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

Content Provider	Springer Nature Link
Author	Barron, Yonit Perry, David Stadje, Wolfgang
Copyright Year	2014
Abstract	We 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.
Starting Page	373
Ending Page	409
Page Count	37
File Format	PDF
ISSN	02545330
Journal	Annals of Operations Research
Volume Number	241
Issue Number	1-2
e-ISSN	15729338
Language	English
Publisher	Springer US
Publisher Date	2014-08-19
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Make-to-stock model Cost functionals MAP Phase-type distribution Multi-dimensional martingale Operation Research/Decision Theory Combinatorics Theory of Computation
Content Type	Text
Resource Type	Article
Subject	Management Science and Operations Research

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