“A Risk Analytics Approach to Production Planning” by Ms. Liao Wang
Ms. Liao Wang
We study production planning integrated with risk hedging to minimize certain specific risk measures such as shortfall. In addition to the one-time production quantity decision, there is a real-time hedging strategy throughout the horizon; and the goal is to minimize the gap between a pre-specified target and the total terminal wealth achieved by both production and hedging. To this end, we model demand as a stochastic process with two random components: in addition to the usual Gaussian component to capture forecast noise, the demand rate takes the form of a function of an asset price (itself being another stochastic process). We do not assume any specific form of this rate function, allowing it to be machine-learned from demand and asset price data. Using a duality based method, we derive the optimal hedging strategy, which can be expressed as a portfolio of two options, a digital option and a put option. With the hedging strategy optimized, we show that optimizing production quantity is a convex minimization problem. With both production and hedging optimized, we provide a complete characterization of the efficient frontier: the minimized shortfall as an increasing function of the target. Other model features include partial information and a budget constraint, both are motivated by practical implementations. A brief overview of two other related projects in risk/business analytics will also be highlighted.