基于多面体不确定性需求的鲁棒枢纽选址研究

Robust hub location based on demand with polyhedral uncertainty

针对枢纽选址问题中的P枢纽中值问题,枢纽决策往往会受到外界因素的干扰。如何解决检验枢纽网络在面对干扰时的调节能力,即枢纽网络的鲁棒性研究,对外界因素造成流量需求的不确定性进行建模,不确定性以不确定性集的形式表现,对不确定性集通过2种方式建模:一是软管模型,对经过所有枢纽总流量的上限进行建模;二是混合模型,对经过所有OD(运输网络中流量的起始点和目的地点)流量的上限和下限进行建模。模型求解方面,运用极大极小准则和Benders分解算法解决混合整数规划问题。算例分析建立在对比标准模型和多面体需求不确定性模型的计算结果上,在不同规模参数和不确定性集参数下设置算法试验,模型更直观、有效的研究枢纽位置在外界干扰下的鲁棒性。Benders算法通过仅分解枢纽变量解决问题,更有效的实现了模型的应用;运用CPLEX求解器实现算法实验。

P-hub median problem in the hub location problem, always tends to be influenced by outsideconditions. This paper aimed to test hub network adjustment ability against interference and if the robust researchwith the polyhedral demand is uncertain by modeling uncertainty set in two ways： one is the hose model thatassumes supper bound of total demand though the traffic hub; and the second is hydird model that assumes supperbound and lower bound of total demand though OD, original point and destination point of traffic network. Usingthe minmax rule and Benders decomposition algorithm, the linear mixed integer programming problem wassolved. Results combining with analysis based on the standard model and the polyhedral uncertainty model wereobtained. Under the parameters of different scale uncertain sets, the model of this paper is more intuitive andeffective to study the robust hub location outsides interference condition. In this paper, Benders decomposition ismore effective to solve the model through the decomposition of hub only variable. Utilizing CPLEX solver tocomplete the algorithm was presented.