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Single-machine serial-batch delivery scheduling with two competing agents and due date assignment

  • Yunqiang Yin
  • Doudou Li
  • Dujuan Wang
  • T. C. E. Cheng
S.I.: CoDIT2017-Combinatorial Optimization

Abstract

We consider a set of single-machine batch delivery scheduling problems involving two competing agents under two due date assignment models. Belonging to one of the two agents, each job is processed and delivered in a batch to its agent, where the jobs in each batch come from the same agent. The jobs in a batch are processed sequentially and the processing time of a batch is equal to the sum of the processing times of the jobs in it. A setup time is required at the start of each batch. The dispatch date of a job equals the delivery date of the batch it is in, i.e., the completion time of the last job in the batch. There is no capacity limit on each delivery batch, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. The due date of each job is a decision variable, which is to be assigned by the decision maker using one of two due date models, namely the common and unrestricted due date models. Given the due date assignment model, the overall objective is to minimize one agent’s scheduling criterion, while keeping the other agent’s criterion value from exceeding a threshold given in advance. Two kinds of scheduling criteria are involved: (i) the total cost comprising the earliness, tardiness, job holding, due date assignment, and batch delivery costs; and (ii) the total cost comprising the earliness, weighted number of tardy jobs, job holding, due date assignment, and batch delivery costs. For each of the problems considered, we show that it is \(\mathcal {NP}\)-hard in the ordinary sense and admits a fully polynomial-time approximation scheme.

Keywords

Scheduling Due date assignment Batch delivery Two agents Dynamic programming 

Notes

Acknowledgements

We thank the Editor, an Associate Editor, and two anonymous referees for their helpful comments on earlier versions of our paper. This paper was supported in part by the National Natural Science Foundation of China under Grant Numbers 11561036, 71501024, 71532007, and 71520107002; and in part by Project funded by China Postdoctoral Science Foundation under Grant Number 2017M612099. Cheng was supported in part by The Hong Kong Polytechnic University under the Fung Yiu King-Wing Hang Bank Endowed Professorship in Business Administration.

