Design of a government-subsidized collection system for incentive-dependent returns

We address the problem of locating collection centers for a company that aims to collect used products (cores) in order to capture their remaining value by recovery operations. A pick-up strategy is in place according to which vehicles are dispatched from collection centers to the locations of product holders to transport their returns. Each product holder has an inherent willingness to return a core, and decides on the basis of the quality-dependent financial incentive offered by the company. Since the company seeks only economic profitability, the collected amounts may not be aligned with the target collection ratio imposed by the government. In this case, the government may alleviate the under-collection issue through a subsidy paid to the company for each core collected. From the government´s perspective the problem is to find the minimum subsidy level while meeting the target collection ratio. We propose a bilevel programming formulation for this collection system design problem. Since the problem is NP-hard, a heuristic method is developed to solve medium and large size instances. This approach explicitly focuses on the relationship between government authorities and profit- oriented companies, and yields a frontier between the concurrent objectives of collection ratio satisfaction and subsidy minimization.