Properties of a multifacility location problem involving euclidian distances

This paper considers a problem of locating new facilities in the plane with respect to existing facilities, the locations of which are known. The problem consists of finding locations of new facilities which will minimize a total cost function which consists of a sum of costs directly proportional to the Euclidian distances among the new facilities, and costs directly proportional to the Euclidian distances between new and existing facilities. It is established that the total cost function has a minimum; necessary conditions for a mimumum are obtained; necessary and sufficient conditions are obtained for the function to be strictly convex (it is always convex); when the problem is “well structured,” it is established that for a minimum cost solution the locations of the new facilities will lie in the convex hull of the locations of the existing facilities. Also, a dual to the problem is obtained and interpreted; necessary and sufficient conditions for optimum solutions to the problem, and to its dual, are developed, as well as complementary slackness conditions. Many of the properties to be presented are motivated by, based on, and extend the results of Kuhn's study of the location problem known as the General Fermat Problem.     

Heuristic solution to a discrete collection model

A discrete time Collection Model is formulated, involving the completion of a touring objective on a network with stochastic node states. Heuristic touring strategies are constructed, there being as yet inadequate analytic results for its optimal solution. Effectiveness of the heuristics is assessed by comparing expected tour times under the heuristics with expected tour times given perfect information. A branch and bound algorithm is presented for computing the perfect information tour times.     

Statistical concepts in computational mathematics

For a young science and even for most old ones, the intensity and variety of activities involved in computer science are unsurpassed. In an effort to provide the extremely varied training needed in the field, curriculum planners have tended to slight probability and statistics. Rarely has it been a requisite and only occasionally a desired elective However, not only is an adequate foundation in probability and statistics necessary for such external computer applications as tracking and other data reduction, Monte Carlo techniques, gaming, operations research, traffic analyses, etc., but it also plays an important role in internal applications to computer science and technology This effort in Rand's continuing study of computational mathematics and its applications offers a number of examples in various areas of computational mathematics and computing machine arithmetic-to say nothing of computer design, time sharing, and the like-to support the thesis that probability and statistics should be a requisite, not simply an elective or, even worse, ignored, at any institution offering a program in computer science. Further more, a potentially profitable source of research problems can be found in the interface between probability and statistics and computer science.     

A branch-bound algorithm for the capacitated facilities location problem

This paper discusses a mixed integer programming method for solving the Facilities Location Problem with capacities on the facilities. The algorithm uses a Decomposition technique to solve the dual of the associated continuous problem in each branch-bound iteration. The method was designed to produce the global optimum solution for problems with up to 100 facilities and 1,000 customers. Computational experience and a complete example are also presented in the appendix.     

Vessel allocation by linear programming

This paper presents a linear programming model of a fleet of vessels which is required to transport quantities of cargo, such as coal, iron ore, limestone, and salt from certain producing ports to specific destination ports. This model has been implemented and is currently being used both for planning purposes and as an aid in scheduling the trips to be made by each vessel.     

Application of renewal theory to continuous sampling plans

Renewal theory is used to study the effectiveness of a class of continuous sampling plans first introduced by Dodge. This approach provides a simple way of viewing and computing the long-run Average Outgoing Quality (AOQ) and its maximum AOQL. More importantly, it is used to study the average outgoing quality in a short production run through an approximation formula AOQ^*(t). Formulas for AOQ and AOQ^*(t) are provided. By simulation, it is found that AOQ^*(t) is sufficiently accurate in situations corresponding to actual practice.     

多退化模式下的电子装备可靠性建模

通常加速退化分析中退化失效只考虑或者假设只有一个退化通道,而实际上很多情况下会存在多退化模式.产品的各个退化通道间的关系存在随机性,即任意两个退化通道间不可能只是单一的相关或者独立.在考虑这种相关性的条件下,深入研究了电子产品的性能退化理论和机理,提出了两个多退化模式竞争失效的数学模型,分别阐述了退化通道相关与独立的两种不同情况下产品可靠度评估方法.     

基于圆阵的二维DOA估计新方法

通过分析圆阵阵列流形,提出一种新的圆阵二维谱估计模型,可以直接应用MUSIC算法进行二维DOA估计,从而避免了对圆阵输出信号进行模式激励.应用此模型仿真分析了均匀圆阵和均匀半圆阵的二维DOA估计性能,相比模式激励方法,减小了计算量;半圆阵与圆阵的DOA性能差别很小,但是半圆阵减少近一半的阵元数.     

飞机电传操纵系统控制律的神经网络实现

现代多功能战机多用电传操纵系统替代传统的机械杆系,但由于飞机的多变量、强耦合和不稳定等强非线性特点,使得其电传控制律的工程实现相当复杂.为此,对电传操纵系统控制律的神经网络实现方法进行了研究.通过利用径向基函数(RBF)网络良好的非线性跟踪性能,探讨了用RBF网络实现电传控制律的一般方法,并以某型飞机电传操纵系统纵向通道为例,对该方法进行了验证.