Critical events based hierarchical flow control policy of production systems involving aging

A production line in a processing industry is studied with a set of unreliable equipment, and the jump rate of the system state depends on the aging of the system. At any given time it can only produce one type of product. A setup (with setup time and cost) is required if production is to be switched from one type of product to another. The objective of the problem is to minimize the whole cost of setup, production, and inventory. Based on the nature of production systems, the age function is considered, and a new state variable and a new time horizon of the objective function are introduced. Thus the original problem is decomposed and a new hierarchical optimal production rate control and setup scheduling model is constructed. An algorithm framework of a receding horizon according to optimal inventory is also addressed. Simulation results show the feasibility of the proposed approach in practice.