Inventory Control under Supplier Disruption Risk: Optimal Policies with Bernoulli Yield

We study the multi-period inventory planning problem when demand is uncertain and the supplier is subject to disruption risk. The latter is modeled using Bernoulli supply yield uncertainty, so that, in any replenishment period, a complete order is received with probability $p\in [0,1]$ and the supplier defaults and nothing is received w.p. $1-p$. We prove that the optimal policy for the finite and infinite horizon problems, both for discounted and average cost minimization, is the classic order-up-to (base stock) policy. Explicit formulae are given for deterministic and exponentially-distributed demand.