A Markovian continuous review inventory model with leadtimes and disasters

We consider a continuous review (s, S) model with lost sales in the presence of unexpected events. Such unexpected events include external disasters (e.g. theft or earthquakes) and internal disasters (e.g. malfunctioning of a storage equipment or fire). Once a disaster occurs the inventory drops instantaneously to zero. The total cost includes the cost of: ordering, unsatisfied demand, units destroyed, holding and fixed cost of disasters. Both the time between disasters and leadtimes are assumed to be exponentially distributed while two cases of demand distribution are considered: Poisson and compound Poisson with general demand sizes. We study the average cost criterion and discuss an extension for the discounted cost criterion. We also provide asymptotic expressions for some of the cost functionals and computational results on the problem of finding the optimal re-order, s, and order up to, S, levels. None of the known work on the subject is as general as the model presented here. We compared the cost resulting from the exact analysis to the one of a heuristic that ignores disasters (and is also analyzed here). This comparison shows that ignoring disasters is more costly when demand variability is high and, not surprisingly, when disasters are frequent. Subject Classification: Inventory/Production: Perishable/aging items, Uncertainty: Stochastic Area of Review: Stochastic Processes