The impacts of stockout cost on a stochastic production-inventory system in minimizing total cost conditional value-at-risk

Conditional value-at-risk (CVaR) is a metric for downside risks and increasingly used in supply chain management. Under this metric, we build a single-item production-inventory model with stochastic demand. The production capacity, too, is stochastic due to random unit processing time. The total cost includes stockout, inventory holding, and backordering costs and accumulates. After presenting convexity properties of the total cost CVaR within a finite time horizon, we propose a two-moment closed-form normal approximation of it using Markov reward chain theory. The approximated total cost CVaR is exact with respect to the length of the horizon asymptotically. The desirable base-stock levels obtained perform satisfactorily for industry settings. In an extension, we have also benchmarked the proposed approximation with alternative formulations and show that the proposed approximation works satisfactorily. With a numerical simulation experiment, we outline observations and findings that characterize how relevant economic factors could impact the approximately optimal base-stock levels.