Single-Stage, Multi-Product Production/Inventory Systems

A production/inventory system consisting of a single-stage facility producing multiple product types and a warehouse is considered. Demand process is assumed to be Poisson and the excess demand is backordered. Products have a priority structure and the processor is shared according to a switching rule. (R,r) continuous-review inventory control policy is used to start and stop production of each product. Production of a product continues until its target level is reached. Then, a switch-over takes place to the highest priority product a the ones that need the processor´s attention. A set-up takes place every time a switch-over occurs. Both processing and set-up times are assumed to have arbitrary distributions. The objective is to obtain performances measures such as the average inventory and backorder levels as well as the probability of having a backorder upon arrival for each product. We have developed an approximation procedure which emphasizes the characterisation of the delay each product type experiences in receiving the processor´s attention, once they place a request for it.