Inventory dispensation and restocking in multiclass inventory systems: A decoupling approach

We consider an inventory system with Poisson demand arrivals arising from multiple classes. Restocking epochs are specified by a given sequence. At each epoch, we can place an order for any number of items for immediate delivery. We have to decide the inventory dispensation policy, which determines whether we should satisfy a demand, or reject it, or backlog it until the next restocking epoch. We allow class‐dependent rejection and backlogging costs. We also incorporate holding costs and procurement costs. We obtain the optimal restocking and inventory dispensation policies under the total discounted cost criterion as well as the long‐run average cost criterion. In particular, we develop efficient algorithms to compute the optimal policies (OPs) by decoupling the inventory dispensation policy from the restocking policy. We show that the OP operates as follows: At the restocking epochs, we order up to a fixed base‐stock level. We satisfy the demands from a class if the inventory is above a critical level that depends on the class and time to the next restocking epoch; else we reject or backlog it depending on whether the next restocking epoch is later or earlier than a class‐dependent critical number. The numerical experiments for the stochastic and deterministic interstocking periods are conducted to compare the OPs and costs.