Maximizing recyclable materials and user utility in waste collection: a linear-quadratic bilevel optimization approach

In this paper, we present the problem in which a municipal company operating in the waste management sector willing to encourage users to use differentiated waste collection facilities, designs a utility user function to attain such a goal. The problem is modeled in terms of bilevel optimization where the leader is the municipal firm which aims at maximizing the concurrent fraction of user waste demand thrown in recycling facilities, and the follower are users aiming at maximizing the utility function proposed by the leader. The resulting bilevel model is analysed in terms of stability showing that its optimistic solution value equals the pessimistic solution value. A solution approach is presented. Finally, a computational study shows the effectiveness of our proposal.