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Minimizing maximum delivery completion time for order scheduling with rejection

Author

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  • Ren-Xia Chen

    (Zhongyuan University of Technology)

  • Shi-Sheng Li

    (Zhongyuan University of Technology)

Abstract

We study an order scheduling problem with rejection, in which each order consists of multiple product types and each product type should be manufactured on a dedicated machine. The aim is to find a solution to minimize a linear sum of the maximum delivery completion time of the accepted orders and the total penalty of the rejected orders. Even if the delivery times of all orders are zero, the problem is shown to be binary $$\mathcal{NP}$$ NP -hard in the two-machine case and it is shown to be unary $$\mathcal{NP}$$ NP -hard when the number of machines is arbitrary. Three approximation algorithms are proposed and their worst-case performance ratios are analyzed. For the scenario where the number of machines is fixed, a pseudo-polynomial dynamic programming algorithm and a fully polynomial time approximation scheme are devised for it.

Suggested Citation

  • Ren-Xia Chen & Shi-Sheng Li, 2020. "Minimizing maximum delivery completion time for order scheduling with rejection," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1044-1064, November.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00649-2
    DOI: 10.1007/s10878-020-00649-2
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    References listed on IDEAS

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    1. Chang Sup Sung & Sang Hum Yoon, 1998. "Minimizing total weighted completion time at a pre-assembly stage composed of two feeding machines," International Journal of Production Economics, Elsevier, vol. 54(3), pages 247-255, May.
    2. Carlier, Jacques, 1982. "The one-machine sequencing problem," European Journal of Operational Research, Elsevier, vol. 11(1), pages 42-47, September.
    3. Lingfa Lu & Liqi Zhang, 2017. "Single-machine scheduling with production and rejection costs to minimize the maximum earliness," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 331-342, August.
    4. Framinan, Jose M. & Perez-Gonzalez, Paz, 2018. "Order scheduling with tardiness objective: Improved approximate solutions," European Journal of Operational Research, Elsevier, vol. 266(3), pages 840-850.
    5. Joseph Leung & Haibing Li & Michael Pinedo, 2008. "Scheduling orders on either dedicated or flexible machines in parallel to minimize total weighted completion time," Annals of Operations Research, Springer, vol. 159(1), pages 107-123, March.
    6. Imed Kacem & Hans Kellerer & Maryam Seifaddini, 2016. "Efficient approximation schemes for the maximum lateness minimization on a single machine with a fixed operator or machine non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 970-981, October.
    7. Lin, B.M.T. & Kononov, A.V., 2007. "Customer order scheduling to minimize the number of late jobs," European Journal of Operational Research, Elsevier, vol. 183(2), pages 944-948, December.
    8. C. N. Potts, 1980. "Technical Note—Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times," Operations Research, INFORMS, vol. 28(6), pages 1436-1441, December.
    9. Xianzhao Zhang & Dachuan Xu & Donglei Du & Chenchen Wu, 2018. "Approximation algorithms for precedence-constrained identical machine scheduling with rejection," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 318-330, January.
    10. Cheng He & Joseph Y.-T. Leung & Kangbok Lee & Michael L. Pinedo, 2016. "Improved algorithms for single machine scheduling with release dates and rejections," 4OR, Springer, vol. 14(1), pages 41-55, March.
    11. Xueling Zhong & Jinwen Ou, 2017. "Improved approximation algorithms for parallel machine scheduling with release dates and job rejection," 4OR, Springer, vol. 15(4), pages 387-406, December.
    12. 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.
    13. Reza Ahmadi & Uttarayan Bagchi & Thomas A. Roemer, 2005. "Coordinated scheduling of customer orders for quick response," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 493-512, September.
    14. Wang, Guoqing & Cheng, T.C. Edwin, 2007. "Customer order scheduling to minimize total weighted completion time," Omega, Elsevier, vol. 35(5), pages 623-626, October.
    15. Liqi Zhang & Lingfa Lu, 2016. "Parallel-machine scheduling with release dates and rejection," 4OR, Springer, vol. 14(2), pages 165-172, June.
    16. Framinan, Jose M. & Perez-Gonzalez, Paz & Fernandez-Viagas, Victor, 2019. "Deterministic assembly scheduling problems: A review and classification of concurrent-type scheduling models and solution procedures," European Journal of Operational Research, Elsevier, vol. 273(2), pages 401-417.
    17. Ou, Jinwen & Zhong, Xueling & Wang, Guoqing, 2015. "An improved heuristic for parallel machine scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 241(3), pages 653-661.
    18. Wagneur, E. & Sriskandarajah, C., 1993. "Openshops with jobs overlap," European Journal of Operational Research, Elsevier, vol. 71(3), pages 366-378, December.
    19. Xiuli Wang & Guodong Huang & Xiuwu Hu & T C Edwin Cheng, 2015. "Order acceptance and scheduling on two identical parallel machines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(10), pages 1755-1767, October.
    20. Lee, Ik Sun, 2013. "Minimizing total tardiness for the order scheduling problem," International Journal of Production Economics, Elsevier, vol. 144(1), pages 128-134.
    21. Naderi, Bahman & Roshanaei, Vahid, 2020. "Branch-Relax-and-Check: A tractable decomposition method for order acceptance and identical parallel machine scheduling," European Journal of Operational Research, Elsevier, vol. 286(3), pages 811-827.
    22. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    23. Zhongshun Shi & Zewen Huang & Leyuan Shi, 2018. "Customer order scheduling on batch processing machines with incompatible job families," International Journal of Production Research, Taylor & Francis Journals, vol. 56(1-2), pages 795-808, January.
    24. Zhang, Liqi & Lu, Lingfa & Yuan, Jinjiang, 2009. "Single machine scheduling with release dates and rejection," European Journal of Operational Research, Elsevier, vol. 198(3), pages 975-978, November.
    25. Xueling Zhong & Zhangming Pan & Dakui Jiang, 2017. "Scheduling with release times and rejection on two parallel machines," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 934-944, April.
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    1. Lingfa Lu & Liqi Zhang, 2023. "Scheduling problems with rejection to minimize the k-th power of the makespan plus the total rejection cost," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-17, August.

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