Minimizing conditional value‐at‐risk under a modified basestock policy

Abstract

Consider a single‐product, make‐to‐stock, risk‐averse company that manages its finished goods inventory by a basestock policy. Item demand is modeled as a Poisson process, and unit production time is modeled as an exponential random variable. Annual cost is equal to the sum over one year of the inventory‐holding and back‐ordering costs. The company wants to minimize the annual cost conditional value‐at‐risk by an appropriate basestock selection called the optimal basestock. After offering evidence that the optimal basestock is analytically intractable, we derive a closed‐form approximation of the optimal basestock. In two independent simulation experiments, we found that the average penalty for using the approximation is less than 1%; we believe this accuracy would be acceptable for practical applications. Leveraging the approximation's accuracy and simplicity, we establish several results that may serve as predictors of the company's appropriate basestock adjustments to changes in operational, economic, and risk aversion parameters. We illustrate how our research results were successfully applied in a Fortune 10 energy company. We extend the problem setting in two different directions to widen the applicability of our research results.