A stochastic model of a production-inventory system with consideration of production disruption

In this paper, we develop a stochastic production-inventory model that faces random production disruption. In each fixed time planning horizon, the inventory position is affected by production disruption. The production disruption time and the disruption recovery time in a single planning horizon are stochastic. The process of the inventory levels at the beginning of the time horizon is formulated by using a finite state discrete-time Markov chain. We derive expressions of the transition probability and the long-run average cost. The optimum solution is obtained through numerical experiments. The result shows that under the circumstance of production time constraint, the incorporation of safety stock in a disruption prone production-inventory system helps to minimise the long run average cost. Finally, sensitivity analysis has been given to demonstrate the usefulness of the model. This model assists decision makers to not only determine the optimal safety stock quantity but also reveal distinct effect and/or joint impacts of individual cost parameters, disruption probability on the decision regarding selection of safety stock.