搭接网络中的路长悖论及其特性研究

本文发现在搭接网络中存在“工序间加入不同表现形式的同一时间约束，可能会产生不同的最大路长”这个悖论。通过研究此悖论形成原因从而提出搭接网络的一种新表示方法。该方法不但与经典的CPM网络在表示形式上完全统一，而且在求解时间参数及关键路线的方法上也保持一致。该新表示法使得CPM网络中许多基础理论可以推广到搭接网络中来，例如工序的总时差T_ij等于关键路长μ^∇与过该工序（ij）的最大路长μ_ij^∇之差（μ^∇-μ_ij^∇）;任意一条路线μ上自由时差的和都等于关键路长μ与该条路的路长之差（μ^∇-μ_ij^∇）等。利用这些定理与规律，本文解决了搭接网络中如何正确求解时间参数问题，提出在搭接网络中评估关键路长与次关键路长之差的简便方法以及求解搭接网络次关键路线的一系列精确算法，并通过算例表明这些方法在搭接网络应用中的具有有效性与简便性。

Tresearch on Path Lengths Paradox and Its Characteristics Under Spliced Network

A paradox in spliced network is found in this paper, that is when adding a time constraint but in two different types between activities may produce different longest path. A whole new presentation of spliced network is given by studying the paradox. The new spliced network presentation is quite simple but also unified with the classic CPM network in forms. This unification not only helps to solve the problems of how to calculate the time parameters, activity floats and how to find the critical path in spliced network, but also makes extension of the theory found in CPM network to spliced network becomes possible. For example, the activity total float T_ij equals to the critical path length μ^∇ minus the longest path length μ_ij^∇ through activity(ij), that is (μ^∇-μ_ij^∇); the sum of activity free float of any path μ equals to the critical path lengthμ^∇ minus the length of this path μ, that is (μ^∇-μ_ij^∇). By using these extended theory, three convenient methods are designed to detect the difference of critical and sub-critical path lengths and to find out the sub-critical path. These methods are illustrated both effective and convenient in spliced network applications.