Critical supply chains such as semiconductor and pharmaceutical supply chains require long-term resiliency in addition to efficiency. The challenge of balancing resiliency and efficiency with limited resources in industrial-scale supply chains requires a principled approach. To this end, we propose an end-to-end methodology for robust designs of critical supply chains. Among other things, our framework captures the trade-off between cost and robustness under worst-case supply and demand disruptions; as well as the multiple time scales of resiliency building and contingency planning. We formulate a two-stage supply chain design model under uncertainty, the model optimizes for the risk-mitigating first-stage network design and resource allocation that maximize the total profit under uncertainty. We deploy a recently popular approximate solution method — affinely adjustable robust optimization (AARO) formulations — to our problem. With extensive numerical experiments, we show that this method outperforms other solution methods, such as sample average approximation, by orders of magnitude in this type of robust network design problems. We also provide theoretical support for the (near) optimality and tractability of this method. Most interestingly, we collect large and real-world datasets for both types of supply chains and conduct case studies. Our case studies show an important insight: a small amount of risk-mitigating resources meticulously placed at strategic locations can lead to a significant gain in supply chain resilience. Our methodology allows the systematic identification of such leverages at an industrial scale under highly uncertain supply and demand environments. This insight implies that with the right data and analytical tools, there is an opportunity to strengthen critical supply chains with relatively affordable investments.

We study distributionally robust chance-constrained programs (DRCCPs) with right-hand side uncertainty. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints (DRCCs) as decision variables to trade off between the system cost and risk of violations by penalizing the risk tolerances in the objective function. We consider two types of Wasserstein ambiguity sets: one with finite support and one with a continuum of realizations. By exploring the hidden discrete structures, we develop mixed integer programming reformulations under the two types of ambiguity sets to determine the optimal risk tolerance for the chance constraint. Valid inequalities are derived to strengthen the formulations. We test instances with transportation problems of diverse sizes and a demand response management problem.

We propose a new data-driven trade-off (TRO) approach for modeling uncertainty that serves as a middle ground between the optimistic approach, which adopts a distributional belief, and the pessimistic distributionally robust optimization approach, which hedges against distributional ambiguity. We equip the TRO model with a TRO ambiguity set characterized by a size parameter controlling the level of optimism and a shape parameter representing distributional ambiguity. We first show that constructing the TRO ambiguity set using a general star-shaped shape parameter with the empirical distribution as its star center is necessary and sufficient to guarantee the hierarchical structure of the sequence of TRO ambiguity sets. Then, we analyze the properties of the TRO model, including quantifying conservatism, quantifying bias, and establishing asymptotic properties. Specifically, we show that the TRO model could generate a spectrum of decisions, ranging from optimistic to conservative decisions. Additionally, we show that it could produce an unbiased estimator of the true optimal value. Furthermore, we establish the almost-sure convergence of the optimal value and the set of optimal solutions of the TRO model to their true counterparts. We exemplify our theoretical results using an inventory control problem and a portfolio optimization problem.

We consider a residuals-based distributionally robust optimization model, where the underlying uncertainty depends on both covariate information and our decisions. We adopt regression models to learn the latent decision dependency and construct a nominal distribution (and thereby ambiguity sets) around the learned model using empirical residuals from the regressions. Ambiguity sets can be formed via the Wasserstein distance, a sample robust approach, or with the same support as the nominal empirical distribution (e.g., phi-divergences), where both the nominal distribution and the radii of the ambiguity sets could be decision- and covariate-dependent. We provide conditions under which desired statistical properties, such as asymptotic optimality, rates of convergence, and finite sample guarantees, are satisfied. Via cross-validation, we devise data-driven approaches to find the best radii for different ambiguity sets, which can be decision-(in)dependent and covariate-(in)dependent. Through numerical experiments, we illustrate the effectiveness of our approach and the benefits of integrating decision dependency into a residuals-based DRO framework.