A periodic review inventory model with Markovian supply availability

Occasional unavailability of materials and products has an impact on inventory decisions of utility companies, manufacturers, wholesalers and retailers. The possibility of periods of supply unavailability that start and end at random times has been recognized by inventory researchers, and incorporated into continuous-review models. The goal of this work is to address a periodic-review setting, with setup costs, where the probability that an order placed now is filled in full, as opposed to not at all, depends on whether supply was available in the previous period. We prove that the optimal inventory policy is of an (s, S) type, where s depends on the state of the supplier in the last period, while S does not. Some other issues are briefly discussed.