Essays on Supply Chain Management with Model Uncertainty
Traditional supply chain management models typically require complete model information, including structural relationships (e.g., how pricing decisions affect customer demand), probabilistic distributions, and parameters. However, in practice, the model information may be uncertain. My dissertation research seeks to address model uncertainty in supply chain management problems using data-driven and robust methods. Incomplete information typically comes in two forms, namely, historical data and partial information. When historical data are available, data-driven methods can be used to obtain decisions directly from data, instead of estimating the model information and then using these estimates to find the optimal solution. When partial information is available, robust methods consider all possible scenarios and make decisions to hedge against the worst-case scenario effectively, instead of making simplified assumptions that could lead to significant loss.
Chapter 1 provides an overview of model uncertainty in supply chain management, and discusses the limitations of the traditional methods. The main part of the dissertation is on the application of data-driven and robust methods to three widely-studied supply chain management problems with model uncertainty.
Chapter 2 studies the reliable facility location problem where the joint-distribution of facility disruptions is uncertain. For this problem, usually, only partial information in the form of marginal facility disruption probabilities is available. Most existing models require the assumption that the disruptions at different locations are independent of each other. However, in practice, correlated disruptions are widely observed. We present a model that allows disruptions to be correlated with an uncertain joint distribution, and apply distributionally-robust optimization to minimize the expected cost under the worst-case distribution with the given marginal disruption probabilities. The worst-case distribution has a practical interpretation, and its sparse structure allows us to solve the problem efficiently. We find that ignoring disruption correlation could lead to significant loss. The robust method can significantly reduce the regret from model misspecification. It outperforms the traditional approach even under very mild correlation. Most of the benefit of the robust model can be captured at a relatively small cost, which makes it easy to implement in practice.
Chapter 3 studies the pricing newsvendor problem where the structural relationship between pricing decisions and customer demand is unknown. Traditional methods for this problem require the selection of a parametric demand model and fitting the model using historical data, while model selection is usually a hard problem in itself. Furthermore, most of the existing literature on pricing requires certain conditions on the demand model, which may not be satisfied by the estimates from data. We present a data-driven approach based only on the historical observations and the basic domain knowledge. The conditional demand distribution is estimated using non-parametric quantile regression with shape constraints. The optimal pricing and inventory decisions are determined numerically using the estimated quantiles. Smoothing and kernelization methods are used to achieve regularization and enhance the performance of the approach. Additional domain knowledge, such as concavity of demand with respect to price, can also be easily incorporated into the approach. Numerical results show that the data-driven approach is able to find close-to-optimal solutions. Smoothing, kernelization, and the incorporation of additional domain knowledge can significantly improve the performance of the approach.
Chapter 4 studies inventory management for perishable products where a parameter of the demand distribution is unknown. The traditional separated estimation-optimization approach for this problem has been shown to be suboptimal. To address this issue, an integrated approach called operational statistics has been proposed. We study several important properties of operational statistics. We find that the operational statistics approach is consistent and guaranteed to outperform the traditional approach. We also show that the benefit of using operational statistics is larger when the demand variability is higher. We then generalize the operational statistics approach to the risk-averse newsvendor problem under the conditional value-at-risk (CVaR) criterion. Previous results in operational statistics can be generalized to maximize the expectation of conditional CVaR. In order to model risk-aversion to both the uncertainty in demand sampling and the uncertainty in future demand, we introduce a new criterion called the total CVaR, and find the optimal operational statistic for this new criterion.