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Two-stage production scheduling with an option of outsourcing from a remote supplier

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Abstract

This paper studies a two-stage production system with n job orders where each job needs two sequential operations. In addition to the two in-house production facilities, the manufacturer has another option of outsourcing some stage-one operations to a remote outside supplier. The jobs with their stage-one operations outsourced are subject to a batch transportation delay from the outside supplier before their respective stage-two operations can be started in-house. The problem is to design an integrated schedule that considers both the in-house production and the outsourcing with the aim of optimally balancing the outsourcing cost and the makespan. The problem is NP-hard. We have developed an optimal algorithm and a heuristic algorithm to solve the problem, and conducted computational experiments to validate our model and algorithms. Our modeling and algorithm framework can be extended to handle other more general cases such as when the outside supplier has a production facility with a different processing efficiency and when there are many outside suppliers on a spot market.

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References

  1. Agnetis, A., Hall, N.G. & Pacciarelli, D. (2006). Supply chain scheduling: sequence coordination. Discrete Applied Mathematics, 154: 2044–2063

    Article  MATH  MathSciNet  Google Scholar 

  2. Aydinliyim, T. & Vairaktarakis, G.L. (2006). Coordination of outsourcing operations. Working paper

  3. Cai, X., Lee, C.Y. & Vairaktarakis, G.L. (2005). Optimization of processing and delivery decisions involving third-party machines. Nonlinear Analysis, 63: 2269–2278

    Article  Google Scholar 

  4. Chang, Y.C. & Lee, C.Y. (2004). Machine scheduling with job delivery coordination. European Journal of Operational Research, 158: 470–487

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, Z.L. & Li, C.L. (2008). Scheduling with subcontracting options. IIE Transactions, 40: 1171–1184

    Article  Google Scholar 

  6. Chen, Z.L. & Pundoor, G. (2006). Order assignment and scheduling in a supply chain. Operations Research, 54: 555–572

    Article  MathSciNet  Google Scholar 

  7. Chen, Z.L. & Vairaktarakis, G.L. (2005). Integrated scheduling of production and distribution operations. Management Science, 51: 614–628

    Article  MATH  Google Scholar 

  8. Cheng, T.C.E. & Kovalyov, M.Y. (2001). Single supplier scheduling for multiple deliveries. Annals of Operations Research, 107: 51–63

    Article  MATH  MathSciNet  Google Scholar 

  9. Chung, D., Lee, K., Shin, K. & Park, J. (2005). A new approach to job shop scheduling problems with due date constraints considering operation subcontracts. International Journal of Production Economics, 98: 238–250

    Article  Google Scholar 

  10. Dawande, M., Geismar, H.N., Hall, N.G. & Sriskandarajah, C. (2006). Supply chain scheduling: distribution systems. Production and Operations Management, 15: 243–261

    Google Scholar 

  11. Hall, N.G. & Potts, C.N. (2003). Supply chain scheduling: batching and delivery. Operations Research, 51: 566–584

    Article  MathSciNet  Google Scholar 

  12. Hall, N.G. & Potts, C.N. (2005). The coordination of scheduling and batch deliveries. Annals of Operations Research, 135: 41–64

    Article  MATH  MathSciNet  Google Scholar 

  13. Kreipl, S. & Pinedo, M. (2004). Planning and scheduling in supply chains: an overview of issues in practice. Production and Operations Management, 13: 77–92

    Google Scholar 

  14. Kyparisis, G.J. & Koulamas, C. (2006). A note on makespan minimization in two-stage flexible flow shops with uniform machines. European Journal of Operational Research, 175: 1321–1327

    Article  MATH  Google Scholar 

  15. Lee, C.Y. & Vairaktarakis, G.L. (1994). Minimizing makespan in hybrid flowshops. Operations Research Letters, 16: 149–158

    Article  MATH  MathSciNet  Google Scholar 

  16. Lee, C.Y. & Chen, Z.L. (2001). Machine scheduling with transportation considerations. Journal of Scheduling, 4: 3–24

    Article  MATH  MathSciNet  Google Scholar 

  17. Lee, C.Y., Leung, J.Y.T. & Yu, G. (2006). Two machine scheduling under disruptions with transportation considerations. Journal of Scheduling, 9: 35–48

