Regulating the rebound effect in the traveling purchaser problem

Despite engineers’ best intentions, technological innovations intended to reduce resource consumption are not assured to achieve their desired effects. As self-interested agents utilize the technological innovation, theretofore unprofitable activities may be rendered profitable, leading to a disparity between the expected reduction in resource consumption and what is actually achieved. This rebound effect is particularly salient given the current global climate crisis. In practice, many national governments are promoting fuel efficiency gains via new, cutting-edge technologies. However, to maximize the effectiveness of such technological innovations, additional regulation is likely required to avoid unfavorable rebound effects. To further study the dynamics of this setting, we set forth a logistics-based Stackelberg game underpinned by the Traveling Purchaser Problem. More specifically, we develop a bilevel programming formulation wherein the upper-level player is a regulator and the lower-level player is the purchaser. The regulator encounters a multi-objective problem and desires to reduce resource consumption while minimally disrupting commerce on the network. Mathematical conditions are derived and proved to determine when the null regulator action is optimal. These results are leveraged to develop a preprocessing algorithm and customized heuristic solution methodology. Extensive empirical testing is conducted on these methods and their results are analyzed using statistical techniques to quantitatively characterize their behavior. Analysis confirms the supposition that regulation and technological innovations are often required in tandem to achieve a regulator’s aims; however, it also reveals that, under select conditions, the regulator is better served by not intervening.