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Optimal Capacity Expansion with Inventory

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  • M. R. Rao

    (University of Rochester, Rochester, New York)

Abstract

In a given region over a finite time horizon, a known nondecreasing demand for a single commodity has to be satisfied by production in that period and/or by inventory from the previous period. There is no initial production capacity or inventory, but the capacity and production may be increased at the beginning of each discrete time period. We assume that the capacity and production are nondecreasing over the time periods. The total time discounted costs to be minimized include the capacity expansion, production, inventory carrying, and idle capacity costs, which are assumed to be concave. The problem is to determine an optimal capacity expansion and production schedule, together with the associated inventory carrying and idle capacity schedules. Based on some interesting properties of an optimal solution, we devise an efficient dynamic programming algorithm to solve this problem.

Suggested Citation

  • M. R. Rao, 1976. "Optimal Capacity Expansion with Inventory," Operations Research, INFORMS, vol. 24(2), pages 291-300, April.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:2:p:291-300
    DOI: 10.1287/opre.24.2.291
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    Cited by:

    1. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Lee, Chia-Yen & Charles, Vincent, 2022. "A robust capacity expansion integrating the perspectives of marginal productivity and capacity regret," European Journal of Operational Research, Elsevier, vol. 296(2), pages 557-569.
    3. Alexandar Angelus & Evan L. Porteus, 2002. "Simultaneous Capacity and Production Management of Short-Life-Cycle, Produce-to-Stock Goods Under Stochastic Demand," Management Science, INFORMS, vol. 48(3), pages 399-413, March.
    4. Josh Reed & Bo Zhang, 2017. "Managing capacity and inventory jointly for multi-server make-to-stock queues," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 61-94, June.
    5. Yong Tan & Kamran Moinzadeh & Vijay S. Mookerjee, 2005. "Optimal Processing Policies for an e-Commerce Web Server," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 99-110, February.
    6. Xiuli Chao & Hong Chen & Shaohui Zheng, 2009. "Dynamic Capacity Expansion for a Service Firm with Capacity Deterioration and Supply Uncertainty," Operations Research, INFORMS, vol. 57(1), pages 82-93, February.
    7. Sampath Rajagopalan & Jayashankar M. Swaminathan, 2001. "A Coordinated Production Planning Model with Capacity Expansion and Inventory Management," Management Science, INFORMS, vol. 47(11), pages 1562-1580, November.

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