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Multicommodity Production Planning: Qualitative Analysis and Applications

Author

Listed:
  • Iara Ciurria-Infosino

    (Resource Analysis Branch, U.S. Air Force/A9RP, Pentagon, Washington, DC 20330)

  • Daniel Granot

    (Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada)

  • Frieda Granot

    (Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada)

  • Arthur F. Veinott

    (Formerly at the Department of Management Science and Engineering, Stanford University, Stanford, California)

Abstract

We develop a qualitative analysis theory for the convex-cost dynamic multicommodity production planning problem, which can be used, without performing any computational work, to provide invaluable insight to managers when faced with the task of deciding how to respond to changes in problem environment. We first formulate the problem as a multicommodity flow problem with parameters associated with each arc–commodity pair. We then reduce the problem to an equivalent single-commodity flow problem and develop a complete characterization of conformality among production, sales, and inventory activities in various instances of the problem. By combining the conformality characterizations with the monotonicity theory of Granot and Veinott [Granot F, Veinott AF Jr (1985) Substitutes, complements and ripples in network flow. Math. Oper. Res. 10:471–497] for single-commodity problems, we study the effects of changes in problem environment on optimal production, sales, and inventory schedules in the multicommodity problem. Numerous applications are presented and analyzed.

Suggested Citation

  • Iara Ciurria-Infosino & Daniel Granot & Frieda Granot & Arthur F. Veinott, 2015. "Multicommodity Production Planning: Qualitative Analysis and Applications," Manufacturing & Service Operations Management, INFORMS, vol. 17(4), pages 589-607, October.
    • Handle: RePEc:inm:ormsom:v:17:y:2015:i:4:p:589-607
    DOI: 10.1287/msom.2015.0549
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    References listed on IDEAS

    as
    1. Arthur F. Veinott, Jr., 1964. "Production Planning with Convex Costs: A Parametric Study," Management Science, INFORMS, vol. 10(3), pages 441-460, April.
    2. Alan S. Manne, 1957. "A Note on the Modigliani-Hohn Production Smoothing Model," Management Science, INFORMS, vol. 3(4), pages 371-379, July.
    3. Arthur F. Veinott, 1969. "Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems," Operations Research, INFORMS, vol. 17(2), pages 262-291, April.
    4. Shoshana Anily, 1991. "Multi-Item Replenishment and Storage Problem (MIRSP): Heuristics and Bounds," Operations Research, INFORMS, vol. 39(2), pages 233-243, April.
    5. Willard I. Zangwill, 1969. "A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System--A Network Approach," Management Science, INFORMS, vol. 15(9), pages 506-527, May.
    6. Edward H. Bowman, 1956. "Production Scheduling by the Transportation Method of Linear Programming," Operations Research, INFORMS, vol. 4(1), pages 100-103, February.
    7. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    8. John A. Muckstadt & Robin O. Roundy, 1987. "Multi-Item, One-Warehouse, Multi-Retailer Distribution Systems," Management Science, INFORMS, vol. 33(12), pages 1613-1621, December.
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