Optimizing Critical Spare Parts and Location Based on the Conditional Value-At-Risk Criterion

This article considers the problem of managing the risks associated with random equipment failures by optimizing decisions regarding the quantity and placement of critical spares over a network of related industrial sites. To develop the model and provide a practical example, we focus on the allocation of electrical transformer spares for a large-scale industrial producer, such as a mining company or chemical manufacturer, operating several different sites across a geographic region. In particular, we consider the risk of financial loss due to interrupted business and lost production following an unexpected transformer failure. A two-stage stochastic integer programming model with a conditional value-at-risk (CVaR) criterion to incorporate risk aversion is developed. Computational results are presented to illustrate the advantages of the CVaR approach compared to a corresponding expected cost minimization approach. The CVaR model results in policies that have lower loss than the corresponding risk neutral model since, at sufficiently high risk aversion levels, the CVaR model introduces the acquisition of more spares as a hedge against catastrophic scenarios.