Control of make-to-stock production systems with setup costs

This study considers the joint control of production and inventory in a Markovian make-to-stock environment with parallel production lines, production start-up costs, several customer classes and lost sales. At the production completion and demand arrival epochs, there are two types of decisions. The first is the determination of the number of lines that should be active (producing) and the second one is whether to satisfy an arriving demand. Especially, at the states where inventory position is low, it would be more economical to reject the arriving demands of lower priority classes and reserve on-hand stock for future demands of more valuable classes. This study contributes to the control literature of make-to-stock systems with the simultaneous consideration of fixed production costs, multiple lines and several customer classes. The dynamic programming formulation of the system, which we model as a Markov Decision Process, is developed by defining a two-dimensional system state vector. The model is solved with the value iteration algorithm. It is shown with the numerical examples that the optimal production and stock rationing policies have dynamic structures. Due to the dynamic nature of the optimal policies, we also propose easy-to-apply and well-performing alternative policies. The proposed production policy is an extended version of the twocritical-number policy, which is frequently considered in the literature. The proposed rationing policy is a dynamic one that considers the value of outstanding production orders in addition to inventory level.