具有转运站的设施选址问题优化模型研究

发布时间：2018-04-21 22:12

  本文选题：设施选址问题 + 转运站　； 参考：《哈尔滨理工大学》2016年博士论文

【摘要】：在公共部门或私人企业的战略规划阶段,设施选址决策是一个关键要素,其好坏对企业操作层的决策以及物流决策具有长期影响,从而深刻影响着企业在市场竞争中的胜负。设施选址问题主要研究为一个或多个设施确定位置,以求在某些条件约束下所考虑的目标达到最优。很多设施在为需求点服务的过程中需要在某些已经建成并正在运营的资源点(如垃圾处理中心、仓库等)中选取一个作为中转点(称之为转运站),其中选择的原则是使服务该需求点的成本最小。设施选址的目标是为所有需求点服务的成本最小。这类具有转运站的设施选址问题可以看作是经典的设施选址问题(Weber问题或中心问题)的推广。因此,对具有转运站的设施选址问题的研究不仅是对设施选址问题理论研究成果的丰富和发展,而且可以使经典Weber问题和中心问题得到深化和完善。距离度量是设施选址问题中的一个关键因素。不同设施的选址问题选用的距离度量通常也不尽相同,但大多数情况下假设两点间的往返距离(或时间)是一样的,即距离度量满足对称性。然而在现实生活中,由于某些因素的影响,两点间往返的速度或路线不同,导致了往返时间或距离有所差异。因此,将不满足对称性的距离度量引入到设施选址问题中具有重要的理论和现实意义。另一方面,需求点的权重可以体现该需求点的需求量。在设施建成后并为需求点提供服务的时期内,需求点的需求量通常不是固定不变的,即需求点权重不是固定的数值。如果权重是服从概率分布的随机变量,则服务成本也将为随机的。当追求成本最小目标时,企业可以将最小期望成本作为设施选址的成本预算上限即成本阈值的参考值。但在为设施选址的实际操作过程中可能会发生实际成本大于成本阈值即成本超支的情况。如果企业管理者可以容忍这种情况的发生,那么选址的目标则转化为使发生成本超支的概率最小。因此,将成本超支概率作为目标引入到设施选址问题更符合现实情况。针对距离度量缺乏对称性以及需求点权重发生变化的问题,本文对具有转运站的设施选址问题开展了较为深入系统的研究工作,以期丰富对具有转运站的设施选址问题的研究成果,并为具有这种服务特点的设施的选址问题提供一种理论方法指导。本文首先总结了连续设施选址问题中常用的距离度量,其中大部分距离度量都是由gauge度量定义的凸距离函数的特殊情况;针对具有不确定性的选址问题,重点总结并介绍基于其中两种求解方法即概率方法和场景规划法的选址模型;对于具有转运站的设施选址问题,分析了采用不同目标以及不同服务路径的选址模型。在此基础上,提出了本文具有转运站的设施选址问题优化模型研究的总体框架。针对实际选址问题中距离度量不满足对称性的情况,构建了凸距离下具有转运站的设施选址问题minimax模型和minisum模型。针对不同的服务路径,将选址模型分别细分为环形路径模型和单向路径模型。利用几何学和凸分析方法,研究凸距离下平分集的性质和优势解的存在性,由此证明选址模型最优解的存在性。利用凸分析中的次梯度,有效地构造模型目标函数的下界,并结合大三角形小三角形方法提出了凸距离下具有转运站的设施选址问题的求解方案。在具有转运站的设施选址问题中,当需求点权重为服从概率分布的独立随机变量时,将成本表示为服务所有需求点并且经过某个转运站的最大加权服务距离,分别建立了minimax目标下成本超支概率最小化问题的环形路径模型和两种单向路径模型。研究成本超支概率最小化问题优化模型的性质,证明模型最优解在需求点和转运站点的凸包中的存在性。通过分别给出环形路径距离和单向路径距离的上下界、相应目标函数的下界并结合大三角形小三角形方法,为随机minimax模型提出一个相应的求解方案,并通过数值算例验证该求解方案的可行性。当需求点权重服从概率分布时,将成本表示为到需求点且经过某个转运站的加权服务距离之和,建立采用不同服务路径的成本超支概率最小化问题minisum模型。一方面,将成本超支概率最小化问题等价转化为阈值的标准化最大化问题,研究阈值标准化最大化问题优化模型的性质,并给出模型最优解存在性的充分条件。另一方面,当成本超支概率为已知定值时,通过标准正态分布上侧?分位数给出阈值函数,建立阈值函数最小化问题优化模型,给出该优化问题最优解存在性的充分条件。通过分别给出相应目标函数的上下界并结合大三角形小三角形方法,提出这两个优化模型相应的求解方案,并通过数值算例验证求解方案的可行性。采用本文提出的具有转运站的设施选址问题凸距离模型和随机模型及相应求解算法,针对哈尔滨市香坊区第一环境卫生运输中心进行实证研究。在分析其垃圾清运服务现状的基础上,在凸距离和随机需求环境下对运输中心位置进行优化以应对人口的增长,为其未来重新选址提供科学合理的理论依据。
[Abstract]:In the strategic planning stage of the public or private enterprises, the decision of facility location is a key factor. It has a long influence on the decision of the enterprise operation and the logistics decision, which has a profound influence on the success and defeat of the enterprise in the market competition. In the process of serving the demand point, many facilities need to select one as a transfer point (called a transport station) in some of the already built and running resource points (such as garbage disposal centers, warehouses, etc.). The selection principle is to minimize the cost of the service demand point. The goal of site selection is to minimize the cost of service for all demand points. This kind of facility location problem with transport stations can be regarded as a generalization of the classic facility location problem (Weber or central problem). Therefore, the research on the location of the facility with the transport station is not only rich in the theoretical research results of the facility location problem. The classic Weber and central problems can be deepened and perfected. Distance measurement is a key factor in the location of facilities. The distance measurement of the location of different facilities is usually different, but in most cases the distance between two points is the same, that is, the distance measure is satisfied. However, in real life, due to the influence of some factors, the speed or route of round-trip between two points is different, and the return time or distance is different. Therefore, it is important to introduce the distance measure of symmetry to the problem of facility location. On the other hand, the weight of the demand point can be reflected. In a period when the facilities are built and provided for the demand point, the demand point is usually not fixed, that is, the demand point weight is not a fixed value. If the weight is a random variable that obeys the probability distribution, the service cost will also be on the machine. The minimum expected cost is used as the cost limit of the facility location, that is, the reference value of the cost threshold. But in the actual operation of the facility location, the actual cost may be greater than the cost overrun. The probability of overspending on cost is the smallest. Therefore, it is more realistic to introduce the cost overspending probability as the target to the facility location problem. In this paper, the problem that the distance measurement is not symmetrical and the demand point weight change, this paper has carried