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The Single Machine Problem with Quadratic Penalty Function of Completion Times: A Branch-and-Bound Solution

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  • W. Townsend

    (Leeds Polytechnic, England)

Abstract

N jobs are to be sequenced on a single machine, each job carrying a penalty cost which is a quadratic function of its completion time. The objective is to find a sequence which minimizes the total penalty. Criteria are developed for ordering a pair of adjacent jobs in a sequence and these are incorporated into a branch-and-bound procedure.

Suggested Citation

  • W. Townsend, 1978. "The Single Machine Problem with Quadratic Penalty Function of Completion Times: A Branch-and-Bound Solution," Management Science, INFORMS, vol. 24(5), pages 530-534, January.
    • Handle: RePEc:inm:ormnsc:v:24:y:1978:i:5:p:530-534
    DOI: 10.1287/mnsc.24.5.530
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    Citations

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    Cited by:

    1. Mondal, Sakib A. & Sen, Anup K., 2000. "An improved precedence rule for single machine sequencing problems with quadratic penalty," European Journal of Operational Research, Elsevier, vol. 125(2), pages 425-428, September.
    2. Wang, Ji-Bo, 2007. "Single-machine scheduling problems with the effects of learning and deterioration," Omega, Elsevier, vol. 35(4), pages 397-402, August.
    3. Ji-Bo Wang & Ming-Zheng Wang, 2011. "Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects," Annals of Operations Research, Springer, vol. 191(1), pages 155-169, November.
    4. Janiak, Adam & Krysiak, Tomasz & Pappis, Costas P. & Voutsinas, Theodore G., 2009. "A scheduling problem with job values given as a power function of their completion times," European Journal of Operational Research, Elsevier, vol. 193(3), pages 836-848, March.
    5. Li, Gang & Wang, Xiao-Yuan & Wang, Ji-Bo & Sun, Lin-Yan, 2013. "Worst case analysis of flow shop scheduling problems with a time-dependent learning effect," International Journal of Production Economics, Elsevier, vol. 142(1), pages 98-104.
    6. Tao Ren & Yan Zhang & Shuenn-Ren Cheng & Chin-Chia Wu & Meng Zhang & Bo-yu Chang & Xin-yue Wang & Peng Zhao, 2020. "Effective Heuristic Algorithms Solving the Jobshop Scheduling Problem with Release Dates," Mathematics, MDPI, vol. 8(8), pages 1-25, July.
    7. Sen, Tapan & Dileepan, Parthasarati & Lind, Mary R., 1996. "Minimizing a weighted quadratic function of job lateness in the single machine system," International Journal of Production Economics, Elsevier, vol. 42(3), pages 237-243, April.
    8. Kai-biao Sun & Hong-xing Li, 2009. "Some single-machine scheduling problems with actual time and position dependent learning effects," Fuzzy Information and Engineering, Springer, vol. 1(2), pages 161-177, June.
    9. Xiao, Qian & Xu, Hongquan, 2021. "A mapping-based universal Kriging model for order-of-addition experiments in drug combination studies," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    10. Cheng, T. C. Edwin & Shakhlevich, Natalia V., 2005. "Minimizing non-decreasing separable objective functions for the unit-time open shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 165(2), pages 444-456, September.
    11. J-B Wang & J-J Wang & P Ji, 2011. "Scheduling jobs with chain precedence constraints and deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1765-1770, September.
    12. Szwarc, Wlodzimierz & Mukhopadhyay, Samar K., 1996. "Solution of the generalized Townsend single machine scheduling model," European Journal of Operational Research, Elsevier, vol. 91(1), pages 203-210, May.
    13. Schaller, Jeffrey, 2002. "Minimizing the sum of squares lateness on a single machine," European Journal of Operational Research, Elsevier, vol. 143(1), pages 64-79, November.
    14. Xu, Zhiyong & Sun, Linyan & Gong, Juntao, 2008. "Worst-case analysis for flow shop scheduling with a learning effect," International Journal of Production Economics, Elsevier, vol. 113(2), pages 748-753, June.
    15. Xiaoqiang Cai & Xiaoqian Sun & Xian Zhou, 2004. "Stochastic scheduling subject to machine breakdowns: The preemptive‐repeat model with discounted reward and other criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 800-817, September.
    16. J-B Wang, 2010. "Single-machine scheduling with a sum-of-actual-processing-time-based learning effect," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 172-177, January.
    17. Nikhil Bansal & Christoph Dürr & Nguyen Kim Thang & Óscar C. Vásquez, 2017. "The local–global conjecture for scheduling with non-linear cost," Journal of Scheduling, Springer, vol. 20(3), pages 239-254, June.
    18. D-L Yang & W-H Kuo, 2007. "Single-machine scheduling with an actual time-dependent learning effect," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(10), pages 1348-1353, October.
    19. Dar-Li Yang & Wen-Hung Kuo, 2009. "Single-machine scheduling with both deterioration and learning effects," Annals of Operations Research, Springer, vol. 172(1), pages 315-327, November.

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