A stochastic programming model for hub-and-spoke network with uncertain flows

Hub-and-spoke network (HSN) exploits economy of scale in transportation and reduces logistics operational cost through collaborations among nodes. Because of the uncertainty of origin-destination (OD) flows between nodes, the uncertainty increases the risk of selecting capacities for nodes and affects the analysis of contribution of the nodes to the HSN. First, considering the characteristics of the uncertainty of OD flows, the throughput capacities of spoke nodes are determined based on stochastic programming approach and expectation theory; then, a stochastic mixed-integer linear programming model for designing hub-and-spoke network is established based on the capacities of spokes, and the structure of the HSN and throughput capacities of the hubs are designed. Second, the classification method of nodes is formulated based on the transportation flows between spokes, resource utilisation degree, and the branch and trunk convective equilibrium degree. A multi-attribute utility evaluation function for evaluating contribution rates of nodes to the HSN is established based on the proposed evaluation indices. Finally, the existing problems about network operational and adjustment strategies are analysed based on the contribution rates of the nodes to the HSN.