The Study On P-Hub Median Problem By Robust Optimization Method

With the rapid development of economic globalization and economies of scale,the study on p-hub median problem has become a hot field in logistics network design.The main re-search content of this problem is to select a fixed number of nodes from the known nodes as hubs,and assign the remaining non-hub nodes to hubs.Most of the previous researchs are to minimize the total transportation cost or time.However,with the increasing awareness of envi-ronmental protection,carbon emissions in transportation also affect the design of hub network structure.In addition,due to the influence of uncontrollable factors such as weather conditions,road congestion and road conditions,carbon emissions in transportation are uncertain,and pre-cise probability distribution information of carbon emissions cannot be obtained through the available historical data.Therefore,when the probability distribution information of carbon emissions is unknown or partially known,this thesis applies the robust optimization method to study the p-hub median problem under uncertain carbon emissions.Under the carbon tax policy,this thesis first establishes the p-hub median model.Based on this model,this thesis studies the uncertain p-hub median problem,in which the distribu-tion information of carbon emissions is unknown.In the case of distribution free,this thesis assumes that the carbon emissions belong to an uncertainty set,and presents a robust p-hub median model.Then,aiming at the frequently-used uncertainty set,the equivalent form of ro-bust counterpart model is derived by using dual theory.Furthermore,the effectiveness of the proposed model is verified by numerical experiments.In addition,under the carbon trade policy,this thesis characterizes uncertain carbon emis-sions as an affine transformation of random variables,and the distribution information of ran-dom variables is partially known.That is to say,the real distribution of random variables be-longs to an ambiguity set.Thus,the distributionally robust p-hub median model is established in this thesis.Under two different ambiguity sets,the computationally tractable form of the proposed model is derived.Finally,the proposed model is applied to the hub network design of Southeast Asia,and the optimal hub network structures are given.The main work of this thesis can be summarized as the following four aspects:(1)The p-hub median problem under carbon policy is studied;(2)Depending on the uncertainty set,a robust p-hub median model is established,and its equivalent form is derived;(3)When the dis-tribution information of uncertain carbon emissions is only partially known,a distributionally robust p-hub median model is established.Under two kinds of ambiguity sets,the computation-ally tractable form is deduced;(4)The effectiveness of the proposed model is demonstrated by case study and comparative analysis.