Data-driven Wasserstein distributionally robust optimization for biomass with agricultural waste-to-energy network design under uncertainty

This paper addresses the problem of biomass with agricultural waste-to-energy network design under uncertainty. We propose a novel data-driven Wasserstein distributionally robust optimization model for hedging against uncertainty in the optimal network design. Instead of assuming perfect knowledge of probability distribution for uncertain parameters, we construct a data-driven ambiguity set of candidate distributions based on the Wasserstein metric, which is utilized to quantify their distances from the data-based empirical distribution. Equipped with this ambiguity set, the two-stage distributionally robust optimization model not only accommodates the sequential decision making at design and operational stages, but also hedges against the distributional ambiguity arising from finite amount of uncertainty data. A solution algorithm is further developed to solve the resulting two-stage distributionally robust mixed-integer nonlinear program. To demonstrate the effectiveness of the proposed approach, we present a case study of a biomass with agricultural waste-to-energy network including 216 technologies and 172 compounds. Computational results show that the data-driven Wasserstein distributionally robust optimization approach has a better out-of-sample performance in terms of a 5.7% lower average cost and a 37.1% smaller cost standard deviation compared with the conventional stochastic programming method.