out a more thorough and systematic research on the facility location problem with the transport station, in order to enrich the problem. This paper provides a theoretical method guidance for the location of facilities with the characteristics of this service. This paper first summarizes the common distance measurement in the location problem of continuous facilities, most of which are the special cases of the convex distance function defined by the gauge degree; For the location problem with uncertainty, this paper mainly summarizes and introduces the location model based on two solution methods, the probability method and the scene planning method, and analyzes the location model with different targets and different service paths for the facility location problem with the transport station. On this basis, this paper puts forward the establishment of this paper with the transfer station. In view of the fact that the distance measurement is not symmetrical in the actual location problem, the minimax model and the minisum model of the facility location problem with the transport station are constructed under the convex distance, and the location model is divided into ring path model and one-way path model for different service paths. By using geometry and convex analysis, we study the properties of the flat diversity under convex distance and the existence of the superiority solution, thus prove the existence of the optimal solution of the location model. By using the subgradient in the convex analysis, the lower bounds of the model objective function are constructed effectively, and the transport station with the convex distance is proposed with the large triangle small triangle method. In the facility location problem, when the weight of the demand point is an independent random variable that obeys the probability distribution, the cost is expressed as all the service demand points and the maximum weighted service distance of a certain transport station, and the minimum cost overspending under the minimax target is established. The properties of the optimization model for the minimization of the cost overspending probability are studied, and the existence of the optimal solution of the model is proved in the convex hull of the demand point and the transport site. By giving the upper and lower bounds of the distance of the ring path and the one-way path distance, the lower bound of the corresponding objective function and the combination of the big triangle, respectively. A small triangle method is used to provide a corresponding solution for the random minimax model, and the feasibility of the solution is verified by a numerical example. When the demand point weight obeys the probability distribution, the cost is expressed as the demand point and the weighted service distance of a transport station is passed, and the cost over the different service paths is established. On one hand, the equivalence of the cost overspending minimization problem is converted to the maximization of the threshold, and the properties of the optimization model of the maximization of the threshold standardization are studied, and the sufficient conditions for the existence of the optimal solution of the model are given. The other side, when the cost overspending is known, passes through the minisum model. The threshold function is given in the upper side of the normal normal distribution, the optimization model of the threshold function minimization problem is established, and the sufficient condition for the existence of the optimal solution is given. By giving the upper and lower bounds of the corresponding objective functions and combining the large triangle small triangle method, the corresponding solutions of the two optimization models are proposed and the solutions are put forward. A numerical example is given to verify the feasibility of the solution. A convex distance model, a random model and a corresponding algorithm are used to solve the facility location problem of the transport station. The first environmental health transport center in Xiangfang District, Harbin, is carried out an empirical study. On the basis of the analysis of the status of the service, the convex distance and the following are analyzed. The location of transportation center is optimized to meet the population growth under the machine demand environment, so as to provide a scientific and reasonable theoretical basis for its future location.

【学位授予单位】：哈尔滨理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TU993;F252
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本文编号：1784282