Locating collection centers for distance- and incentive-dependent returns

We address the problem of locating collection centers of a company that aims to collect used products from consumers. The remaining value in the used products that can be captured by recovery operations is the company's main motivation for the collection operation. We assume that a drop-off strategy is in place according to which product holders travel to the collection centers established by the company for returning their used goods. Each product holder has an inherent willingness to return, and decides whether or not to return based on both the financial incentive offered by the company for the returned item and the proximity to the nearest collection center. Returned items are categorized with respect to their quality level into classes called return types, and a different incentive is offered for each return type. We formulate a mixed-integer nonlinear facility location–allocation model to determine both the optimal locations of the collection centers and the optimal incentive values for each return type so as to maximize the profit from the returns.