Service constrained inventory models with random lifetimes and lead times

We consider continuous review inventory models with Poisson demands, exponentially distributed lifetimes and replenishment order processing times. The model is unique in that complete backorders, complete lost sales and partial backorders are all addressed. We derive exact expressions of the key operating characteristics. Based on these performance measures, we optimise the system parameters subject to fill rate and waiting time constraints. Numerical examples are also provided to validate our models and to generate useful managerial insights.