网络计划更新调整的时差传递法

网络计划面对变化后的新情况，如何充分利用原图．简单易行地更新调整，这一直是难题。本文提出时差传递法，为解决这一难题给出了新思路．这种方法利用网络图的结构特征，把更新调整内容归类整理后，计算传递时差，再根据时差特征定义传递通道、决定传递方式，用时差传递方法，简单易行地更新调整网络计划．     

绘制统筹网络图的一个标号算法及应用

本文给出了一个绘制统筹网络图的有效算法，称之为标号算法．利用标号算法可使计算机在只接收到各工序间紧前紧后关系的数据后，便可生成网络优化中必需的网络图形．利用该算法我们还建立了网络优化计算机辅助设计系统，该方法和计算机辅助设计系统，目前已在山东省兴隆庄煤矿井下的拆除和安装工程中得到了具体应用，收到了良好的效果．     

基于节点时差特性的CPM网络次关键路线的简单算法

为寻找求解CPM网络次关键路线的一种简单算法,快速、高效、准确地找到次关键路线,确保大型复杂工程项目的进度,在相关理论和概念的基础上,着眼于整体网络的化简,深入剖析CPM网络计划中最为直观的节点时差,从节点时差与最小非零总时差的关系的角度,分析研究了节点时差的三个特性;并在此基础上提出了运用节点时差实现CPM网络的层层化简,进而快速求解次关键路线的具体步骤;最后,以某工程项目的网络图为例,进行实证分析。案例计算过程表明,在CPM网络中,利用节点时差能够快速、准确地找到大型复杂工程项目的次关键路线。     

运用总时差求CPM网络中次关键路线的方法研究

次关键路线在项目进度控制和工期压缩问题中具有重要意义。本文在给出CPM网络计划的一些新概念的基础上，提出了前主链定理、后主链定理和总时差定理，并且找到了一种运用总时差快速求解网络次关键路线的方法。文章对该方法进行了正确性证明，并给出了应用实例。     

网络计划图的工序关系及其复杂性研究

本文研究了将原始的施工工序关系表转换为规范网络计划图的活动关系的算法.在理论上讨论了网络图中活动与紧前活动的关系以及与节点的关系,研究了网络图中添加虚活动的规律,进一步提出了生成网络计划图的按先行工序类生成算法的补充研究.     

紧－凸性与紧－光滑性

本文首先通过暴露集和暴露泛函的概念引入了闭凸集的紧－严格凸、紧－强凸、紧－一致凸及紧－非常凸等概念。并用对偶映射给出了Ｂａｎａｃｈ空间的两种新光滑性—紧－一致光滑与紧－非常光滑。然后特别研究了Ｂａｎａｃｈ空间的紧－非常凸与紧－非常光滑。此外还得到关于对偶映射的两个新结果。     

紧—凸性与紧—光滑性

本文首先通过暴露集和暴露泛函的概念引入卫闭凸集的紧－严格凸、紧－强凸、紧－一致凸及紧－非常凸等概念。用对偶映射给出了Ｂａｎａｃｈ空间的两种新光滑性－紧－一致光滑与紧－非常光滑。然后特别研究了Ｂａｎａｃｈ空间的紧－非常凸与紧－非常光滑。此外还得到关于对偶映射的两个新结果。     

箭线网络图的唯一性特征和最优箭线图判定

提出箭线网络图由完全工序关系唯一确定、最优箭线图实工序子图唯一确定等结论和由相交紧前工序集直和分解得出的基准箭线图作最优箭线图和判定最优箭线图的概念和方法.     

德摩根拓扑代数上的紧性与q—收敛性

在文（１），（２），（３）的基础上，我们首先在德摩根拓扑代数上用有限覆盖性质定义了紧性，并引入ω－元，ω－ｄ－ｑ－聚点等概念，并着重讨论了紧性与ｑ－收敛性之间的关系。     

基于CPM原理和Dijkstra算法的SPM网络计划模型及性质

CPM(关键路线法)网络计划适用于分析工序间存在严格紧前关系(任意工序只能在它的所有紧前工序都结束时才能开始)的进度计划.针对工序间不存在严格紧前关系(任意工序只要其紧前工序中的一个结束它就可以开始)的进度计划,以CPM原理和Dijkstra算法为基础,提出SPM(最短路线法)网络计划以及拟机动时间概念,根据不同的建模原理,建立了两个SPM网络计划模型,并给出了其建立方法以及各模型拟机动时间的求法,分析了每个模型的性质,最后通过算例对其中的一类模型进行了验证.     

求解CPM网络计划的最大网络时差

CPM网络计划的网络时差表示项目中各工序实际可使用的机动时间的总和(绝非理论上机动时间的简单加总),即CPM网络计划的总机动时间,它决定着在总工期不变的前提下,所有工序实际可以达到的最大工期的总和,与项目的成本管理和时间管理密切相关。网络时差是变量,取决于各工序的时间进度安排,说明可以通过调整工序的时间进度来决定该时差的取值,特别是其最大值,进而实现成本和时间优化。本文首先从新的角度分析了网络时差的含义;然后,在此基础上设计了求解最大网络时差的算法,其思路为,通过建立和分析最大网络时差模型,将其转化为特殊的“时间-费用权衡问题”,进而可运用Fulkerson算法等经典算法求解;最后,通过应用举例对该算法进行了演示。     

Multiple schedules and measures of resource constrained float

The conventional analysis of a resource constrained network produces a single schedule. A measure of float for each activity can be defined by examining the sequences of activities, incorporating the linkages implied by the sharing of resources in this particular schedule. However, the resultant floats are specific to one schedule and the analysis ignores the flexibility inherent in many resource constrained networks. It is often possible to employ alternative resource allocations resulting in schedules with identical overall durations but different timings for individual activities; in one schedule an activity may be critical but in another it may have significant float. A systematic exploration of alternative schedules reveals the flexibility of the network and the consequent variation in activities' floats. This paper defines new parameters describing these characteristics of activities in resource constrained networks. The practical value of the parameters is demonstrated in an example in which the measures of float guide the project planner to an alternative schedule, avoiding a critical dependency on a problematic activity and reducing the risk to the project at no additional cost.     

