Design and analysis of government subsidized collection systems for incentive-dependent returns

We present and solve two bilevel programming (BP) models describing the subsidization agreement between the government and a company engaged in collection and recovery operations. These enable the company to capture the remaining value in cores, referring to used products of different quality types. To pick up the cores, the company needs to open collection centers, and dispatch vehicles on direct routes to customer sites. Customers have an inherent willingness to return their core, and decide to do so according to the quality-dependent financial incentive offered by the company. In order to promote collection and recovery the government pays a uniform subsidy to the company for each core collected. We introduce a supportive and a legislative BP model to tackle this comprehensive collection system design problem. In both models, the outer problem of the BP formulation involves the government, which is the leader and wants to minimize the unit subsidy. The company is the follower in the inner problem, and tries to maximize its net profit from the cores subject to the government's subsidy decision. In the supportive model, the company itself is not bound by the minimum collection rate targeted by the government, thus the amount of collected cores may not be sufficient. The government tries to resolve this situation with increased subsidization. The legislative model assigns the minimum collection rate responsibility to the company, but also entitles it to a certain profitability ratio guaranteed by the government. The solution methodology proposed for both models consists of Brent's method for the outer problem and a tabu search heuristic solving the inner problem. Its effectiveness is tested in computational experiments. The results show that for the same collection rate and profitability ratio the government has to grant a higher subsidy in the supportive model than in the legislative model.