【作者】 郝春艳；

【导师】 杨超；

【作者基本信息】 华中科技大学 ， 管理科学与工程， 2006， 博士

【摘要】 在我们的实际生活中会遇到多种类型的网络,例如城市交通网络,电信通讯网络,电力输送网络,计算机网络等。这些各种各样的网络在国家的经济建设中占有重要的地位,是经济建设与发展的载体和桥梁。这些年来,随着中国经济建设的迅速发展,各种网络都在发生着翻天覆地的变化。因此研究网络优化模型对于实际网络建设的决策具有很重要的参考价值。网络优化模型在国内外的文献中研究很多,所包括的内容非常广泛。本文所研究的内容主要是网络优化模型中的容量扩张模型。在实际生活中,特定的网络所能提供的容量一般而言是有限的,所以当网络所能提供的容量不能满足顾客对网络容量的需求时,就会出现网络容量扩张要求。本文主要研究目标是网络容量扩张过程中的成本和效益模型及其算法,即研究在容量扩张过程如何使成本最小或者网络运行效益最大。该问题具有非常重要的理论意义和实际应用意义。全文分为六章,首先为导论,论述了研究容量扩张成本效益模型研究的背景,意义和方法;其次为容量扩张基本模型和基本算法概述,是后续研究的必要基础;再次是第三章到第五章,为本文的主要内容,分别讨论了网络容量扩张成本预算模型及算法研究,网络容量扩张的成本效益最优均衡模型及算法研究,和随机约束下的网络容量扩张成本效益最优均衡模型及算法研究。本文的最后一章总结全文内容,并展望了未来的研究方向。在本文主要内容所研究的模型如下。首先是网络容量扩张中的成本预算模型及算法,主要研究在预算给定情况下有向网络的容量扩张策略。本章提出的两个模型考虑的是在预算给定情况下,针对不同的假设条件,网络的容量扩张策略。其次探讨了网络容量扩张规划中的成本效益最优均衡模型及算法。研究的是容量扩张的效益函数与成本函数之间的关系的模型,即效益函数与成本函数之差模型和效益函数与成本函数之比模型。最后讨论的是随机约束下的网络容量扩张成本效益均衡模型及算法研究。考虑的是在有向网络中,为使网络运行产生的纯效益最大,在不确定需求下的多阶段容量扩张策略。除了多阶段容量扩张模型,还考虑了几个相关的随机容量扩张模型。网络容量扩张中还有很多问题值得去研究,例如随机约束下的网络扩张模型,特殊网络中的网络容量扩张等。这些模型在实际生活中应用非常广泛,有非常重要的实际应用价值。在今后的研究中,还要加强这方面的研究。更多还原

【Abstract】 In our real life there are many kinds of network, such as urban traffic network, telecommunication network, power generation network and computer network. All these networks play important roles in our economic life and they are the carrier of the country economic growth. During all these years of quick development of Chinese economy, network is going through deep changes. Therefore, research on network optimization is very critical reference for decision makers in real network construction.It is well known that the network optimization model attains great attentions in international research field and there are many aspects of models mentioned. In this dissertation, some models and their corresponding algorithms about cost-benefit trade-offs raised in capacity expansion of network are presented. For, in reality, a certain network’s capacity could be limited, when the capacity need be expanded because of increasing demands, the network capacity expansion problem comes up.There are six chapters in this dissertation except the abstract. The first chapter gives the application background of the models, and, also research methods and creative idears in the dissertation is put forward in detail. The second chapter presents research background, including basic models and basic algorithms in network flow theory and capacity expansion models. Chapter three to Chapter five are the main content, in which five main models and some related models are presented and discussed in this part. Last chapter presents the conclusion of the whole dissertation; meanwhile, some future research on models of cost-benefit about capacity expansion is presented.The main models and algorithms are discussed in three chapters. Firstly, it is the research of cost budget models and algorithms in network capacity expansion, which considers two models’capacity expansion strategy under given budget with different assumptions. Secondly, it is about research of optimum cost-benefit trade-off models and algorithms in network expansion. In this part the relationship between benefit function and cost function are discussed, including difference and ratio of two functions. Finally, it presents cost-benefit models and algorithms under stochastic factors. It discusses multi-stage network capacity expansion strategy with stochastic demand, in which demand is uncertain but the probability distribution function is known. There are still many problems worth researching in this field and stochastic conditions get highly attention recently in international literature because of its characteristic is closer to realistic description. The future research in capacity expansion should take more consideration on this aspect.更多还原