Analysis of an inventory system under supply uncertainty

In this paper, we analyze a periodic review, single-item inventory model under supply uncertainty. The objective is to minimize expected holding and backorder costs over a finite planning horizon under the supply constraints. The uncertainty in supply is modelled using a three-point probability mass function. The supply is either completely available, partially available, or the supply is unavailable. Machine breakdowns, shortages in the capacity of the supplier, strikes, etc., are possible causes of uncertainty in supply. We demonstrate various properties of the expected cost function, and show the optimality of order-up-to type policies using a stochastic dynamic programming formulation. Under the assumption of a Bernoulli-type supply process, in which the supply is either completely available or unavailable, and when the demand is deterministic and dynamic, we provide a newsboy-like formula which explicitly characterizes the optimal order-up-to levels. An algorithm is given that computes the optimal inventory levels over the planning horizon. Extensions and computational analysis are presented for the case where the partial supply availability has positive probabillity of occurrence.