Mathematical modeling for the forward and reverse logistics network design

Nowadays, reverse logistics is one of the major activities of supply chain management that are included all of physical activities related to returned products (e.g., collection, recovery and recycle). So that, designing and implementing of appropriate reverse logistics, not only lead to increase customer loyalty, but also it will be reduce the inventory and transportation costs. This paper presents a mixed-integer linear programming (MILP) model for the network design of forward and reverse logistics, which minimizes the costs consisting of the fixed cost, material cost and construction of the potential center cost. To validate this model, a number of test problems are generated, and then its parameters are determined. The presented model is solved by the Lingo software and the associated computational results along with the sensitivity analysis are illustrated. Additionally, the returned products with different demands for one and two products are illustrated. Finally, the remarkable conclusion is presented.