of jobs in a two identical-parallel-machine scheduling problem with a machine availability constraint," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(9), pages 1542-1554, September.
    5. Gretz, Richard T., 2010. "Hardware quality vs. network size in the home video game industry," Journal of Economic Behavior & Organization, Elsevier, vol. 76(2), pages 168-183, November.
    6. Luis Henrique Magalhães Costa & Bruno Prata & Helena M. Ramos & Marco Aurélio Holanda Castro, 2016. "A Branch-and-Bound Algorithm for Optimal Pump Scheduling in Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(3), pages 1037-1052, February.
    7. Asmaa Khoudi & Ali Berrichi, 2020. "Minimize total tardiness and machine unavailability on single machine scheduling problem: bi-objective branch and bound algorithm," Operational Research, Springer, vol. 20(3), pages 1763-1789, September.
    8. Rabia Nessah & Imed Kacem, 2009. "Branch-and-bound method for minimizing the weighted completion time scheduling problem on a single machine with release dates," Working Papers 2010-ECO-08, IESEG School of Management.
    9. R. Nessah & Farouk Yalaoui & C. Chu, 2008. "A branch and bound algorithm to minimize total weighted completion time on identical parallel machines with job release date," Post-Print hal-00580602, HAL.
    10. Kacem, Imed & Chu, Chengbin, 2008. "Efficient branch-and-bound algorithm for minimizing the weighted sum of completion times on a single machine with one availability constraint," International Journal of Production Economics, Elsevier, vol. 112(1), pages 138-150, March.
    11. Ghirardi, M. & Potts, C. N., 2005. "Makespan minimization for scheduling unrelated parallel machines: A recovering beam search approach," European Journal of Operational Research, Elsevier, vol. 165(2), pages 457-467, September.
    12. Jen-Ya Wang, 2020. "Minimizing the total weighted tardiness of overlapping jobs on parallel machines with a learning effect," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(6), pages 910-927, June.
    13. Onur Ozturk & Mehmet A. Begen & Gregory S. Zaric, 2017. "A branch and bound algorithm for scheduling unit size jobs on parallel batching machines to minimize makespan," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1815-1831, March.
    14. Tanaka, Shunji & Araki, Mituhiko, 2008. "A branch-and-bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines," International Journal of Production Economics, Elsevier, vol. 113(1), pages 446-458, May.
    15. Cheng-Hsiung Lee, 2018. "A dispatching rule and a random iterated greedy metaheuristic for identical parallel machine scheduling to minimize total tardiness," International Journal of Production Research, Taylor & Francis Journals, vol. 56(6), pages 2292-2308, March.
    16. Chengbin Chu, 1992. "A branch‐and‐bound algorithm to minimize total tardiness with different release dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(2), pages 265-283, March.
    17. Zhi Pei & Mingzhong Wan & Ziteng Wang, 2020. "A new approximation algorithm for unrelated parallel machine scheduling with release dates," Annals of Operations Research, Springer, vol. 285(1), pages 397-425, February.
    18. S-O Shim & Y-D Kim, 2007. "Minimizing total tardiness in an unrelated parallel-machine scheduling problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(3), pages 346-354, March.
    19. Mensendiek, Arne & Gupta, Jatinder N.D. & Herrmann, Jan, 2015. "Scheduling identical parallel machines with fixed delivery dates to minimize total tardiness," European Journal of Operational Research, Elsevier, vol. 243(2), pages 514-522.
    20. Edward G. Anderson & Geoffrey G. Parker & Burcu Tan, 2014. "Platform Performance Investment in the Presence of Network Externalities," Information Systems Research, INFORMS, vol. 25(1), pages 152-172, March.
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