Scheduling Diagrams for Edexcel Decision Mathematics 1 | Edexcel 决策数学 1 中的调度图

📚 Scheduling Diagrams for Edexcel Decision Mathematics 1 | Edexcel 决策数学 1 中的调度图

A scheduling diagram is a visual model that places activities on a horizontal time axis after a critical path analysis has been completed. In Edexcel Decision Mathematics 1, you are expected to draw Gantt or cascade charts, produce resource histograms, and adjust start times when workers or machines are limited.

调度图是将活动放置在水平时间轴上的可视化模型，通常在完成关键路径分析后绘制。在 Edexcel 决策数学 1 中，考生需要掌握甘特图或级联图的绘制、资源直方图的制作，以及在工人或机器数量受限时调整开始时间。

1. What is a Scheduling Diagram? | 什么是调度图？

A scheduling diagram, often called a Gantt chart or cascade chart, shows each activity as a bar. The bar begins at an activity’s start time and ends at its finish time. Critical activities are usually shaded differently, and non-critical activities can be moved within their float to smooth resource use.

调度图通常称为甘特图或级联图，用条形表示每项活动。条形从活动的开始时间延伸到结束时间。关键活动通常用不同颜色或阴影标出，非关键活动则可以在其浮动时间范围内移动，以平滑资源使用。

In D1 exams, scheduling diagrams are used after the earliest start times and latest start times have been found. They help answer questions such as ‘What is the minimum number of workers needed?’ or ‘Can the project still finish in 17 days if only two workers are available?’

在 D1 考试中，调度图是在求出最早开始时间和最晚开始时间之后使用的。它帮助回答诸如“最少需要多少名工人？”或者“如果只有两名工人，项目还能在 17 天内完成吗？”等问题。

2. From Precedence Tables to Activity Networks | 从先后关系表到活动网络

Before drawing a scheduling diagram, you must have a correct activity network. The network comes from a precedence table, which lists each activity, its duration, and the activities that must finish before it can start.

在绘制调度图之前，必须先建立正确的活动网络。活动网络来自先后关系表，表中列出每项活动的持续时间以及它开始前必须完成的先行活动。

This worked example will be used throughout the article. Activities A and B have no predecessors, so they can begin at time 0. Activity D cannot start until both A and B are complete. Activity G cannot start until both E and F are complete.

本文后续将一直使用这个例题。活动 A 和 B 没有先行活动，因此可以从时间 0 开始。活动 D 必须等到 A 和 B 都完成后才能开始。活动 G 必须等到 E 和 F 都完成后才能开始。

If two activities share some but not all predecessors, a dummy activity may be needed to preserve unique dependencies. In this example, the precedence relationships are simple, so no dummy is required.

如果两项活动共享部分但非全部先行活动，可能需要引入虚活动来保持唯一的依赖关系。在本例中，先后关系比较简单，因此不需要虚活动。

3. Early and Late Start Times | 最早开始时间和最晚开始时间

The forward pass gives the earliest start time (EST) and earliest finish time (EFT) for every activity. The backward pass gives the latest finish time (LFT) and latest start time (LST). The two key equations are:

正向推算给出每项活动的最早开始时间（EST）和最早完成时间（EFT）。反向推算给出最晚完成时间（LFT）和最晚开始时间（LST）。两个关键公式如下：

EFT = EST + Duration

LST = LFT − Duration

Forward pass rule: an activity can start only when all its predecessors have finished. Therefore, its EST is the maximum EFT of its predecessors. Backward pass rule: an activity’s LFT is the minimum LST of all activities that depend on it.

正向推算规则：一项活动只有在所有先行活动完成后才能开始。因此，它的 EST 是所有先行活动 EFT 的最大值。反向推算规则：一项活动的 LFT 是所有依赖于它的活动的 LST 的最小值。

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