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Optimal Inventory Policies When Sales Are Discretionary



Inventory models customarily assume that demand is fully satisfied if sufficient stock is available. We analyze the form of the optimal inventory policy if the inventory manager can choose to meet a fraction of the demand. Under classical conditions we show that the optimal policy is again of the (S,s) form. The analysis makes use of a novel property of K-concave functions.

Suggested Citation

  • Herbert E. Scarf, 2000. "Optimal Inventory Policies When Sales Are Discretionary," Cowles Foundation Discussion Papers 1270, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1270
    Note: CFP 1104.

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    References listed on IDEAS

    1. Suresh P. Sethi & Feng Cheng, 1997. "Optimality of ( s , S ) Policies in Inventory Models with Markovian Demand," Operations Research, INFORMS, vol. 45(6), pages 931-939, December.
    2. George Hall & John Rust, 2007. "The (S,s) Policy is an Optimal Trading Strategy in a Class of Commodity Price Speculation Problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(3), pages 515-538, March.
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    Cited by:

    1. Mart, Turgut & Duran, Serhan & Bakal, ─░smail Serdar, 2013. "Tactical inventory and backorder decisions for systems with predictable production yield," International Journal of Production Economics, Elsevier, vol. 143(2), pages 294-303.
    2. Lap Mui Ann Chan & David Simchi-Levi & Julie Swann, 2006. "Pricing, Production, and Inventory Policies for Manufacturing with Stochastic Demand and Discretionary Sales," Manufacturing & Service Operations Management, INFORMS, vol. 8(2), pages 149-168, January.

    More about this item


    Inventory theory; optimal ordering policies; (S; s) policies; K-concavity;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General


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