A note on activity floats in activity-on-arrow networks

In project scheduling, the free float (slack) of an activity represents the leeway for scheduling the activity without affecting any subsequent activity. In the context of activity-on-arrow (AOA) network representation, textbooks on project management, based on our survey, have for decades been using a popular formula to calculate free floats that may lead to erroneous results in the presence of dummy arcs. In this note, we present a correct version of the formula. Extensions of the proposed formula to other floats such as safety float and interference float are also discussed.     

Tools for resource-constrained project scheduling and control: forward and backward slack analysis

Project managers generally consider slack as a measure of the scheduling flexibility associated with the activities in the project network. Nevertheless, when resource constraints appear, this information must be calculated and analysed carefully. In this context, to handle project feasible schedules is very hard work for project managers. In order to develop useful tools for decision making, the authors extend the concepts of activity slack and define a new activity criticality index based on them that permits us to classify the activities in the resource-constrained project scheduling and control context. Additionally, these new concepts have been integrated into standard project management software as new commands. Hence the capabilities of project management software are improved. Finally, an example that illustrates the use and application of the new activity classification is also included.     

A new approach to find project characteristics and multiple possible critical paths in a fuzzy project network

Graphs are widely used to represent data and relationships. Among all graphs, a particularly useful family is the family of trees. In this paper, we utilize a rooted tree to describe a fuzzy project network as it enables simplification in finding earliest starting times and trapezoidal fuzzy numbers to express the operation times for all activities in project network. As there is an increasing demand that the decision maker needs “Multiple possible critical paths” to decrease the decision risk for project management, in this paper, we introduce an effective graphical method to compute project characteristics such as total float, earliest and latest times of activities in fuzzy project network and a new ranking to find possible critical paths. Numerical example is provided to explain the proposed procedure in detail; the results have shown that the procedure is very useful and flexible in finding total floats. By comparing the critical paths obtained by this method with the previous methods, it is shown that the proposed method is effective in finding possible critical paths.     

The Cichoń diagram for degrees of relative constructibility

Following a line of research initiated in [4], we describe a general framework for turning reduction concepts of relative computability into diagrams forming an analogy with the Cichoń diagram for cardinal characteristics of the continuum. We show that working from relatively modest assumptions about a notion of reduction, one can construct a robust version of such a diagram. As an application, we define and investigate the Cichoń diagram for degrees of constructibility relative to a fixed inner model W. Many analogies hold with the classical theory as well as some surprising differences. Along the way, we introduce a new axiom stating, roughly, that the constructibility diagram is as complex as possible.     

A methodology for analyzing decision networks, based on information theory

This paper assumes the organization as a distributed decision network. It proposes an approach based on application and extension of information theory concepts, in order to analyze informational complexity in a decision network, due to interdependence between decision centers.Based on this approach, new quantitative concepts and definitions are proposed in order to measure the information in a decision center, based on Shannon entropy and its complement in possibility theory, U uncertainty. This approach also measures the quantity of interdependence between decision centers and informational complexity of decision networks.The paper presents an agent-based model of organization as a graph composed of decision centers. The application of the proposed approach is in analyzing and assessing a measure to the organization structure efficiency, based on informational communication view. The structure improvement, analysis of information flow in organization and grouping algorithms are investigated in this paper. The results obtained from this model in different systems as distributed decision networks, clarifies the importance of structure and information distribution sources effect’s on network efficiency.     

一个绘制统筹图的算法

统筹图又叫计划网络图。任给一个其元素叫做工序（或作业或活动）的有限偏序集，要绘制它的一个最优统筹图，限含虚工序数目为最少者，是一个尚未从理论上解决的问题。本文讨论了虚工序产生的原因和如何减少虚工序数量的一些途径；指出了高度为二的编序集其最优统筹图含虚工序数目达到最大且等于该偏序集框图的边数的充分必要条件；本文给出了一个绘制最优统筹图的近似算法，此算法弥补了文[2]和[3]所给算法的一些不足之处。     

Encoding and decoding of analog signals with a population of neurons

In this paper, we discuss how an analog signal can be encoded using biophysically realistic neural networks. Using the activity curve of a single neuron, we argue that the activities can be pooled over a population so that the weighted sum of the activities approximate a given function. Since the activities of neurons are not available as a variable, we propose to generate them in real time by a suitable low-pass filter. Using the proposed scheme, we demonstrate how simple ordinary differential equations can be solved. In effect, the ordinary differential equations are solved by dynamically updating the activities of the neurons. In an actual biological neural network, the activities of the cells are not obtained by a low-pass filter. They are integrated in the network by a suitable synaptic input. A new optimization algorithm for finding a set of optimal synaptic weights has been proposed and successfully implemented using a software package GENESIS. The difference between biological neural networks and artificial neural networks is discussed in somewhat greater details. The important concepts are illustrated by implementing a memory and by solving a periodic ordinary differential equation, the Van der Pol oscillator.