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Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes

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  • F. G. Badía
  • C. Sangüesa

Abstract

In this article, we study generalizations of some of the inventory models with nonlinear costs considered by Rosling in (Oper. Res. 50 (2002) 797–809). In particular, we extend the study of both the periodic review and the compound renewal demand processes from a constant lead time to a random lead time. We find that the quasiconvexity properties of the cost function (and therefore the existence of optimal (s, S) policies), holds true when the lead time has suitable log‐concavity properties. The results are derived by structural properties of renewal delayed processes stopped at an independent random time and by the study of log‐concavity properties of compound distributions. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 345–356, 2015

Suggested Citation

  • F. G. Badía & C. Sangüesa, 2015. "Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(5), pages 345-356, August.
    • Handle: RePEc:wly:navres:v:62:y:2015:i:5:p:345-356
    DOI: 10.1002/nav.21637
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    References listed on IDEAS

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    1. Woonghee Tim Huh & Ganesh Janakiraman & Alp Muharremoglu & Anshul Sheopuri, 2011. "TECHNICAL NOTE---Inventory Systems with a Generalized Cost Model," Operations Research, INFORMS, vol. 59(4), pages 1040-1047, August.
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