Inventory systems with stochastic demand and supply: Properties and approximations

We model a retailer whose supplier is subject to complete supply disruptions. We combine discrete-event uncertainty (disruptions) and continuous sources of uncertainty (stochastic demand or supply yield), which have different impacts on optimal inventory settings. This prevents optimal solutions from being found in closed form. We develop a closed-form approximate solution by focusing on a single stochastic period of demand or yield. We show how the familiar newsboy fractile is a critical trade-off in these systems, since the optimal base-stock policies balance inventory holding costs with the risk of shortage costs generated by a disruption.