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2018-12Zeitschriftenartikel DOI: 10.18452/23887
A weak convergence approach to inventory control using a long-term average criterion
dc.contributor.authorHelmes, K. L.
dc.contributor.authorStockbridge, R. H.
dc.contributor.authorZhu, C.
dc.date.accessioned2022-01-10T13:35:29Z
dc.date.available2022-01-10T13:35:29Z
dc.date.issued2018-12none
dc.identifier.issn0001-8678
dc.identifier.other10.1017/apr.2018.50
dc.identifier.urihttp://edoc.hu-berlin.de/18452/24545
dc.description.abstractIn this paper we continue the examination of inventory control in which the inventory is modeled by a diffusion process and a long-term average cost criterion is used to make decisions. The class of such models under consideration has general drift and diffusion coefficients, and boundary points that are consistent with the notion that demand should tend to reduce the inventory level. The conditions on the cost functions are greatly relaxed from those in Helmes et al. (2017). Characterization of the cost of a general (s, S) policy as a function of two variables naturally leads to a nonlinear optimization problem over the ordering levels s and S. Existence of an optimizing pair (s*, S*) is established for these models under very weak conditions; nonexistence of an optimizing pair is also discussed. Using average expected occupation and ordering measures and weak convergence arguments, weak conditions are given for the optimality of the (s*, S*) ordering policy in the general class of admissible policies. The analysis involves an auxiliary function that is globally C2 and which, together with the infimal cost, solves a particular system of linear equations and inequalities related to but different from the long-term average Hamilton‒Jacobi‒Bellman equation. This approach provides an analytical solution to the problem rather than a solution involving intricate analysis of the stochastic processes. The range of applicability of these results is illustrated on a drifted Brownian motion inventory model, both unconstrained and reflected, and on a geometric Brownian motion inventory model under two different cost structures.eng
dc.language.isoengnone
dc.publisherHumboldt-Universität zu Berlin
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectinventoryeng
dc.subjectimpulse controleng
dc.subjectlong-term average costeng
dc.subjectgeneral diffusion modeleng
dc.subject(s,S) policyeng
dc.subjectweak convergenceeng
dc.subject.ddc510 Mathematiknone
dc.titleA weak convergence approach to inventory control using a long-term average criterionnone
dc.typearticle
dc.identifier.urnurn:nbn:de:kobv:11-110-18452/24545-2
dc.identifier.doihttp://dx.doi.org/10.18452/23887
dc.type.versionpublishedVersionnone
local.edoc.container-titleAdvances in Applied Probabilitynone
local.edoc.pages43none
local.edoc.anmerkungThis publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.none
local.edoc.type-nameZeitschriftenartikel
local.edoc.institutionWirtschaftswissenschaftliche Fakultätnone
local.edoc.container-typeperiodical
local.edoc.container-type-nameZeitschrift
local.edoc.container-publisher-nameCambridge University Pressnone
local.edoc.container-publisher-placeCambridgenone
local.edoc.container-volume50none
local.edoc.container-issue4none
local.edoc.container-firstpage1032none
local.edoc.container-lastpage1074none
dc.description.versionPeer Reviewednone
dc.identifier.eissn1475-6064

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