    Article  MATH  MathSciNet  Google Scholar 

  18. Lee, I.S. & Sung, C.S. (2008a). Minimizing due date related measures for a single machine scheduling problem with outsourcing allowed. European Journal of Operational Research, 186: 931–952

    Article  MATH  MathSciNet  Google Scholar 

  19. Lee, I.S. & Sung, C.S. (2008b). Single machine scheduling with outsourcing allowed. International Journal of Production Economics, 101: 623–634

    Article  Google Scholar 

  20. Lee, Y.H., Jeong, C.S. & Moon, C. (2002). Advanced planning and scheduling with outsourcing in manufacturing supply chain. Computers and Industrial Engineering, 43: 351–374

    Article  Google Scholar 

  21. Lenstra, J.K., Rinnooy Kan, A.H.G. & Brucker, P. (1977). Complexity of machine scheduling problems. Annuals of Discrete Mathematics, 1: 343–362

    Article  MathSciNet  Google Scholar 

  22. Li, C.L. & Xiao, W.Q. (2004). Lot streaming with supplier-manufacturer coordination. Naval Research Logistics, 51: 522–542

    Article  MATH  MathSciNet  Google Scholar 

  23. Li, C.L., Vairaktarakis, G.L. & Lee, C.Y. (2005). Machine scheduling with deliveries to two customer locations. European Journal of Operational Research, 164: 39–51

    Article  MATH  MathSciNet  Google Scholar 

  24. Oguz, C. & Ercan, M. (2005). A genetic algorithm for hybrid flow-shop scheduling ith multiprocessor tasks. Journal of Scheduling, 8: 323–351

    Article  MATH  MathSciNet  Google Scholar 

  25. Qi, X. (2005). A logistics scheduling model: inventory cost reduction by batching. Naval Research Logistics, 52: 312–320

    Article  MATH  MathSciNet  Google Scholar 

  26. Qi, X. (2006). A logistics scheduling model: scheduling and transshipment for two processing centers. IIE Transactions, 38: 609–618

    Article  Google Scholar 

  27. Qi, X. (2008). Coordinated logistics scheduling for in-house production and outsourcing. IEEE Transactions on Automation Science and Engineering, 5: 188–192

    Article  Google Scholar 

  28. Ruiz-Torres, A.J., Ho, J.C. & Lopez, F.J. (2006). Generating Pareto schedules with outsource and internal parallel resources. International Journal of Production Economics, 103: 810–825

    Article  Google Scholar 

  29. Sundararaghavan, P.S., Kunnathur, A.S. & Viswanathan, I. (1997). Minimizing makespan in parallel flowshops. Journal of the Operational Research Society, 48: 834–842

    Article  MATH  Google Scholar 

  30. Tang, L., Xuan, H. & Liu, J. (2006). A new Lagrangian relaxation algorithm for hybrid lowshop scheduling to minimize total weighted completion time. Computers & Operations Research, 33: 3344–3359

    Article  MATH  Google Scholar 

  31. Vairaktarakis, G.L. (2006a). Non-cooperative outsourcing games. Working paper

  32. Vairaktarakis, G.L. (2006b). Cooperative strategies for manufacturing planning with negotiable third-party capacity. Working paper.

  33. Wang, H. & Lee, C.Y. (2005). Production and transport logistics scheduling with two transport mode choices. Naval Research Logistics, 52: 796–809

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Xiangtong Qi.

Additional information

This work was supported in part by the Hong Kong RGC CERG under grant No. 618606. Part of this paper was presented in the 5th International Conference on Service Systems and Service Management, Melbourne, Australia.

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Qi, X. Two-stage production scheduling with an option of outsourcing from a remote supplier. J. Syst. Sci. Syst. Eng. 18, 1–15 (2009). https://doi.org/10.1007/s11518-009-5094-1

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  • DOI: https://doi.org/10.1007/s11518-009-5094-1

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