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Optimal policies for inventory systems with concave ordering costs

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  • Saif Benjaafar
  • David Chen
  • Yimin Yu

Abstract

In this paper we study the structure of optimal policies for periodic review inventory systems with concave ordering costs and general demand distributions. By extending the Scarf () model to systems with piecewise linear concave ordering costs, we show that, except for a bounded region, the generalized (s, S) policy is optimal. We do so by (a) introducing the notion of c‐convexity and (b) proving a conditional monotonicity property for the optimal order‐up‐to levels. We also provide conditions under which the generalized (s, S) policy is optimal for all regions of the state space.

Suggested Citation

  • Saif Benjaafar & David Chen & Yimin Yu, 2018. "Optimal policies for inventory systems with concave ordering costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 291-302, June.
    • Handle: RePEc:wly:navres:v:65:y:2018:i:4:p:291-302
    DOI: 10.1002/nav.21808
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    References listed on IDEAS

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    1. Evan L. Porteus, 1971. "On the Optimality of Generalized (s, S) Policies," Management Science, INFORMS, vol. 17(7), pages 411-426, March.
    2. Ye Lu & Miao Song, 2014. "Inventory Control with a Fixed Cost and a Piecewise Linear Convex Cost," Production and Operations Management, Production and Operations Management Society, vol. 23(11), pages 1966-1984, November.
    3. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Infinite Horizon Case," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 698-723, August.
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    5. Evan L. Porteus, 1972. "The Optimality of Generalized (s, S) Policies under Uniform Demand Densities," Management Science, INFORMS, vol. 18(11), pages 644-646, July.
    6. Edward J. Fox & Richard Metters & John Semple, 2006. "Optimal Inventory Policy with Two Suppliers," Operations Research, INFORMS, vol. 54(2), pages 389-393, April.
    7. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case," Operations Research, INFORMS, vol. 52(6), pages 887-896, December.
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    Cited by:

    1. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
    2. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.

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