Multiperiod and stochastic formulations for a closed loop supply chain with incentives

Reverse logistics network design problem we focus on is about locating distribution centers, inspection centers and remanufacturing facilities, and determining the acquisition price as well as the amount of returned goods to be collected depending on the unit cost savings and competitor's acquisition price. We introduce the multiple periods setting and stochastic demand formulated by scenarios. We develop two mathematical programming models to determine the pricing strategy of the recovered products together with the optimal network that must be designed to be the most profitable closed cycle. Our methodology is based on a Golden Section Search with some flexibility that enables us to fix the used product acquisition price and then solve the model as an integer linear programming. Moreover, we establish dependent size fixed costs of opening a distribution, an inspection, and a remanufacturing centers, and show that they have a strong impact on the Golden Section search behavior.