Abstract
This paper discusses a discrete-time make-to-order production-inventory system with stochastic production capacity and stochastic demand. Parts used in the production process are supplied by a vendor utilizing a constant lead time. The inventory of parts is controlled by a replenishing point system. The state of the production-inventory system is modeled as a discrete time M/G/1 type Markov chain. A performance evaluation method is derived using the structure of the transition probability matrix of the system. The average back-logged demand and average inventory of parts in the equilibrium state are derived from the demand distribution, production capacity distribution, lead time and replenishing point of parts. With these results, an algorithm is developed for determining an optimal replenishing point of parts that minimizes the average total cost per period consisting of the average back-logged cost of demand and average inventory cost of parts. Some numerical examples are given.
