On minimizing downside risk in make‐to‐stock, risk‐averse firms

Consider a single‐product, make‐to‐stock, risk‐averse firm with stochastic demand and manufacturing capacity. Temporarily unfilled demands are back‐ordered. Total cost is equal to the sum of inventory‐holding and back‐ordering costs over a continuous‐time, finite planning horizon. In this article, we study the problem of finding the base‐stock level that minimizes total cost conditional value‐at‐risk (CVaR), or total cost CVaR for short. We demonstrate that total cost CVaR is both convex in the base‐stock level and increasing in risk aversion. We derive a closed‐form approximation of total cost which is asymptotically exact in the planning horizon length. The approximation leads to a relatively simple determination of optimal base‐stock levels which are reasonably accurate for practical applications. We make observations and identify findings regarding the impact on optimal base‐stock levels of changes in risk aversion, manufacturing capacity, inventory‐holding and back‐ordering costs, and planning horizon length. We provide a detailed description of how our research results were applied in a real‐world, supply‐chain design project.