📚 Modelling a Project | 项目建模
Project modelling is the process of turning a real-world project into a mathematical network of activities, durations and precedence constraints. It allows decision mathematicians to calculate the shortest possible completion time, identify which activities cannot slip, and schedule resources efficiently.
项目建模是将现实项目转化为由活动、工期和前置约束组成的数学网络的过程。它使决策数学家能够计算最短完工时间、识别哪些活动不能延误，并高效地安排资源。
1. What Project Modelling Involves | 项目建模涉及什么
A project model uses three building blocks: activities, durations, and precedence relations. Activities are the tasks that consume time, durations are their lengths, and precedence relations show which tasks must finish before another can start.
项目模型使用三个基本组件：活动、工期和前置关系。活动是消耗时间的任务，工期是这些任务的长度，前置关系表示哪些任务必须在另一任务开始之前完成。
Once the model is built, it answers three practical questions. How long will the whole project take if nothing goes wrong? Which tasks can be delayed without delaying the project? Where should limited staff, machines or money be directed first?
模型建好之后可以回答三个实际问题：如果一切顺利，整个项目需要多久？哪些任务可以推迟而不影响项目？有限的人力、机器或资金应该优先投到哪里？
The main outputs in Edexcel Decision Mathematics are the minimum project completion time, the critical path, and the float for every non-critical activity. These outputs come from a network built from a precedence table.
在爱德思决策数学中，主要输出结果是最短项目工期、关键路径以及每个非关键活动的浮动时间。这些结果来自根据前置关系表建立的网络图。
Modelling is therefore a translation exercise: real tasks become nodes, real estimates become numbers, and real statements of the form 'this must happen first' become arrows. Everything after that translation is arithmetic.
因此，建模本质上是一种翻译工作：现实任务变成节点，现实估计变成数字，现实中"这件事必须先做"的说法变成箭头。翻译完成之后，剩下的都是算术运算。
2. Precedence Tables and Immediate Predecessors | 前置关系表与紧前活动
A precedence table lists every activity together with its duration and its immediate predecessors. An immediate predecessor is a task that must be completely finished before the activity in question can begin.
前置关系表列出每一个活动，以及它的工期和紧前活动。紧前活动是指必须完全结束之后，当前活动才能开始的任务。
Only direct relationships are recorded. If A precedes B and B precedes C, then in reality A must also finish before C starts, but A is not an immediate predecessor of C, so it is not written in the row for C.
表中只记录直接关系。如果 A 先于 B，B 先于 C，那么现实中 A 也必须在 C 开始前结束，但 A 并不是 C 的紧前活动，因此不写在 C 的那一行。
| Activity 活动 | Duration (days) 工期（天） | Immediate predecessors 紧前活动 |
|---|---|---|
| A | 3 | none 无 |
| B | 4 | A |
| C | 5 | A |
| D | 2 | B |
| E | 6 | C |
| F | 3 | B, C |
| G | 4 | D, E, F |
Durations must all use the same unit, and the table must be complete before any network is drawn. The table above is used throughout this article as a running example.
所有工期必须使用相同单位，并且在绘制任何网络图之前，表格必须完整无误。上表在本文中作为贯穿全文的示例使用。
3. From Table to Network: Activity-on-Node Diagrams | 从表格到网络图：节点式活动图
The Edexcel convention is activity-on-node. Each activity is a box, called a node, and the arrows between boxes show precedence. A node normally carries the activity letter, the duration, the earliest start time at the bottom left and the latest finish time at the bottom right.
爱德思的惯例是节点式活动图。每个活动是一个方框，称为节点，方框之间的箭头表示前置关系。节点中通常写有活动字母、工期、左下角的最早开始时间以及右下角的最迟完成时间。
Every network has exactly one start node and one finish node. Activities with no predecessors leave the start node, and activities with no successors enter the finish node. This convention gives the calculation a single beginning and a single end.
每个网络图只有一个起始节点和一个终止节点。没有前置活动的活动从起始节点出发，没有后续活动的活动汇入终止节点。这一约定使计算拥有唯一的起点和唯一的终点。
Two drawing rules keep the diagram valid. Arrows always point from left to right so that time
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