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An Extension to Modigliani and Hohn's Planning Horizons Results

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  • Zvi Lieber

    (Tel Aviv University, Israel)

Abstract

This paper deals with the planning horizon issues of the problem of finding the optimal production schedule over a [0, T] period, for a product having: (1) deterministic demand, (2) strictly convex production costs, and (3) linear holding and back-logging costs. A set of solutions defined as extrapolations is defined, and a property of nonintersection of extrapolations is proved. Using this property uniqueness and planning horizon theorems are proved. It is shown that the reason for the planning horizons is the jump (discontinuity) in the derivative of the inventory cost function when inventory is zero. In addition, the paper deals with the following question: What kinds of changes (variations) in demand may occur such that the optimal solution (production schedule) on some time interval will remain unchanged? This question is associated with the following one: What information is needed about demand in order that the optimal solution on some time interval may be found?

Suggested Citation

  • Zvi Lieber, 1973. "An Extension to Modigliani and Hohn's Planning Horizons Results," Management Science, INFORMS, vol. 20(3), pages 319-330, November.
    • Handle: RePEc:inm:ormnsc:v:20:y:1973:i:3:p:319-330
    DOI: 10.1287/mnsc.20.3.319
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    Cited by:

    1. Nuthall, Peter L., 1980. "A Survey of Methods for Determining A Planning Horizon," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 48(01), pages 1-15, April.
    2. S. P. Sethi & H. Yan & H. Zhang & Q. Zhang, 2002. "Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey," Manufacturing & Service Operations Management, INFORMS, vol. 4(2), pages 133-170.
    3. 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.
    4. Riddalls, C. E. & Bennett, S., 2001. "The optimal control of batched production and its effect on demand amplification," International Journal of Production Economics, Elsevier, vol. 72(2), pages 159-168, July.

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