运输问题的改进算法探讨

探讨了运输问题表上作业法初始解的取得和最优解的判断，在一定程度上可以省略表上作业法的方案调整过程，从而简便了求解运输问题的最优解的过程。     

初始可行基的判定

用高等数学的理论和方法,对无初始可行基的线性规划问题解的存在性及求解方法进行研究,得出关于无初始可行基的线性规划问题解的存在性的六个定理,回答了无初始可行基的线性规划问题解的存在条件和该问题的初始可行基的确定方法.     

需求区间型运输问题的求解算法

为了便于建立与需求区间型运输问题有关的决策支持系统，本给出了一个求解需求区间型运输问题的数值算法，证明了算法的理论依据，并举例说明算法的应用，该算法能求得问题的最优解，并具有易于编程实现、收敛性好等优点，大量数值实验表明该算法有较高的计算效率。     

基于出行方式选择的运输通道客运结构的协调研究

针对区域综合运输通道客运交通供给和需求量大,出行方式多,各出行方式竞争激烈的特点.为了避免各出行方式之间存在恶性竞争,扰乱运输市场的正常秩序,建立了区域综合运输通道协同的多目标非线性规划数学模型.模型建立在出行者对交通方式的选择遵守效用极大化原理的基础上,系统目标为各出行方式的供给量与需量相适应.采用模糊折中算法将多目标转化为单目标,同时采用广义牛顿法对非线性规划问题进行求解,为了避免求得的解为局部最优解,提出了随机从不同的初始点进行寻优,尔后对各个结果进行比较,从中选出较优者作为全局最优解.该方法极大的提高了所求解为全局最优解的可靠性.最后通过算例证明了模型的正确性和可行性.     

一类双参数奇摄动非线性反应扩散方程

本文研究了一类双参数非线性反应扩散奇摄动问题的模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的情形下作了讨论.得到了该问题的渐近解,由解的展开式看出本问题的解同时具有初始层和边界层.     

多目标运输问题的Fuzzy线性规划解法

经典运输问题是一类特殊的单目标线性规划问题，可用表上作业法或单纯形法求其最优解。近年来，许多学研究了多目标运输问题，提出了相应的求解算法。本应用Fuzzy线性规划的方法，给出了多目标运输问题的又一求解算法。     

具广义非线性源的波动方程的高能爆破

研究一类具广义非线性源的非线性波动方程的初边值问题在高初始能级状态下解的有限时间爆破.利用经典的凹函数方法找到了导致该问题具任意正初始能级的解有限时间爆破的初值.     

关于<用初等行变换解一类线性规划问题>一文的注记

本指出，在献[1]提出的求解线性规划的方法中，对于初始可行基、最优解和零解的存在性问题所得出的某些结论是错误的，特殊是如果含n个变量的约束条件的增广矩阵经初等行变换后，其中某行的前n个分量非正，而最后一个分量为0时，应认为该线性规划问题可能有非零解，且不一定存在零解，而非[1]所述的结论。     

一类非线性方程解的存在和唯一性及在图像中的应用

本文我们给出一个修正的非线性扩散方程模型，与Cotte Lions和Morel的模型相比该模型有许多实质上的优点。主要的想法是把原来去噪声部分：卷积Gauss过程替代为解一个有界区域上的线性抛物方程问题，因此避开了对初始数值如何全平面延拓的问题。我们从数学上的证明该问题解的存在性和适定性，同时给出对矩形域情况的解的级数形式。最后我们给基于本模型的数值计算差分模型，并且给出几个具体图像在该模型下处理结果。     

矩阵方程AX＋XB=C的双对称解及其最佳逼近

提出一种求解线性矩阵方程AX＋XB=C双对称解的迭代法.该算法能够自动地判断解的情况,并在方程相容时得到方程的双对称解,在方程不相容时得到方程的最小二乘双对称解.对任意的初始矩阵,在没有舍入误差的情况下,经过有限步迭代得到问题的一个双对称解.若取特殊的初始矩阵,则可以得到问题的极小范数双对称解,从而巧妙地解决了对给定矩...     

On minimizing the duration of transportation

The problem of minimizing the duration of transportation has been studied. The problem has been reduced to a goal programming-type problem which readily lends itself to solution by the standard transportation method. This approach to the solution of the problem is very much different from all other existing ones.     

