Optimal design of two levels reverse logistic supply chain by considering the uncertain quantity of collected multi-products

In the recent years, the reverse logistic supply chain has taken an important part in manufacturing systems. Due to the pressures from both environmental awareness and business sustainability, several companies must work in collaboration to solve partially the problem of waste recovery. The purpose of this work is to help those companies who would like to pursue reverse logistics as axe of profit. In this paper we present a mixed-integer linear programming (MILP) model which includes several costs of collection, treatment and sales income from secondary market. The goal of study is to investigate the best material flows between different specialized facilities under capacities constraints and costs minimization. The model is sub divides in two levels: the first level concerns the collect process while a size of each product is compared to a standard size to optimize the storage capacity of collection centers. Then to unify the request of several products or classes of products, in the second level a running time is added instead a processing capacity by product and used to facilitate the study of multi-product case. This proposed optimization model can help to determine the optimal facility location and the material flows of network for multiproduct in pseudo dynamic case. The usefulness of the proposed model is a real design of reverse network with considering the uncertain quantity of collected product and a progressive investment. To give to the study an illustration, we present an example to regard the recovery rate using Lingo 12.0 solver.