Transshipment and safety stock under stochastic supply interruption in a production system

We consider a two-echelon system with one source supplying two locations with the same product. The random occurrence of interruptions at the source where downtime is also stochastic can result in stockouts at the two receiving locations. Our model studies the benefit of allowing each location to carry a safety stock where holding costs can be different at each location. The objective is to reduce overall cost at both locations. In some cases it is optimal to allow for a transshipment of inventory from the safety stock of one location to the other. We jointly solve for the optimal safety stock at each location and the optimal amount to be transshipped from a location to the other. We show that by conditioning on the transshipment direction the total cost becomes convex as a function of the safety stock levels at the receiving locations and the amount to be transshipped from a location to the other. Numerical examples are presented for different system cost parameters and probability distributions.