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We consider a two-product inventory system with independent Poisson demands,limited joint storage capacity and partial demand substitution. Replenishmentis performed simultaneously for both products and the replenishment time may befixed or exponentially distributed. For both cases we develop a Continuous TimeMarkov Chain model for the inventory levels and derive expressions for theexpected profit per unit time. We prove that the profit function is submodularin the order quantities, which allows for a more efficient algorithm todetermine the optimal ordering policy. Using computational experiments weassess the effect of substitution and replenishment time uncertainty on theorder quantities and the profit as a function of the storage capacity.

Inventory Policies for Two Products under Poisson Demand: Interaction  between Demand Substitution, Limited Storage Capacity and Replenishment Time  Uncertainty