A periodic review inventory model facing different disruption profiles

We study a periodic review inventory system with alternations of periods with supply availability and unavailability. The system is controlled by a periodic review base stock policy (S,T). While periodic review inventory models have been studied assuming supply disruption, they mainly invoke the limiting disruption probabilities overlooking that these probabilities may correspond to different disruption profiles (ranging from rare-long disruptions to frequent-short ones). In this context, we use a continuous-time Markov chain (CTMC), in order to formulate a periodic review inventory model that can distinguish the different disruption profiles. Through theoretical results, we determine the policy variables (order-up-to level and review interval) that minimize the long-run average cost. We show that when the disruption profile is considered, the optimal order-up-to level, although Newsvendor-styled form, is not always linear in the review interval. We present analytical properties demonstrating the impact of the different disruption profiles (under the same limiting disruption probability) and the impact of the limiting probability on the optimal policy. Furthermore, we propose an approximation to obtain a closed-form (near-)optimal solution for the review interval. Finally, numerical comparisons highlight the impact on system's cost performance of deploying approaches that either use the above mentioned closed-form solution for the review interval or the limiting disruption probabilities instead of the time dependent ones in the cost formulation.