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Exact and Approximate Cost Functions for Product Aggregates

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  • Paul Zipkin

    (Columbia University)

Abstract

We show that certain large, multiproduct problems can be well approximated by smaller models of the same form, representing only one aggregate product (or a few such products). This reduction follows from a new technique to approximate the minimal cost of a special allocation or "disaggregation" problem, by a simple, closed-form aggregate cost function. This function, moreover, has the same form as the cost functions for the original, individual products. For special cases the "approximation" is exact. (This latter result is related to economic-theoretic research on aggregation with homothetic preferences.) The results are applied to a one-stage, multiperiod, multi-item production smoothing model, and then to a similar model of a two-stage system, yielding a reduction in the number of items to one or to relatively few.

Suggested Citation

  • Paul Zipkin, 1982. "Exact and Approximate Cost Functions for Product Aggregates," Management Science, INFORMS, vol. 28(9), pages 1002-1012, September.
    • Handle: RePEc:inm:ormnsc:v:28:y:1982:i:9:p:1002-1012
    DOI: 10.1287/mnsc.28.9.1002
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    Citations

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    Cited by:

    1. Bitran, Gabriel R. & Tirupati, Devanath., 1989. "Hierarchical production planning," Working papers 3017-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Yossi Aviv & Awi Federgruen, 2001. "Design for Postponement: A Comprehensive Characterization of Its Benefits Under Unknown Demand Distributions," Operations Research, INFORMS, vol. 49(4), pages 578-598, August.
    3. Shapiro, Jeremy F., 1939-, 1998. "Bottom-up vs. top-down approaches to supply chain management and modeling," Working papers WP 4017-98., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Yossi Aviv & Awi Federgruen, 2001. "Capacitated Multi-Item Inventory Systems with Random and Seasonally Fluctuating Demands: Implications for Postponement Strategies," Management Science, INFORMS, vol. 47(4), pages 512-531, April.
    5. Sali, Mustapha & Ghrab, Yahya & Chatras, Clément, 2023. "Optimal product aggregation for sales and operations planning in mass customisation context," International Journal of Production Economics, Elsevier, vol. 263(C).
    6. Özalp Özer, 2003. "Replenishment Strategies for Distribution Systems Under Advance Demand Information," Management Science, INFORMS, vol. 49(3), pages 255-272, March.

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