Premium
Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes
Author(s) -
Badía F. G.,
Sangüesa C.
Publication year - 2015
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21637
Subject(s) - economic shortage , lead time , nonlinear system , lead (geology) , constant (computer programming) , function (biology) , mathematics , mathematical optimization , computer science , econometrics , mathematical economics , economics , operations management , physics , geology , programming language , linguistics , philosophy , quantum mechanics , geomorphology , evolutionary biology , government (linguistics) , biology
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