A finite horizon scheduling model based on optimal inventory

An optimal production and setup scheduling model is discussed in an inflexible manufacturing system with jump Markov disturbances consisting of a single machine. The system can produce several types of products, but at any given time it can only produce one type of product. A setup (with setup time or cost or both) is required if production is to be switched from one type of product to another. The objective of the problem is to minimize the costs of setup, production, and inventory. The decision variables are a sequence of setups and the production plan. The optimality condition in the case of finite horizon based on the optimal inventory is also addressed