Optimal continuous production-inventory systems subject to stockout risk

This paper studies a continuous-review production-inventory system with a constant production rate and compound Poisson demands, in which the cost of the system is assessed with holding cost and stockout penalty. For any initial inventory, we derive closed form expression for the expected discounted cost function until stockout occurrence. We quantify the risk of stockout in terms of the average time to stockout occurrence. The objective is to derive the optimal production rate that minimizes the expected discounted system cost subject to a given risk level of stockout. With the aid of the explicit forms of stockout risk and the cost function, we present a computation-efficient algorithm for the optimal solution. For the special cases with proportional stockout penalty function, if the demands follow an exponential distribution, we have a closed form expression for the expected discounted cost. Some numerical studies are conducted to illustrate our results with further insights. Numerically, we show that it is outrageously costly to reduce stockout risk especially when the stockout risk is relatively low. Our results shed light on the inventory risk control and cost optimization. The major results and the developed algorithm can be leveraged to facilitate continuous-production manufacturers, especially pharmaceutical firms, with their Production Process Validation.