A mathematical model for optimization of an integrated network logistic design

In this study, the integrated forward/reverse logistics network is investigated, and a capacitated multi-stage, multi-product logistics network design is proposed by formulating a generalized logistics network problem into a mixed-integer nonlinear programming model (MINLP) for minimizing the total cost of the closed-loop supply chain network. Moreover, the proposed model is solved by using optimization solver, which provides the decisions related to the facility location problem, optimum quantity of shipped product, and facility capacity. Numerical results show the power of the proposed MINLP model to avoid th sub-optimality caused by separate design of forward and reverse logistics networks and to handle various transportation modes and periodic demand.