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Infinite Horizon Production Planning in Time-Varying Systems with Convex Production and Inventory Costs

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  • Robert L. Smith

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

  • Rachel Q. Zhang

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

Abstract

We consider the planning of production over the infinite horizon in a system with time-varying convex production and inventory holding costs. This production lot size problem is frequently faced in industry where a forecast of future demand must be made and production is to be scheduled based on the forecast. Because forecasts of the future are costly and difficult to validate, a firm would like to minimize the number of periods into the future it needs to forecast in order to make an optimal production decision today. In this paper, we first prove that under very general conditions finite horizon versions of the problem exist that lead to an optimal production level at any decision epoch. In particular, we show it suffices for the first period infinite horizon production decision to solve for a horizon that exceeds the longest time interval over which it can prove profitable to carry inventory. We then develop a closed-form expression for computing such a horizon and provide a simple finite algorithm to recursively compute an infinite horizon optimal production schedule.

Suggested Citation

  • Robert L. Smith & Rachel Q. Zhang, 1998. "Infinite Horizon Production Planning in Time-Varying Systems with Convex Production and Inventory Costs," Management Science, INFORMS, vol. 44(9), pages 1313-1320, September.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:9:p:1313-1320
    DOI: 10.1287/mnsc.44.9.1313
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    References listed on IDEAS

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    Cited by:

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    2. Huang, Kai & Ahmed, Shabbir, 2010. "A stochastic programming approach for planning horizons of infinite horizon capacity planning problems," European Journal of Operational Research, Elsevier, vol. 200(1), pages 74-84, January.
    3. A Diponegoro & B R Sarker, 2007. "Operations policy for a supply chain system with fixed-interval delivery and linear demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(7), pages 901-910, July.
    4. Konur, Dinçer & Geunes, Joseph, 2016. "Supplier wholesale pricing for a retail chain: Implications of centralized vs. decentralized retailing and procurement under quantity competition," Omega, Elsevier, vol. 65(C), pages 98-110.
    5. Torpong Cheevaprawatdomrong & Robert L. Smith, 2004. "Infinite Horizon Production Scheduling in Time-Varying Systems Under Stochastic Demand," Operations Research, INFORMS, vol. 52(1), pages 105-115, February.
    6. Archis Ghate & Robert L. Smith, 2009. "Optimal Backlogging Over an Infinite Horizon Under Time-Varying Convex Production and Inventory Costs," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 362-368, June.
    7. Archis Ghate & Robert L. Smith, 2013. "A Linear Programming Approach to Nonstationary Infinite-Horizon Markov Decision Processes," Operations Research, INFORMS, vol. 61(2), pages 413-425, April.
    8. Erica L. Plambeck, 2013. "OM Forum —Operations Management Challenges for Some “Cleantech” Firms," Manufacturing & Service Operations Management, INFORMS, vol. 15(4), pages 527-536, October.
    9. Herbon, Avi & Khmelnitsky, Eugene & Maimon, Oded, 2004. "Effective information horizon length in measuring off-line performance of stochastic dynamic systems," European Journal of Operational Research, Elsevier, vol. 157(3), pages 688-703, September.
    10. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    11. Li, Xiang & Li, Yongjian & Cai, Xiaoqiang, 2013. "Double marginalization and coordination in the supply chain with uncertain supply," European Journal of Operational Research, Elsevier, vol. 226(2), pages 228-236.
    12. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.

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