Bilevel programming methods in waste-to-energy plants' price-setting game

Abstract

This paper deals with the problem of waste treatment pricing in the waste-to-energy (WtE) plants' network. The correct and stable estimate of gate fees should ensure efficient and financially sustainable waste energy recovery. The main contribution is a new price-setting approach, combining bilevel optimization techniques and game theory. The proposed approach dwells on two challenging steps. The first step is to solve the bilevel program, where the WtE plant on the upper level maximizes its income by setting the optimal gate fee, whereas waste producers on the lower level minimize the sum of their waste treatment costs. This optimization problem considers cities' waste production amounts, WtE plants' capacities, and locations. The novel heuristic algorithm, which can handle this bilevel program time-efficiently, is presented. It is based on the reformulations of bilevel problems of highway networks and pricing. The functionality of the heuristic has been validated using artificial waste management network scenarios. The second step is to establish the stable gate fee outcome in the waste management network, where numerous WtE plants are presented. This task is reformulated as a search for the Nash equilibrium in a normal-form game. The best-response dynamics algorithm enables establishing the game's equilibrium with numerous WtE plants and continuous strategy sets. The potential application of the proposed approach is demonstrated in the exemplary problem motivated by the Czech Republic. The found stable gate fee outcome is then used to estimate the optimal capacity of the prepared WtE facility project and ensure its financial viability in the existing waste management network.