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Taut-string solution of the equilibrium no-lag Clark-Scarf serial inventory problem

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  • Arthur Veinott

Abstract

This note is dedicated in memoriam to Cyrus Derman with whom I had the privilege of studying operations research. He was my teacher, mentor, thesis advisor, advocate, collaborator and friend. He and his colleagues guided me through the mathematical worlds of optimization, stochastic models, dynamic programming and their applications in OR. He was a gifted creative mathematician and operations researcher who profoundly influenced my life. Veinott (Manag. Sci. 17(9):547–567, 1971 ) shows how to reduce the one-period equilibrium version of the Clark-Scarf (Manag. Sci. 6(4):475–490, 1960 ) serial-facility inventory problem with no delivery lead time between facilities to an instance of Veinott’s (Manag. Sci. 17(9):547–567, 1971 ) theory of d-majorized network flows. That instance can be solved graphically with the aid of the taut-string solution for the dual problem. This expository note elaborates on this work by giving an example and showing that the optimal amount to stock at the most downstream facility rises as the distribution F of demand there rises stochastically. In addition, the optimal amount to stock at every other facility rises as the spread of F rises. The multi-period equilibrium version is also solved. Copyright Springer Science+Business Media, LLC 2013

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  • Arthur Veinott, 2013. "Taut-string solution of the equilibrium no-lag Clark-Scarf serial inventory problem," Annals of Operations Research, Springer, vol. 208(1), pages 27-30, September.
    • Handle: RePEc:spr:annopr:v:208:y:2013:i:1:p:27-30:10.1007/s10479-012-1183-5
    DOI: 10.1007/s10479-012-1183-5
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    1. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    2. Stuart A. Bessler & Arthur F. Veinott, 1966. "Optimal policy for a dynamic multi‐echelon inventory model," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 13(4), pages 355-389, December.
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