📚 Dummy Activities in Critical Path Analysis | 关键路径分析中的虚拟活动
In Edexcel A-Level Decision Mathematics 1 (D1), critical path analysis is a vital modelling tool for scheduling complex projects. One of the most frequently examined and commonly misunderstood ideas is the dummy activity. A dummy activity has zero duration and uses no resources, but it is essential for preserving logical dependencies in an activity-on-arc network. This article explains what dummy activities are, when to use them, how to draw them correctly, and how to avoid common mistakes.
在 Edexcel A-Level 决策数学 1（D1）中，关键路径分析是为复杂项目排程的重要建模工具。虚拟活动（dummy activity）是考试中经常出现且常被误解的概念之一。虚拟活动的持续时间为零，也不消耗资源，但它在活动-弧线网络中对保持逻辑依赖关系至关重要。本文将解释什么是虚拟活动、何时使用、如何正确绘制以及如何避免常见错误。
1. What Is a Dummy Activity? | 什么是虚拟活动？
In an activity-on-arc network, each real activity is drawn as a solid arrow from one event node to another. A dummy activity is drawn as a dashed arrow and is used only to show a dependency. It has no duration, no cost, and no resource requirement. In Edexcel D1, dummies are mainly needed to ensure that the network correctly represents every precedence relationship without violating the rules of graph drawing.
在活动-弧线网络中，每个真实活动用从一个事件节点指向另一个事件节点的实线箭头表示。虚拟活动用虚线箭头表示，仅用于显示依赖关系。它的持续时间为零，没有成本，也不需要资源。在 Edexcel D1 中，虚拟活动主要用于确保网络正确表示所有先后关系，同时不违反图形绘制规则。
2. Why Use Dummy Activities? | 为什么要使用虚拟活动？
Dummy activities solve two graphical and logical problems. First, if two or more activities share exactly the same start node and end node, the diagram would have parallel edges with the same endpoint pair, which makes the activities impossible to identify uniquely. Second, when an activity depends on two predecessors but another activity depends on only one of those predecessors, a simple arrow cannot express this partial dependency without introducing a false relationship.
虚拟活动解决两个图形和逻辑问题。第一，如果两个或多个活动具有完全相同的开始节点和结束节点，图中就会出现具有相同端点对的平行边，这使活动无法被唯一标识。第二，当一个活动依赖于两个前置活动，而另一个活动只依赖于其中一个前置活动时，简单的箭头无法表达这种部分依赖关系，否则会引入虚假的逻辑关系。
3. The Two Classical Cases for Dummies | 使用虚拟活动的两种经典情形
Case 1: Unique endpoint pair. Suppose activities A and B both start at node 1 and finish at node 2. To separate them, draw A from 1 to 3, draw B from 1 to 2, and insert a dummy from 2 to 3. Now A and B have different end nodes, and the dummy from 2 to 3 means that the event at node 3 depends on B as well; this does not add any time or resource.
情形一：唯一端点对。假设活动 A 和 B 都从节点 1 开始并在节点 2
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