The (Q,r) inventory system with an unreliable supplier

This paper examines the impact on operating costs of having an unreliable supplier in a continuous review, fixed order quantity (Q) - reorder point (r) inventory system. We assume Poisson demand and exponentially distributed lengths of the supplier's on and off periods. On (off) periods represent time lengths during which the supplier is able (unable) to fill new orders. Any unsatisfied demand is assumed to be lost. We analyze two situations. The first has a negligible lead time but allows the number of outstanding orders, each of a fixed size Q, to be arbitrary. The second situation, on the other hand, has a constant lead time but there the number of outstanding orders is restricted to at most one. In each case, exact expressions necessary to find the average cost minimizing (Q,r) pair are developed and several numerical examples are solved. Computational results show the cost function to be well behaved and suggest that ignoring supply uncertainty or approximate modeling can be relatively very expensive, especially when the off periods are long or shortage penalty is high or both. We also identify regions where the average operating cost associated with the computationally simpler approximate solution is not far from its optimum value.