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Optimal Backlogging Over an Infinite Horizon Under Time-Varying Convex Production and Inventory Costs

Author

Listed:
  • Archis Ghate

    () (Industrial Engineering, University of Washington, Seattle, Washington 98195)

  • Robert L. Smith

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

Abstract

We consider an infinite horizon production planning problem with nonstationary, convex production and inventory costs. Backlogging is allowed, unlike as in related previous work, and inventory cost is interpreted as backlogging cost when inventory is negative. We create finite horizon truncations of the infinite horizon problem and employ classic results on convex production planning to derive a closed-form formula for the minimum forecast horizon. We show that optimal production levels are monotonically increasing in the length of horizon, leading to solution convergence and a rolling horizon procedure for delivering an infinite horizon optimal production plan. The minimum forecast horizon formula is employed to illustrate how cost parameters affect how far one must look into the future to make an infinite horizon optimal decision today.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormsom:v:11:y:2009:i:2:p:362-368
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    File URL: http://dx.doi.org/10.1287/msom.1080.0218
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    References listed on IDEAS

    as
    1. 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.
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    6. 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.
    7. Suresh Chand & Suresh P. Sethi & Gerhard Sorger, 1992. "Forecast Horizons in the Discounted Dynamic Lot Size Model," Management Science, INFORMS, vol. 38(7), pages 1034-1048, July.
    8. Howard C. Kunreuther & Thomas E. Morton, 1974. "General Planning Horizons for Production Smoothing with Deterministic Demands," Management Science, INFORMS, vol. 20(7), pages 1037-1046, March.
    9. Dwight R. Lee & Daniel Orr, 1977. "Further Results on Planning Horizons in the Production Smoothing Problem," Management Science, INFORMS, vol. 23(5), pages 490-498, January.
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    11. Joseph D. Blackburn & Howard Kunreuther, 1974. "Planning Horizons for the Dynamic Lot Size Model with Backlogging," Management Science, INFORMS, vol. 21(3), pages 251-255, November.
    12. Awi Federgruen & Michal Tzur, 1991. "A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time," Management Science, INFORMS, vol. 37(8), pages 909-925, August.
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