Incorporating data envelopment analysis solution methods into bilevel multi-objective optimization

This study illustrates the use of Data Envelopment Analysis (DEA) solution methods in bilevel optimization problems. Here, we show that DEA and bilevel optimization can also be used together as part of an integrated solution framework. We work with a policy-oriented problem in which the regulator´s multi-objective optimization problem at the upper level is constrained by the profit-maximizing decisions of individual firms at the lower level. Each firm´s response to the policy is a prori unknown to the regulator, and depends on the underlying production technology. Rather than assuming a common production relationship across firms, DEA allows us to model each firm´s response to the policy without imposing a functional form on the production technology. We use DEA to estimate the technology facing each producer, based on observed practices of other producers. Doing so endogenizes the cost of responding to prospective policies at the lower level, providing a more realistic solution set at the upper level. Our application addresses the design of a policy to reduce fertilizer runoff from agriculture, an important problem in environmental economics. We employ a multi-objective bilevel evolutionary algorithm to solve for the approximate optimal frontier.