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A nonlinear model for a capacitated stochastic transportation network using multiple linear regression

机译：多元线性回归的容量随机运输网络非线性模型

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摘要

Here, a capacitated location-multi-allocation-routing problem with intelligent stochastic travel times is considered. In our study, the concept of intelligent stochastic travel times incurs two issues: (1) consideration of some random factors in computing the travel times and (2) impact of the traveling population on these random factors simultaneously. Here, a deterministic factor of road length and two random factors of the time spent in traffic and the number of accidents are considered. It is assumed that the time spent in traffic is distributed based on an exponential distribution function and the other factor is distributed based on a Poisson distribution function. Also, the capacities of server nodes and arcs for accepting the population are assumed to be limited. Using multiple linear regression, we formulate the problem as a mixed-integer nonlinear programming model. The objective is to find appropriate locations as server locations among the candidate locations, allocate the existing population in each demand node to server locations and determine the movement path of each member to reach its corresponding server with respect to the simultaneous change of the stochastic travel times so that the expected total transportation time is minimized. Also, to investigate the validation and behavior of the proposed probabilistic model, a network example is provided and computational results are analyzed.
机译：在此，考虑了具有智能的随机旅行时间的功能受限的位置-多分配-路由问题。在我们的研究中，智能随机旅行时间的概念引起两个问题：（1）在计算旅行时间时考虑一些随机因素；（2）旅行人口同时对这些随机因素的影响。在此，考虑了道路长度的确定性因素以及在交通中花费的时间和事故数量的两个随机因素。假定花费在业务上的时间是基于指数分布函数分布的，而其他因素是基于泊松分布函数分布的。同样，服务器节点和弧的容量被认为是有限的。使用多元线性回归，我们将问题表述为混合整数非线性规划模型。目的是在候选位置中找到合适的位置作为服务器位置，将每个需求节点中的现有人口分配给服务器位置，并针对随机旅行时间的同时变化确定每个成员到达其相应服务器的移动路径从而使预期的总运输时间最小化。另外，为了研究所提出的概率模型的有效性和行为，提供了一个网络示例并分析了计算结果。

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