lp rounding based method

The study of product family and its design as well as issues related to supply chain is as fascinating discussion, and its modeling and optimization consider as a challenge for industries and businesses. In this paper, using a consolidated approach, a comprehensive model in the Mixed Integer Linear Program (MILP) dominant is proposed to concurrent optimization of product family and its supply chain network design by considering reverse logistics. In the proposed model, different levels of bill of material, including components, sub-assemblies, sub-sub-assemblies and finished products is considered while there is possibility of substitution at all levels. The supply chain network, includes 5 levels consist of suppliers, factories, distribution centers, customers and recycling centers. To solve low complexity instances in the view of products design and supply chain network structure, CPLEX solver has been applied. To solve high complexity instances, a heuristic method based on linear programming rounding has been developed, which caused a considerable reduction in solving time with an acceptable gap.