An (r, nQ) inventory model for packaged deteriorating products with compound Poisson demand

We consider a liquid type of a deteriorating item which is packaged by an outside supplier and is delivered to final customers by a distributor. Customers arrive according to a Poisson process and ask for an integer number of packages. Unsatisfied demands are backordered. The inventory is reviewed continuously and replenished from an external supplier with a positive deterministic lead time following an (r, nQ) policy. The product in each package deteriorates continuously over time during transportation and storage. Therefore, the distributor cannot deliver exactly one unit of usable material in each package. We develop a model to determine the optimal inventory control parameters and the required size of a package to minimize expected average costs and illustrate the benefit of this method compared to a sequential approach based on an example from practice.