Locating collection centers for incentive-dependent returns under a pick-up policy with capacitated vehicles

We address the problem of locating collection centers of a company that aims to collect used products from product holders. The remaining value in the used products that can be captured by recovery operations is the company's motivation for the collection operation. We assume that a pick-up strategy is in place according to which vehicles with limited capacity are dispatched from the collection centers to the locations of product holders to transport the returns. Each product holder has an inherent willingness to return, and makes the decision on the basis of the financial incentive offered by the company. The incentive depends on the condition of the returned item referred to as return type. We formulate a mixed-integer nonlinear facility location-allocation model to find both the optimal locations of a predetermined number of collection centers and the optimal incentive values for different return types. Since the problem is , we propose a heuristic method to solve medium and large-size instances. The main loop of the method is based on a tabu search method performed in the space of collection center locations. For each location set prescribed by tabu search, Nelder-Mead simplex search is called to obtain the best incentives and the corresponding net profit. We experiment with different quality profiles when there are two and three return types, and observe the effect of the uniform incentive policy (UIP) in which the same incentive is offered to product holders regardless of the quality of their returns. We conclude that the UIP is inferior to the quality-dependent incentive policy resulting in a higher profit loss when the proportion of lowest quality returns is relatively high.