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Allocating Production Capacity Among Multiple Products

Author

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  • Paul Glasserman

    (Columbia Business School, New York, New York)

Abstract

We consider the problem of allocating production capacity among multiple items, assuming that a fixed proportion of overall capacity can be dedicated exclusively to the production of each item. Given a capacity allocation, production of each item follows a base-stock policy, i.e., each demand triggers a replenishment order to restore safety stocks to target levels. We present procedures for choosing base-stock levels and capacity allocations that are asymptotically optimal. Our objective is to minimize holding and backorder costs, or to minimize holding costs subject to a service-level constraint. Asymptotic optimality refers to large backorder penalties or stringent service-level constraints. Numerical results indicate that our rules perform very well even far from the asymptotic regime. A further approximation step results in allocation rules based on heavy-traffic limits; these, too, perform well.

Suggested Citation

  • Paul Glasserman, 1996. "Allocating Production Capacity Among Multiple Products," Operations Research, INFORMS, vol. 44(5), pages 724-734, October.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:5:p:724-734
    DOI: 10.1287/opre.44.5.724
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    Citations

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    Cited by:

    1. Jun Tong & Xiaotao Zhou & Lei Lei, 2024. "Priority-Based Capacity Allocation for Hierarchical Distributors with Limited Production Capacity," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    2. Oben Ceryan & Ozge Sahin & Izak Duenyas, 2013. "Dynamic Pricing of Substitutable Products in the Presence of Capacity Flexibility," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 86-101, April.
    3. Pinto, Roberto, 2012. "Stock rationing under service level constraints in a vertically integrated distribution system," International Journal of Production Economics, Elsevier, vol. 136(1), pages 231-240.
    4. Nicholas G. Hall & Zhixin Liu, 2010. "Capacity Allocation and Scheduling in Supply Chains," Operations Research, INFORMS, vol. 58(6), pages 1711-1725, December.
    5. Solak, Senay & Li, Zhuoxin & Gumus, Mehmet & Zhuo, Yueran, 2024. "A budgeting resource allocation model for capacity expansion," International Journal of Production Economics, Elsevier, vol. 273(C).
    6. Gregory A. DeCroix & Antonio Arreola-Risa, 1998. "Optimal Production and Inventory Policy for Multiple Products Under Resource Constraints," Management Science, INFORMS, vol. 44(7), pages 950-961, July.
    7. Tang, Dong, 2011. "Managing finished-goods inventory under capacitated delayed differentiation," Omega, Elsevier, vol. 39(5), pages 481-492, October.
    8. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    9. Ioannis Ch. Paschalidis & Yong Liu, 2003. "Large Deviations-Based Asymptotics for Inventory Control in Supply Chains," Operations Research, INFORMS, vol. 51(3), pages 437-460, June.
    10. Jian Yang & Zhaoqiong Qin, 2007. "Capacitated Production Control with Virtual Lateral Transshipments," Operations Research, INFORMS, vol. 55(6), pages 1104-1119, December.
    11. Bora Kat & Zeynep Avṣar, 2011. "Using aggregate fill rate for dynamic scheduling of multi-class systems," Annals of Operations Research, Springer, vol. 182(1), pages 87-117, January.
    12. Dimitris Bertsimas & Ioannis Ch. Paschalidis, 2001. "Probabilistic Service Level Guarantees in Make-to-Stock Manufacturing Systems," Operations Research, INFORMS, vol. 49(1), pages 119-133, February.
    13. James A. Rappold & John A. Muckstadt, 2000. "A computationally efficient approach for determining inventory levels in a capacitated multiechelon production‐distribution system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 377-398, August.
    14. Refael Hassin & Yair Y. Shaki & Uri Yovel, 2015. "Optimal service‐capacity allocation in a loss system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(2), pages 81-97, March.
    15. de Kok, Ton G., 2000. "Capacity allocation and outsourcing in a process industry," International Journal of Production Economics, Elsevier, vol. 68(3), pages 229-239, December.
    16. Kaijie Zhu & Ulrich W. Thonemann, 2009. "Coordination of pricing and inventory control across products," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 175-190, March.
    17. Bintong Chen & Charles L. Munson, 2004. "Resource allocation with lumpy demand: To speed or not to speed?," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 363-385, April.
    18. David A. Goldberg & Martin I. Reiman & Qiong Wang, 2021. "A Survey of Recent Progress in the Asymptotic Analysis of Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1718-1750, June.
    19. Weihua Zhou & Chung‐Yee Lee & David Wu, 2011. "Optimal control of a capacitated inventory system with multiple demand classes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(1), pages 43-58, February.
    20. F. Kleintje-Ell & G. Kiesmüller, 2015. "Cost minimising order schedules for a capacitated inventory system," Annals of Operations Research, Springer, vol. 229(1), pages 501-520, June.

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