發(fā)布時(shí)間：2018-04-21 22:12

  本文選題：設(shè)施選址問(wèn)題 + 轉(zhuǎn)運(yùn)站��； 參考：《哈爾濱理工大學(xué)》2016年博士論文

【摘要】：在公共部門或私人企業(yè)的戰(zhàn)略規(guī)劃階段,設(shè)施選址決策是一個(gè)關(guān)鍵要素,其好壞對(duì)企業(yè)操作層的決策以及物流決策具有長(zhǎng)期影響,從而深刻影響著企業(yè)在市場(chǎng)競(jìng)爭(zhēng)中的勝負(fù)。設(shè)施選址問(wèn)題主要研究為一個(gè)或多個(gè)設(shè)施確定位置,以求在某些條件約束下所考慮的目標(biāo)達(dá)到最優(yōu)。很多設(shè)施在為需求點(diǎn)服務(wù)的過(guò)程中需要在某些已經(jīng)建成并正在運(yùn)營(yíng)的資源點(diǎn)(如垃圾處理中心、倉(cāng)庫(kù)等)中選取一個(gè)作為中轉(zhuǎn)點(diǎn)(稱之為轉(zhuǎn)運(yùn)站),其中選擇的原則是使服務(wù)該需求點(diǎn)的成本最小。設(shè)施選址的目標(biāo)是為所有需求點(diǎn)服務(wù)的成本最小。這類具有轉(zhuǎn)運(yùn)站的設(shè)施選址問(wèn)題可以看作是經(jīng)典的設(shè)施選址問(wèn)題(Weber問(wèn)題或中心問(wèn)題)的推廣。因此,對(duì)具有轉(zhuǎn)運(yùn)站的設(shè)施選址問(wèn)題的研究不僅是對(duì)設(shè)施選址問(wèn)題理論研究成果的豐富和發(fā)展,而且可以使經(jīng)典Weber問(wèn)題和中心問(wèn)題得到深化和完善。距離度量是設(shè)施選址問(wèn)題中的一個(gè)關(guān)鍵因素。不同設(shè)施的選址問(wèn)題選用的距離度量通常也不盡相同,但大多數(shù)情況下假設(shè)兩點(diǎn)間的往返距離(或時(shí)間)是一樣的,即距離度量滿足對(duì)稱性。然而在現(xiàn)實(shí)生活中,由于某些因素的影響,兩點(diǎn)間往返的速度或路線不同,導(dǎo)致了往返時(shí)間或距離有所差異。因此,將不滿足對(duì)稱性的距離度量引入到設(shè)施選址問(wèn)題中具有重要的理論和現(xiàn)實(shí)意義。另一方面,需求點(diǎn)的權(quán)重可以體現(xiàn)該需求點(diǎn)的需求量。在設(shè)施建成后并為需求點(diǎn)提供服務(wù)的時(shí)期內(nèi),需求點(diǎn)的需求量通常不是固定不變的,即需求點(diǎn)權(quán)重不是固定的數(shù)值。如果權(quán)重是服從概率分布的隨機(jī)變量,則服務(wù)成本也將為隨機(jī)的。當(dāng)追求成本最小目標(biāo)時(shí),企業(yè)可以將最小期望成本作為設(shè)施選址的成本預(yù)算上限即成本閾值的參考值。但在為設(shè)施選址的實(shí)際操作過(guò)程中可能會(huì)發(fā)生實(shí)際成本大于成本閾值即成本超支的情況。如果企業(yè)管理者可以容忍這種情況的發(fā)生,那么選址的目標(biāo)則轉(zhuǎn)化為使發(fā)生成本超支的概率最小。因此,將成本超支概率作為目標(biāo)引入到設(shè)施選址問(wèn)題更符合現(xiàn)實(shí)情況。針對(duì)距離度量缺乏對(duì)稱性以及需求點(diǎn)權(quán)重發(fā)生變化的問(wèn)題,本文對(duì)具有轉(zhuǎn)運(yùn)站的設(shè)施選址問(wèn)題開展了較為深入系統(tǒng)的研究工作,以期豐富對(duì)具有轉(zhuǎn)運(yùn)站的設(shè)施選址問(wèn)題的研究成果,并為具有這種服務(wù)特點(diǎn)的設(shè)施的選址問(wèn)題提供一種理論方法指導(dǎo)。本文首先總結(jié)了連續(xù)設(shè)施選址問(wèn)題中常用的距離度量,其中大部分距離度量都是由gauge度量定義的凸距離函數(shù)的特殊情況;針對(duì)具有不確定性的選址問(wèn)題,重點(diǎn)總結(jié)并介紹基于其中兩種求解方法即概率方法和場(chǎng)景規(guī)劃法的選址模型;對(duì)于具有轉(zhuǎn)運(yùn)站的設(shè)施選址問(wèn)題,分析了采用不同目標(biāo)以及不同服務(wù)路徑的選址模型。