Multi-period multi-product closed loop supply chain network design: A relaxation approach

Growing concern about environmental deterioration, manifested in new laws to protect the environment and business competition, has stimulated the idea of Closed Loop Supply Chains (CLSC). This paper develops strategic decision-making models for two different CLSCs with multiple products over multiple periods. One of the networks has six levels, while the other has four levels, and they can be applied to products with different levels of complexity during inspection and remanufacturing operations. The supply chain networks are modeled as Integer Linear Programs (ILP) designed to assist decision-making in terms of location/allocation, transportation, and inventory. Taking advantage of the properties of the formulations, we propose an integer relaxation approach to obtain the optimal solution to ILP. The proposed models and methodologies are illustrated with case studies from the literature and with hypothetical datasets. This research contributes with design standard configurations for CLSCs that can be used for different types of products. Directly using these configurations is advantageous because the models proposed can be quickly solved using the integer relaxation approach. The associated trials confirm the utility of the models for the case studies and demonstrate encouraging results for the hypothetical datasets.