CVaR-Based Approximations of Wasserstein Distributionally Robust Chance Constraints with Application to Process Scheduling

Abstract

Distributionally robust chance constrained programming is a stochastic optimization approach that considers uncertainty in model parameters as well as uncertainty in the underlying probability distribution. It ensures a specified probability of constraint satisfaction for any probability distribution from a defined ambiguity set. In this work, we consider Wasserstein ambiguity sets and derive tractable approximations of individual and joint distributionally robust chance constraints (DRCCs) based on the Worst-Case Conditional Value-at-Risk (WC-CVaR). We further prove that the proposed approximations are exact for individual DRCCs and for joint DRCCs if the scaling factors are simultaneously optimized. The effectiveness of the proposed approach is demonstrated in an illustrative example and in two comprehensive process scheduling cases. The computational results show that the WC-CVaR approximation exhibits significantly better out-of-sample performance than the commonly used Bonferroni approximation, which tends to be overconservative, and classical chance constrained programming.

Multistage distributionally robust optimization for integrated production and maintenance scheduling

“…There have been significant advances in the area of DRO, mainly contributed by the operations research community, over the last decade 18–21 . Only recently, DRO has also started attracting attention from the process systems engineering (PSE) community 22–24 . For a comprehensive review of DRO, see Rahimian and Mehrotra 25…”

Distributionally Robust Multi-Energy Dynamic Optimal Power Flow Considering Water Spillage with Wasserstein Metric

“…Equations ( 8)-( 13) express the joint distributed robust chance constraint (DRCC). According to [20,25], if the function in the distributed robust chance constraint is affine with respect to both control variable x and random variable ω, i.e., the function exhibits the form of Equation (19d), where a T k (x) is an affine function of x; then, the DRCC can be transformed into a set as follows:…”

Multistage Distributionally Robust Design of a Renewable Source Processing Network under Uncertainty

“…63 In practice, quarterly data sets of each year are available. As suggested in the research work by Liu et al 56 and Chen et al 64 about DRO, one of the benefits of DRO lies in its good performance with limited data. In order to hedge against the variations in these parameters, we assume three available scenarios for each season generated following a standard normal distribution (mean equals to the nominal value).…”

“…55 Focusing on the batch process scheduling, Liu et al applied Wasserstein ambiguity sets and derived tractable approximations of individual and joint distributionally robust chance constraints based on the worst-case conditional value at risk. 56 The central element of this work is to design a robust multiproduct production network driven by renewable sources under uncertainty. Specifically, uncertainties in product demands and feedstock availabilities are fully considered.…”

“…Shen formulated a MSDRO framework to deal with the facility location under decision-dependent uncertainty . Recently, DRO has been applied to chemical process design, planning, and scheduling in terms of better out-of-sample performance. − Adaptive moment-based DRO with the affine decision rule was used to investigate the strategic planning of a 10-year multiperiod process network and scheduling of the multipurpose batch process, respectively. , Ning and You applied the Wasserstein two-stage DRO (TSDRO) to the agricultural waste-to-energy network design under demand uncertainty . Focusing on the batch process scheduling, Liu et al applied Wasserstein ambiguity sets and derived tractable approximations of individual and joint distributionally robust chance constraints based on the worst-case conditional value at risk …”