A novel two-phase approach for a sustainable p-hub median problem with multiple service levels and carbon cap-and trade policy under uncertainty

To reduce the carbon emissions for society's sustainable development and satisfy customers' personalized delivery service, this paper addresses the cap-and-trade policy and multiple service levels into a p-hub median problem. In the hub network designing, single-assignment patterns between hubs and demand nodes, the choice of transportation mode for each O-D pair and the uncertainties of carbon emission and price are taken into account. Based on a fuzzy chance-constrained programming approach, a fuzzy mathematical model under an expected cost-minimization context with some fuzzy constraints is first presented. Then a two-phase approach is proposed to solve the proposed model. Finally, in view of the comparative analysis with small- and large-scale Turkish instances, serval managerial insights are finally obtained for government and logistics companies in the reduction of carbon emission and the hub network's total designing cost for the sustainable development.