Unit 9

翻译：吴小菘


1.Free float is the amount of delay which can be assigned to any one activity without delaying subsequent activities. The free float ,FF(i , j),associated with activity(i , j) is: FF(i , j)=E(j)-E(i)-Dij (9 . 1)
developed
of each
by starting each activity as soon as
activity as long as possible but still
possible ,at
finish the
ES(i,j) , Similarly, a latest time schedule would delay the start
project in the minimum possible time.This late schedule can
be developed by setting each activity's start time to LS(i,j).

许多不同的活动时间表可以从关键路径调度程序在上一节中描述的发 展。最早的时间表将由每个活动尽快开始，在ES（i，j ），同样的， 一个新的时间表将延迟每个活动的开始尽可能长的时间，但仍完成项 目中的最小的可能的时间。这晚计划可以建立每个活动的开始时间是 （i，j）。
翻译：刘阳

Activities that have different early and late start times [i.e., ES(i,j) <
LS(i,j)] can be scheduled to start anytime between ES(i,j) and LS(i,j) as shown in Figure 10-6. The concept of float is to use part or all of this allowable range to schedule an activity without delaying the completion of the project. An activity that has the earliest time for its predecessor and successor nodes differing by more than its duration possesses a window in which it can be scheduled. That is, if E(i) + Dij< L(j), then some float is available in which to schedule this activity. 具有不同的早期和晚期启动时间的活动（即，ES（I，J）<LS（I，J））可以 计划在ES（I，J）和LS（I，J）之间的任何时间开始，如图10-6。时差的概念 是利用部分或全部该允许范围内安排的活动不延迟项目完成。如果一项工作的 持续时间小于其前后节点间的最早时间之差，它就拥有了一段可供支配的时差。 也就是说，如果E（i）+ D IJ <L（j）中，那么在安排活动中就有了一段可供 利用的时otal float is the maximum amount of delay which can be assigned to any activity without delaying the entire project.The total float,TF(i , j),for any activity(i , j)is calculated as:



A number of different activity schedules can be developed from
the critical path previous scheduling procedure described in the section . An earliest time schedule would be
preceding activities.Independent
activity (i , j) is calculated as:

float ,IF(i , j),for
(9 . 2）
IF(i , j)={ o }or{ E(j)-L(i)-Dij }

2.独立时差是可以被分配给任何一个工作而不耽误后续工 作或限制前工作的调度量。工作（i ，j）的独立时差 IF（ i， j）的计算公式为： IF(i , j)={ o }or{ E(j)-L(i)-Dij } (9 . 2）
Unit 9 section 2 Activity Float And Schedules
Dragon team
Key Words

float
时差 自由时差 独立时差 总时差 最早时间进度 最迟时间进度 可调整的余地

free float independent total float



earliest time schedule latest time schedule maneuvering room

1.自由时差是可以被分配给任何一个工作而不耽误后续工 作的机动时间。工作（i，j）的自由时差FF（i，j）的计算 公式为： FF(i , j)=E(j)-E(i)-Dij (9 . 1)

翻译：高秋

2.Independent float is the amount of delay which can be assigned to any one activity without delaying subsequent activities or restricting the scheduling of

翻译：何阳

Float is a very valuable concept since it
represents the
to
scheduling flexibility or "maneuvering room" available provide any
complete particular tasks . Activities on the critical path do not flexibility for scheduling nor leeway in case of problems. For activities with some float, the actual starting time might be chosen to balance work loads over time, to correspond with material deliveries, or project's cash flow.
TF(i , j)=L(j)-E(i)-Dij (9 . 3)


3.总时差是可分配给任何工作而不影响整个项目工期的机 动时间。对任何工作（i，j）的总时差，TF（i，j）的计算 公式为： TF(i , j)=L(j)-E(i)-Dij (9 . 3)

翻译：高秋

Each of these “float”indicates an amount of flexibility associated with an activity . In all cases , total float equals or exceeds free float , while independent float is always less than or equal to free float . Also , any activity on a critical path has all three values of float equal to free zero . The converse of this statement is also true , so any activity which has zero total float can be recognized as being on a critical path .

to improve
the
时差是一个非常有价值的概念，因为它代表了调度的灵活性，或者可 用来完成特定的任务的“可调整的余地”。关键路径上的活动没有时 间安排的灵活性，在遇到问题是也没有退路。对于一些有时差的活动， 实际的开始时间可能随着时间的推移被选择来平衡工作负荷，与材料 的交付对应，或改善项目的现金流。
翻译：位隽

Figure 10-6 Illustration of Activity Float

Of course, if one activity is allowed to float or change in the schedule, then the amount of float available for other activities may decrease. Three separate categories of float are defined in critical path scheduling: 当然，如果一个活动被允许在进度内浮动或改变，那么时 差可用于其他活动的量可能会降低。三个不同的类别时差 在关键路径调度定义：
各种类型的工作时差如图9-1所示，是由一条可以及时根据其计划开始时间来 回移动为代表的线为代表来说明的。有三种计划开始时间，分别是与工作最早开 始时间相对应的事件最早开始时间为 E(i)，工作最迟开始时间为LS(i，j)，以及事 件最迟时间为L(i)。这三种时差类型可以直接从图上找到。最后，四分之一条线列 入图来说明一个工作可能开始的可能性，暂时停止，然后重新启动。在这种情况 下，暂时停止了足够短且不那么独立的浮动时间，因此不会干扰其他工作。这种 工作暂时中断是否可行、经济，取决于工作本身的性质。