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A Production-Inventory Control Model with a Mixture of Back-Orders and Lost-Sales

Author

Listed:
  • B. T. Doshi

    (Rutgers University)

  • F. A. van der Duyn Schouten

    (Free University, Amsterdam)

  • J. J. Talman

    (Free University, Amsterdam)

Abstract

We consider a production-inventory control model of finite capacity, in which backordering up to a certain level is allowed. We assume that there exist two possible production rates. The control is based on two critical stock-levels and prescribes to change the production rate used only when one of these levels is reached. A fixed cost is associated with every switch-over. The rate at which customers arrive and the distribution of the demand of an arriving customer depend on the production rate used at that moment. A formula for the long-run average expected costs per unit time is obtained as a function of the chosen critical levels. From this formula we derive expressions for various interesting operating characteristics of this system, amongst which are the joint stationary distribution of the processes describing the production rate used and the inventory of the system and the average number of switch-overs and lost-sales per unit time.

Suggested Citation

  • B. T. Doshi & F. A. van der Duyn Schouten & J. J. Talman, 1978. "A Production-Inventory Control Model with a Mixture of Back-Orders and Lost-Sales," Management Science, INFORMS, vol. 24(10), pages 1078-1087, June.
    • Handle: RePEc:inm:ormnsc:v:24:y:1978:i:10:p:1078-1087
    DOI: 10.1287/mnsc.24.10.1078
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    Cited by:

    1. Lee, Shine-Der & Lan, Shu-Chuan, 2013. "Production lot sizing with a secondary outsourcing facility," International Journal of Production Economics, Elsevier, vol. 141(1), pages 414-424.
    2. van Ooijen, H. P. G. & Bertrand, J. W. M., 2003. "The effects of a simple arrival rate control policy on throughput and work-in-process in production systems with workload dependent processing rates," International Journal of Production Economics, Elsevier, vol. 85(1), pages 61-68, July.
    3. Yonit Barron & David Perry & Wolfgang Stadje, 2016. "A make-to-stock production/inventory model with MAP arrivals and phase-type demands," Annals of Operations Research, Springer, vol. 241(1), pages 373-409, June.
    4. Jim (Junmin) Shi & Michael N. Katehakis & Benjamin Melamed & Yusen Xia, 2014. "Production-Inventory Systems with Lost Sales and Compound Poisson Demands," Operations Research, INFORMS, vol. 62(5), pages 1048-1063, October.
    5. Van der Duyn Schouten, F. A. & Vanneste, S. G., 1995. "Maintenance optimization of a production system with buffer capacity," European Journal of Operational Research, Elsevier, vol. 82(2), pages 323-338, April.
    6. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    7. O. Boxma & A. Löpker & D. Perry, 2016. "On a make-to-stock production/mountain modeln with hysteretic control," Annals of Operations Research, Springer, vol. 241(1), pages 53-82, June.
    8. Pablo Azcue & Esther Frostig & Nora Muler, 2023. "Optimal Strategies in a Production Inventory Control Model," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-43, March.

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