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Inventory policies for two products under Poisson demand: Interaction between demand substitution, limited storage capacity and replenishment time uncertainty
Author(s) -
Burnetas Apostolos,
Kanavetas Odysseas
Publication year - 2018
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.21788
Subject(s) - poisson distribution , lead time , markov chain , profit (economics) , mathematical optimization , substitution (logic) , computer science , economic order quantity , markov process , function (biology) , order (exchange) , supply chain , mathematics , economics , microeconomics , operations management , statistics , machine learning , evolutionary biology , law , political science , programming language , biology , finance
We consider a two‐product inventory system with independent Poisson demands, limited joint storage capacity and partial demand substitution. Replenishment is performed simultaneously for both products and the replenishment time may be fixed or exponentially distributed. For both cases we develop a Continuous Time Markov Chain model for the inventory levels and derive expressions for the expected profit per unit time. We establish analytic expressions for the profit function and show that it satisfies decreasing differences properties in the order quantities, which allows for a more efficient algorithm to determine the optimal ordering policy. Using computational experiments, we assess the effect of substitution and replenishment time uncertainty on the order quantities and the profit as a function of the storage capacity.