Locating collection centers with incentive under a pick-up policy for the entire return products

The main concern of this paper is the problem of location collection center of a company that aims to collect the entire used product returned by product holders. Capturing trapped value in the used product through recovery operations is the main motivation for company to collect the return products. It is assumed 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 her/his decision is reinforced on the quantity of financial incentive offered by the company. The incentive depends on the condition of the returned item referred to as return type. The problem was formulated as 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. Then the model was solved through assigning two distinct values for quality (k).