Optimal carbon emissions in an integrated network of roads and UFTS under the finite construction resources

•The optimal resources allocation method for an integrated transportation network.•The characteristics of underground freight transport system are fully considered.•The method can maximally reduce carbon emissions generated by freight transport.•The applicability and reliability of the proposed method were tested. An urban underground freight transport system (UFTS) can be an alternative for relieving the pressure of traffic congestion, reducing carbon emissions and breaking the bottlenecks of logistics transportation. The construction and operation of UFTSs require many resources invested at early stages, while the resources provided in each city are limited. Properly creating an environmentally friendly UFTS under finite resources is a prerequisite for effective reduction of the carbon emissions generated by freight transportation and is a key basis for guidance regarding operations management and network expansion. The main goal of the present research study is to develop an optimal resources allocation strategy to reduce carbon emissions by using a bi-level programming model under the finite construction resources of an UFTS. Thus, an optimal resources allocation method was developed to optimize carbon dioxide emissions in an integrated network of roads and UFTS under finite construction resources. This method integrates the characteristics of carbon emissions in UFTS and road transportation, together with a relationship between construction resources and initial design speed. Due to the nonconvexity and discreteness of the question, we transform the bi-level programming model to a mixed-integer linear programming (MILP) model to obtain the optimum resource allocation strategy by linearizing the constraints and objective functions. The freight network between the Xiongan New Area and Beijing is taken as an example to verify the superiority of the model. The influences of the changes in resource quantities and typical strategies of transport time, freight volume in a UFTS and rotation volume of freight transport are analyzed, which provides a foundation for further study of the implementation of UFTSs in reality.