在此基礎(chǔ)上,提出了本文具有轉(zhuǎn)運(yùn)站的設(shè)施選址問(wèn)題優(yōu)化模型研究的總體框架。針對(duì)實(shí)際選址問(wèn)題中距離度量不滿足對(duì)稱性的情況,構(gòu)建了凸距離下具有轉(zhuǎn)運(yùn)站的設(shè)施選址問(wèn)題minimax模型和minisum模型。針對(duì)不同的服務(wù)路徑,將選址模型分別細(xì)分為環(huán)形路徑模型和單向路徑模型。利用幾何學(xué)和凸分析方法,研究凸距離下平分集的性質(zhì)和優(yōu)勢(shì)解的存在性,由此證明選址模型最優(yōu)解的存在性。利用凸分析中的次梯度,有效地構(gòu)造模型目標(biāo)函數(shù)的下界,并結(jié)合大三角形小三角形方法提出了凸距離下具有轉(zhuǎn)運(yùn)站的設(shè)施選址問(wèn)題的求解方案。在具有轉(zhuǎn)運(yùn)站的設(shè)施選址問(wèn)題中,當(dāng)需求點(diǎn)權(quán)重為服從概率分布的獨(dú)立隨機(jī)變量時(shí),將成本表示為服務(wù)所有需求點(diǎn)并且經(jīng)過(guò)某個(gè)轉(zhuǎn)運(yùn)站的最大加權(quán)服務(wù)距離,分別建立了minimax目標(biāo)下成本超支概率最小化問(wèn)題的環(huán)形路徑模型和兩種單向路徑模型。研究成本超支概率最小化問(wèn)題優(yōu)化模型的性質(zhì),證明模型最優(yōu)解在需求點(diǎn)和轉(zhuǎn)運(yùn)站點(diǎn)的凸包中的存在性。通過(guò)分別給出環(huán)形路徑距離和單向路徑距離的上下界、相應(yīng)目標(biāo)函數(shù)的下界并結(jié)合大三角形小三角形方法,為隨機(jī)minimax模型提出一個(gè)相應(yīng)的求解方案,并通過(guò)數(shù)值算例驗(yàn)證該求解方案的可行性。當(dāng)需求點(diǎn)權(quán)重服從概率分布時(shí),將成本表示為到需求點(diǎn)且經(jīng)過(guò)某個(gè)轉(zhuǎn)運(yùn)站的加權(quán)服務(wù)距離之和,建立采用不同服務(wù)路徑的成本超支概率最小化問(wèn)題minisum模型。一方面,將成本超支概率最小化問(wèn)題等價(jià)轉(zhuǎn)化為閾值的標(biāo)準(zhǔn)化最大化問(wèn)題,研究閾值標(biāo)準(zhǔn)化最大化問(wèn)題優(yōu)化模型的性質(zhì),并給出模型最優(yōu)解存在性的充分條件。另一方面,當(dāng)成本超支概率為已知定值時(shí),通過(guò)標(biāo)準(zhǔn)正態(tài)分布上側(cè)?分位數(shù)給出閾值函數(shù),建立閾值函數(shù)最小化問(wèn)題優(yōu)化模型,給出該優(yōu)化問(wèn)題最優(yōu)解存在性的充分條件。通過(guò)分別給出相應(yīng)目標(biāo)函數(shù)的上下界并結(jié)合大三角形小三角形方法,提出這兩個(gè)優(yōu)化模型相應(yīng)的求解方案,并通過(guò)數(shù)值算例驗(yàn)證求解方案的可行性。采用本文提出的具有轉(zhuǎn)運(yùn)站的設(shè)施選址問(wèn)題凸距離模型和隨機(jī)模型及相應(yīng)求解算法,針對(duì)哈爾濱市香坊區(qū)第一環(huán)境衛(wèi)生運(yùn)輸中心進(jìn)行實(shí)證研究。在分析其垃圾清運(yùn)服務(wù)現(xiàn)狀的基礎(chǔ)上,在凸距離和隨機(jī)需求環(huán)境下對(duì)運(yùn)輸中心位置進(jìn)行優(yōu)化以應(yīng)對(duì)人口的增長(zhǎng),為其未來(lái)重新選址提供科學(xué)合理的理論依據(jù)。
[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.

【學(xué)位授予單位】：哈爾濱理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TU993;F252
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本文編號(hào)：1784282