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Optimality and Computation of (\sigma, S) Policies in the Multi-Item Infinite Horizon Inventory Problem

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  • Ellis L. Johnson

    (Yale University)

Abstract

A multi-item inventory system with periodic review, single set-up cost K plus linear ordering cost c for changing stock levels, and holding and shortage cost l(x) for being in stock position x at the beginning of a period is considered. Demand in any period is assumed to be \xi with probability \phi (x,\xi ), where x is the stock level at the beginning of the period. The infinite horizon optimum policies found consist of ordering up to S for any point x in \sigma, the reorder region, and not ordering at x not in \sigma. A computational procedure is given, bounds are derived, and, for further assumptions on l, \sigma is further characterized.

Suggested Citation

  • Ellis L. Johnson, 1967. "Optimality and Computation of (\sigma, S) Policies in the Multi-Item Infinite Horizon Inventory Problem," Management Science, INFORMS, vol. 13(7), pages 475-491, March.
    • Handle: RePEc:inm:ormnsc:v:13:y:1967:i:7:p:475-491
    DOI: 10.1287/mnsc.13.7.475
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    Cited by:

    1. Jifan Zhang & Salih Tutun & Samira Fazel Anvaryazdi & Mohammadhossein Amini & Durai Sundaramoorthi & Hema Sundaramoorthi, 2024. "Management of resource sharing in emergency response using data-driven analytics," Annals of Operations Research, Springer, vol. 339(1), pages 663-692, August.
    2. Lien-Chieh Lee & Yuan Wang & Guozhu Mao & Jian Zuo & Zhibin Wang & Musa J. Sanyang & George Zillante & Yun Sun & Tan Xu, 2021. "Spatial characteristic of environmental protection businesses: a study of A-Share Listed Environmental Companies in China," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(12), pages 18598-18617, December.
    3. Yunxia Zhu & Milind Dawande & Chelliah Sriskandarajah, 2011. "Value of Local Cash Reuse: Inventory Models for Medium-Size Depository Institutions Under the New Federal Reserve Policy," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 508-524, October.

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