Abstract
An optimal production and scheduling model is discussed for a general failure-prone inflexible manufacturing system with Markov disturbances. The system can produce several types of products, but at any given time it can only produce several type of products. 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. On the basis of a necessary and sufficient condition for optimal control, we give a new general production policy based on optimal inventory. After we discuss a new scheduling policy, a new dynamic programming is presented.