A cyclic production scheme for multi-item production systems with backlog : part 1

This paper is part 1 of two companion papers dealing with a multi-item production system in which the production is controlled by a fixed cycle scheme. The cycle consists of a production period with a fixed number of production times that can be used for production or idling, followed by a vacation. The duration of the vacation is independent of the production period. Demand arrives according to a (compound) Poisson process and is satisfied from stock or backlogged. The embedded process is modeled in discrete time and analyzed using generating functions. The optimal base stock level is derived from a newsvendor type relation. The model is extended to one with time slot dependent base stock levels. The results are used to construct a presumably optimal fixed cycle policy. In part 2 this fixed cycle policy is used to construct a dynamic production policy