References

  1. Agnetis, A., Mirchandani, P. B., Pacciarelli, D., & Pacifici, A. (2004). Scheduling problems with two competing agents. Operations Research, 52, 229–242.CrossRefGoogle Scholar
  2. Agnetis, A., Pacciarelli, D., & Pacifici, A. (2007). Multi-agent single machine scheduling. Annals of Operations Research, 150, 3–15.CrossRefGoogle Scholar
  3. Ahmadizar, F., & Farhadi, S. (2015). Single-machine batch delivery scheduling with job release dates, due windows and earliness, tardiness, holding and delivery costs. Computers and Operations Research, 53, 194–205.CrossRefGoogle Scholar
  4. Assarzadegan, P., & Rasti-Barzoki, M. (2003). Minimizing sum of the due date assignment costs, maximum tardiness and distribution costs in a supply chain scheduling problem. Applied Soft Computing, 47, 343–356.CrossRefGoogle Scholar
  5. Baker, K. R., & Smith, J. C. (2003). A multiple-criterion model for machine scheduling. Journal of Scheduling, 6, 7–16.CrossRefGoogle Scholar
  6. Bilgen, B., & Çelebi, Y. (2013). Integrated production scheduling and distribution planning in dairy supply chain by hybrid modeling. Annals of Operations Research, 211, 55–82.CrossRefGoogle Scholar
  7. Chen, Z. L. (1996). Scheduling and common due date assignment with earliness-tardiness penalties and batch delivery costs. European Journal of Operational Research, 93, 49–60.CrossRefGoogle Scholar
  8. Chen, Z. L. (2010). Integrated production and outbound distribution scheduling: Review and extensions. Operations Research, 58(1), 130–148.CrossRefGoogle Scholar
  9. Cheng, T. C. E., & Gordon, V. S. (1994). Batch delivery scheduling on a single machine. Journal of the Operational Research Society, 45, 1211–1215.CrossRefGoogle Scholar
  10. Cheng, T. C. E., & Kahlbacher, H. G. (1993). Scheduling with delivery and earliness penalty. Asia-Pacific Journal of Operational Research, 10, 145–152.Google Scholar
  11. Dover, O., & Shabtay, D. (2016). Single machine scheduling with two competing agents, arbitrary release dates and unit processing times. Annals of Operations Research, 238, 145–178.CrossRefGoogle Scholar
  12. Gerstl, E., Mor, B., & Mosheiov, G. (2017). Scheduling with two competing agents to minimize total weighted earliness. Annals of Operations Research, 253, 227–245.CrossRefGoogle Scholar
  13. Gordon, V., Proth, J. M., & Chu, C. (2002a). A survey of the state-of-the-art of common due date assignment and scheduling research. European Journal of Operational Research, 139, 1–25.CrossRefGoogle Scholar
  14. Gordon, V., Strusevich, V., & Dolgui, A. (2012). Scheduling with due date assignment under special conditions on job processing. Journal of Scheduling, 15, 447–456.CrossRefGoogle Scholar
  15. Hall, N. G., & Potts, C. N. (2003). Supply chain scheduling: Batching and delivery. Operations Research, 51, 566–584.CrossRefGoogle Scholar
  16. Hermann, J. W., & Lee, C. Y. (1993). On scheduling to minimize earliness-tardiness and batch delivery costs with a common due date. European Journal of Operational Research, 70, 272–288.CrossRefGoogle Scholar
  17. Kaminsky, P., & Hochbaum, D. (2014). Due-date quotation models and algorithms. In J. Y.-T. Leung (Ed.), Handbook of scheduling: Algorithms, models and performance analysis (pp. 20:1–20:22). Boca Raton: CRC Press.Google Scholar
  18. Kovalyov, M. Y., Oulamara, A., & Soukhal, A. (2015). Two-agent scheduling with agent specific batches on an unbounded serial batching machine. Journal of Scheduling, 18, 423–434.CrossRefGoogle Scholar
  19. Li, F., Chen, Z. L., & Tang, L. (2017). Integrated production, inventory and delivery problems: Complexity and algorithms. INFORMS Journal on Computing, 29(2), 232–250.CrossRefGoogle Scholar
  20. Mor, B., & Mosheiov, G. (2011). Single machine batch scheduling with two competing agents to minimize total flowtime. European Journal of Operational Research, 215, 524–531.CrossRefGoogle Scholar
  21. Mor, B., & Mosheiov, G. (2017). A two-agent single machine scheduling problem with due-window assignment and a common flow-allowance. Journal of the Combinatorial Optimization, 33, 1454–1468.CrossRefGoogle Scholar
  22. Perez-Gonzalez, P., & Framinan, J. M. (2014). A common framework and taxonomy for multicriteria scheduling problem with interfering and competing jobs: Multi-agent scheduling problems. European Journal of Operational Research, 235, 1–16.CrossRefGoogle Scholar
  23. Sahni, S. K. (1976). Algorithms for scheduling independent tasks. Journal of the ACM, 23(1), 116–127.CrossRefGoogle Scholar
  24. Selvarajah, E., & Zhang, R. (2014). Supply chain scheduling to minimize holding costs with outsourcing. Annals of Operations Research, 217, 479–490.CrossRefGoogle Scholar
  25. Shabtay, D. (2010). Scheduling and due date assignment to minimize earliness, tardiness, holding, due date assignment and batch delivery costs. International Journal of Production Economics, 123, 235–242.CrossRefGoogle Scholar
  26. Steiner, G., & Zhang, R. (2009). Approximation algorithms for minimizing the total weighted number of late jobs with late deliveries in two-level supply chains. Journal of Scheduling, 12, 565–574.CrossRefGoogle Scholar
  27. Wang, D., Yin, Y., Cheng, S. R., Cheng, T. C. E., & Wu, C. C. (2016). Due date assignment and scheduling on a single machine with two competing agents. International Journal of Production Research, 54, 1152–1169.CrossRefGoogle Scholar
  28. Webster, S., & Baker, K. (1995). Scheduling groups of jobs on a single machine. Operations Research, 43, 692–703.CrossRefGoogle Scholar
  29. Woeginger, G. J. (2000). When does a dynamic programming formulation guarantee the existence of a fully polynomial time approximation scheme (FPTAS)? INFORMS Journal on Computing, 12, 57–75.CrossRefGoogle Scholar
  30. Yin, Y., Cheng, S. R., Cheng, T. C. E., Wang, D. J., & Wu, C. C. (2016a). Just-in-time scheduling with two competing agents on unrelated parallel machines. Omega, 63, 41–47.CrossRefGoogle Scholar
  31. Yin, Y., Cheng, T. C. E., Hsu, C. J., & Wu, C. C. (2013). Single-machine batch delivery scheduling with an assignable common due window. Omega, 41, 216–225.CrossRefGoogle Scholar
  32. Yin, Y., Cheng, T. C. E., Yang, X., & Wu, C. C. (2015). Two-agent single-machine scheduling with unrestricted due date assignment. Computers and Industrial Engineering, 79, 148–155.CrossRefGoogle Scholar
  33. Yin, Y., Wang, D., Wu, C. C., & Cheng, T. C. E. (2016b). \(CON/SLK\) due date assignment and scheduling on a single machine with two agents. Naval Research Logistics, 63, 416–429.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of ScienceKunming University of Science and TechnologyKunmingChina
  2. 2.School of Management and EconomicsUniversity of Electronic Science and Technology of ChinaChengduChina
  3. 3.Business SchoolSichuan UniversityChengduChina
  4. 4.Department of Logistics and Maritime StudiesThe Hong Kong Polytechnic UniversityHung Hom, KowloonHong Kong

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