供给总量限定需求区间约束型运输问题——时限费用优化模型与算法

本文目的是为建立与运输问题有关的决策支持系统提供方便.本文建立了供给总量限定需求区间约束型运输问题的对时限与费用两个目标进行优化的多目标规划模型,给出了求解模型的算法,并举例说明了算法的应用.该算法能求得问题的最优解,并具有易于编程实现、收敛性好等优点.数值实验表明该算法有较高的计算效率,可用于求解某些类型的指派问题.     

Capacitated transportation problem with bounds on RIM conditions

Motivated by dead-mileage problem assessed in terms of running empty buses from various depots to starting points, we consider a class of the capacitated transportation problems with bounds on total availabilities at sources and total destination requirements. It is often difficult to solve such problems and the present paper establishes their equivalence with a balanced capacitated transportation problem which can be easily solved by existing methods. Sometimes, total flow in transportation problem is also specified by some external decision maker because of budget/political consideration and optimal solution of such problem is of practical interest to the decision maker and has motivated us to discuss such problem. Various situations arising in unbalanced capacitated transportation problems have been discussed in the present paper as a particular case of original problem. In addition, we have discussed paradoxical situation in a balanced capacitated transportation problem and have obtained the paradoxical solution by solving one of the unbalanced problems. Numerical illustrations are included in support of theory.     

满意度优化运输问题

传统运输问题只考虑配送方案的效率, 而不考虑参与者对配送方案的满意度. 通过引入参与者对配送方案的满意度这一概念, 提出了满意度优化运输问题, 构建了以最大化相对公平为目标的满意度优化运输模型, 并证明了: (1) 当运输问题的可行域不空时, 新模型的解集非空; (2) 从满意度的角度来看, 新模型的解是唯一的. 另外, 还给出了新模型的求解方法. 研究结果进一步丰富了运输问题的类型, 可为解决其他类型运输问题提供借鉴.     

Uncertain solid transportation problems

The solid transportation problem arises when bounds are given on three item properties. Usually, these properties are source, destination and type of product or mode of transport, and often are given in a uncertain way. This paper deals with two of the ways in which uncertainty can appear in the problem: Interval solid transportation problem and fuzzy solid transportation problem. The first arises when data problem are expressed as intervals instead of point values, and the second when the nature of the information is vague. Both models are treated in the case in which the uncertainty affects only the constraint set. For interval case, an auxiliary problem is obtained in order to find a solution. This auxiliary problem is a standard solid transportation problem which can be solved with the efficient methods existing. For fuzzy case, a parametric approach which makes it possible to find a fuzzy solution to the former problem is used.     

城市垃圾收运系统中的车辆收运计划问题

将垃圾收运系统中收运小车一天的收运计划问题,分为停车场设在转运站或别处两种情况,以小车行走总距离最小为目标,分别构建了混合整数规划模型.接着提出问题的求解思路:当停车场设在转运站时,可以将问题转化为VRP问题求解;若停车场设在别处,在求解上一问题的基础上设计了最近回路节点插入法将停车场插入离其最近的回路节点即可.最后以实例验证了模型和求解思路的可行性和有效性.     

Solving fixed charge transportation problem with interval parameters

In the present paper the fixed charge transportation problem under uncertainty, particularly when parameters are given in interval forms, is formulated. In this case it is assumed that both cost and constraint parameters are arrived in interval numbers. Considering two different order relations for interval numbers, two solution procedures are developed in order to obtain an optimal solution for interval fixed charge transportation problem (IFCTP). In addition, the two order relations are compared to give a better comprehension of their differences. Furthermore, numerical examples are provided to illustrate each of solution procedures.     

A truck scheduling problem arising in intermodal container transportation

We address a truck scheduling problem that arises in intermodal container transportation, where containers need to be transported between customers (shippers or receivers) and container terminals (rail or maritime) and vice versa. The transportation requests are handled by a trucking company which operates several depots and a fleet of homogeneous trucks that must be routed and scheduled to minimize the total truck operating time under hard time window constraints imposed by the customers and terminals. Empty containers are considered as transportation resources and are provided by the trucking company for freight transportation. The truck scheduling problem at hand is formulated as Full-Truckload Pickup and Delivery Problem with Time Windows (FTPDPTW) and is solved by a 2-stage heuristic solution approach. This solution method was specially designed for the truck scheduling problem but can be applied to other problems as well. We assess the quality of our solution approach on several computational experiments.