mixed-integer nonlinear programming

The competitive market and declined economy have increased the relevant importance of making supply chain network efficient. This has created many motivations to reduce the cost of services, and simultaneously, to increase the quality of them. The network as a tri-echelon one consists of Suppliers, Warehouses or Distribution Centers (DCs), and Retailer nodes. To bring the problem closer to reality, the majority of the parameters in this network consist of retailer demands, lead-time, warehouses holding and shipment costs, and also suppliers procuring and stocking costs all are assumed to be stochastic. The aim is to determine the optimum service level so that total cost could be minimized. Reaching to such issues passes through determining which suppliers nodes, and which DCs nodes in network should be active to satisfy the retailers' needs, the matter that is a network optimization problem per se. Proposed supply chain network for this paper is formulated as a mixed integer nonlinear programming, and to solve this complicated problem, since the literature for related benchmark is poor, three ones of GA-based algorithms called Non-dominated Sorting Genetic Algorithm (NSGA-II), Non-dominated Ranking Genetic Algorithm (NRGA), and Pareto Envelope-based Selection Algorithm (PESA-II) are applied and compared to validate the obtained results.