An optimization model for closed-loop logistic system with uncertain demands

The operation process for a class of closed-loop logistic system with uncertain demands is considered. This system contains multiple suppliers, manufactories, distribution centers and customers, and the demands of customers are uncertainty. Based on the early research results, the integration of forward and reverse logistics was investigated. By using the robust optimization method based on scenario analyses approach, an optimization model is constructed to minimize the total cost of the transportation and the operations, and the total penalty of unsatisfied demands by optimally selecting the places of manufactories, distribution centers with the respective operation units. A numerical example is designed, of which the results shown that the proposed model is able to support the logistic decisions in a closed-loop logistic system with uncertain demands efficiently.