A stock rationing policy in a ( s,S)-controlled stochastic production system with 2-phase Coxian processing times and lost sales

Abstract

This paper analyzes a ( s,S)-controlled stochastic production system with multi-class demands and lost sales. Demands in each class are assumed to arrive according to a Poisson process, and the time required to process an item is assumed to follow a 2-phase Coxian distribution. For each class, a stock rationing level is set. When customers arrive, if the inventory level is lower than the predetermined rationing level, the demands are lost for future demands with higher priorities. A behavior of the production system is modeled as a continuous time Markov chain, and an efficient algorithm to calculate the steady-state probability distribution of the system is proposed. The average operating cost under the stock rationing policy is compared with the one without stock rationing. Numerical experiment shows that the proposed stock rationing policy reduces the average operating cost significantly, depending on the system parameters.