A make-to-stock production/inventory model with MAP arrivals and phase-type demands

DC FieldValueLanguage
dc.contributor.authorBarron, Yonit
dc.contributor.authorPerry, David
dc.contributor.authorStadje, Wolfgang
dc.date.accessioned2021-12-23T16:07:37Z-
dc.date.available2021-12-23T16:07:37Z-
dc.date.issued2016
dc.identifier.issn02545330
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/7969-
dc.description.abstractWe consider a make-to-stock production/inventory model in a random environment with finite storage capacity and restricted backlogging possibility. Our aim is to demonstrate that all cost quantities of interest can be derived in closed form under quite general assumptions on the demand arrival process and on the switches in the production rates. Specifically, the demands arrive according to a Markov additive process governed by a continuous-time Markov chain, and their sizes are independent and have phase-type distributions depending on the type of arrival. The production process switches between predetermined rates which depend on the state of the environment and on the presence or absence of backlogs. Four types of costs are considered: the holding cost for the stock, the cost of lost production due to the finite storage capacity, the shortage cost for the backlogged demand and the cost due to unsatisfied demand. We obtain explicit formulas for these cost functionals in the discounted case and under the long-run average criterion. The derivations are based on optional sampling of a multi-dimensional martingale and on fluid flow techniques.
dc.description.sponsorshipDeutsche ForschungsgemeinschaftGerman Research Foundation (DFG) [306/13-2]; W. Stadje: Supported by Grant No. 306/13-2 of the Deutsche Forschungsgemeinschaft.
dc.language.isoen
dc.publisherSPRINGER
dc.relation.ispartofANNALS OF OPERATIONS RESEARCH
dc.subjectBARRIER
dc.subjectCost functionals
dc.subjectFLUID-FLOW MODELS
dc.subjectINVENTORY
dc.subjectMake-to-stock model
dc.subjectMAP
dc.subjectMARTINGALE
dc.subjectMulti-dimensional martingale
dc.subjectOperations Research & Management Science
dc.subjectPhase-type distribution
dc.subjectPOLICIES
dc.subjectREPLENISHMENT
dc.subjectTIMES
dc.subjectTRANSIENT ANALYSIS
dc.titleA make-to-stock production/inventory model with MAP arrivals and phase-type demands
dc.typejournal article
dc.identifier.doi10.1007/s10479-014-1679-2
dc.identifier.isiISI:000377349300016
dc.description.volume241
dc.description.issue1-2
dc.description.startpage373
dc.description.endpage409
dc.contributor.orcid0000-0001-6635-095X
dc.contributor.researcheridAAF-8779-2019
dc.identifier.eissn15729338
dc.publisher.placeVAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS
dcterms.isPartOf.abbreviationAnn. Oper. Res.
crisitem.author.deptFB 06 - Mathematik/Informatik-
crisitem.author.deptidfb06-
crisitem.author.parentorgUniversität Osnabrück-
crisitem.author.netidStWo325-
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