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Journal of Combinatorial Optimization

, Volume 37, Issue 1, pp 319–329 | Cite as

Two-stage medical supply chain scheduling with an assignable common due window and shelf life

  • Long Zhang
  • Yuzhong ZhangEmail author
  • Qingguo Bai
Article
  • 135 Downloads

Abstract

This paper considers a two-stage medical supply chain scheduling problem from the perspective of the medicine manufacturer in which jobs have an assignable common due window and shelf life. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. The job’s holding time, which is the time interval that passes from the completion time of the job to the delivery date of the job in the batch, must be no more than its shelf life. The objective is to minimize the total cost comprising earliness, weighted number of tardy jobs, holding time, due window starting time, window size, and batch delivery. We first show that the problem is NP-hard and then provide a pseudo-polynomial-time algorithm. We also prove that a special case of the problem can be optimally solved in polynomial time.

Keywords

Medical supply chain scheduling Shelf life Due window assignment NP-hard Pseudo-polynomial-time algorithm 

Notes

Acknowledgements

The authors would like to thank the Editor-in-Chief, Professor Ding-Zhu Du, his Editorial Board, and the two anonymous referees for their valuable comments and suggestions which have significantly improved the quality of the paper. This work was supported by the National Science Foundation of China under Grants 11771251 and 71771138, and the Natural Science Foundation of Shandong Province of China under grants ZR2015GZ009 and ZR2017MG009).

References

  1. Assarzadegan P, Rasti-Barzoki M (2016) Minimizing sum of the due date assignment costs, maximum tardiness and distribution costs in a supply chain scheduling problem. Appl Soft Comput 47:343–356CrossRefGoogle Scholar
  2. Bilgen B, Çelebi Y (2013) Integrated production scheduling and distribution planning in dairy supply chain by hybrid modelling. Ann Oper Res 211:55–82CrossRefzbMATHGoogle Scholar
  3. Chen Z (1996) Scheduling and common due date assignment with earliness-tardiness penalties and batch delivery costs. Eur J Oper Res 93:49–60CrossRefzbMATHGoogle Scholar
  4. Cheng T (1988) Optimal common due-date with limited completion time deviation. Comput Oper Res 15:91–96CrossRefzbMATHGoogle Scholar
  5. Entrup M, Grunow M, Günther H, Beek T (2005) An milp modelling approach for shelf life integrated planning in yoghurt production. Oper Res Proc 33:67–75CrossRefGoogle Scholar
  6. Fan J, Lu X (2015) Supply chain scheduling problem in the hospital with periodic working time on a single machine. J Comb Optim 30:892–905MathSciNetCrossRefzbMATHGoogle Scholar
  7. Gong H, Zhang B, Peng W (2015) Scheduling and common due date assignment on a single parallel-batching machine with batch delivery. Discrete Dyn Nat Soc 2015:1–7MathSciNetCrossRefGoogle Scholar
  8. Günther H, Beek P, Grunow M, Entrup M, Zhang S (2006) An milp modelling approach for shelf life integrated planning and scheduling in scalded sausage production. Deutscher Universitäts-Verlag, Wiesbaden, pp 163–188Google Scholar
  9. Hammoudan Z, Grunder O, Boudouh T, El Moudni A (2016) A coordinated scheduling of delivery and inventory in a multi-location hospital supplied with a central pharmacy. Logist Res 9:1–18CrossRefGoogle Scholar
  10. Hermann J, Lee C (1993) On scheduling to minimize earliness-tardiness and batch delivery costs with a common due date. Eur J Oper Res 70:272–288CrossRefzbMATHGoogle Scholar
  11. Hsu C, Yang S, Yang D (2011) Two due date assignment problems with position-dependent processing time on a single-machine. Comput Ind Eng 60:796–800CrossRefGoogle Scholar
  12. Liu L, Tang G, Fan B, Wang X (2015) Two-person cooperative games on scheduling problems in outpatient pharmacy dispensing process. J Comb Optim 30:938–948MathSciNetCrossRefzbMATHGoogle Scholar
  13. Mohammadi M, Musa S, Bahreininejad A (2015) Optimization of economic lot scheduling problem with backordering and shelf-life considerations using calibrated metaheuristic algorithms. Appl Math Comput 251:404–422MathSciNetzbMATHGoogle Scholar
  14. Mor B, Mosheiov G (2017) A two-agent single machine scheduling problem with due-window assignment and a common flow-allowance. J Comb Optim 33:1454–1468MathSciNetCrossRefzbMATHGoogle Scholar
  15. Nesterov Y, Nemirovski A (1994) Interior point polynomial methods in convex programming: theory and application. SIAM Stud Appl Math 13:387–402Google Scholar
  16. Shabtay D, Itskovich Y, Yedidsion L, Oron D (2010) Optimal due date assignment and resource allocation in a group technology scheduling environment. Comput Oper Res 37:2218–2228MathSciNetCrossRefzbMATHGoogle Scholar
  17. Wang D, Yin Y, Cheng T (2017) A bicriterion approach to common flow allowances due window assignment and scheduling with controllable processing times. Nav Res Logist 64:41–63MathSciNetCrossRefGoogle Scholar
  18. Wang Y (2011) Analysis of the management of medicine logistics in China. Guide China Med 9:371–373 (in Chinese)Google Scholar
  19. Yan C, Liao Y, Banerjee A (2013) Multi-product lot scheduling with backordering and shelf-life constraints. Omega 41:510–516CrossRefGoogle Scholar
  20. Yeung W, Choi T, Cheng T (2010) Optimal scheduling of a single-supplier single-manufacturer supply chain with common due windows. IEEE Trans Autom Control 55:2767–2777MathSciNetCrossRefzbMATHGoogle Scholar
  21. Yin Y, Cheng T, Xu D, Wu C (2012) Common due date assignment and scheduling with a rate-modifying activity to minimize the due date, earliness, tardiness, holding, and batch delivery cost. Comput Ind Eng 63:223–234CrossRefGoogle Scholar
  22. Yin Y, Cheng T, Hsu C, Wu C (2013a) Single-machine batch delivery scheduling with an assignable common due window. Omega 41:216–225CrossRefGoogle Scholar
  23. Yin Y, Cheng T, Wang J, Wu C (2013b) Single-machine common due window assignment and scheduling to minimize the total cost. Discrete Optim 10:42–53MathSciNetCrossRefzbMATHGoogle Scholar
  24. Yin Y, Wang D, Cheng T, Wu C (2016a) Bi-criterion single-machine scheduling and due-window assignment with common flow allowances and resource-dependent processing times. J Oper Res Soc 67:1169–1183CrossRefGoogle Scholar
  25. Yin Y, Wang Y, Cheng T, Wang D, Wu C (2016b) Two-agent single-machine scheduling to minimize the batch delivery cost. Comput Ind Eng 92:16–30CrossRefGoogle Scholar
  26. Zhang L (2017) Two-stage supply chain scheduling with a limited holding time. Oper Res T 21:126–134 (in Chinese) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institute of Operations Research, School of ManagementQufu Normal UniversityRizhaoChina

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