Location of differentiated waste collection centers with user cooperation: a bilevel optimization approach

We focus on the problem of locating differentiated waste collection centers: a municipal firm acts with the goal of locating and installing proper capacities to such facilities with the goal of defining a cooperative behaviour of the users of an urban area, possibly giving economic incentives to the latter in the case they decide to follow a predefined planning on waste recycling. The problem has a hierarchical structure and can be modeled as a bilevel program where the leader decision maker, i.e., the municipal firm, identifies which facilities should be opened along with their capacities minimizing the costs while the follower decision maker acts on behalf of the cooperating users in order to maximize the total utility deriving from delivering wastes to facilities. Besides the mathematical formulation of the problem, we propose a randomized-rounding based heuristic to cope with its solution. Experiments on synthetic instances and a comparison with a known algorithm in the literature are presented to assess the effectiveness of our proposal.