1、PERT(Program Evaluation and Review Technique)即计划评审技术，最早是由美国海军在计划和控制北极星导弹的研制时发展起来的。PERT 技术使原先估计的、研制北极星潜艇的时间缩短了两年。 简单地说，PERT 是利用网络分析制定计划以及对计划予以评价的技术。它能协调整个计划的各道工序，合理安排人力、物力、时间、资金，加速计划的完成。在现代计划的编制和分析手段上，PERT 被广泛的使用，是现代化管理的重要手段和方法。 PERT 网络是一种类似流程图的箭线图。它描绘出项目包含的各种活动的先后次序，标明每项活动的时间或相关的成本。对于 PERT 网络，项目管理者必
2、须考虑要做哪些工作，确定时间之间的依赖关系，辨认出潜在的可能出问题的环节，借助 PERT 还可以方便地比较不同行动方案在进度和成本方面的效果。 构造 PERT 图，需要明确三个概念：事件、活动和关键路线。 1、事件（Events ）表示主要活动结束的那一点； 2、活动（Activities）表示从一个时间到另一个事件之间的过程； 3、关键路线（Critical Path）是 PERT 网络中花费时间最长的事件和活动的序列。 PERT 的计算特点 PERT 首先是建立在网络计划基础之上的，其次是工程项目中各个工序的工作时间不肯定，过去通常对这种计划只是估计一个时间，到底完成任务的把 握有多大，决
3、策者心中无数，工作处于一种被动状态。在工程实践中，由于人们对事物的认识受到客观条件的制约，通常在 PERT 中引入概率计算方法，由于组成 网络计划的各项工作可变因素多，不具备一定的时间消耗统计资料，因而不能确定出一个肯定的单一的时间值。 在 PERT 中，假设各项工作的持续时间服从 分布，近似地用三时估计法估算出三个时间值，即最短、最长和最可能持续时间，再加权平均 算出一个期望值作为工作的持续时间。在编制 PERT 网络计划时，把风险因素引入到 PERT 中，人们不得不考虑按 PERT 网络计划在指定的工期下，完成工程 任务的可能性有多大，即计划的成功概率，即计划的可靠度，这就必须对工程计划进
4、行风险估计。 在绘制网络图时必须将非肯定型转化为肯定型，把三时估计变为单一时间估计，其计算公式为： 式中： ti 为 i 工作的平均持续时间； ai 为 i 工作最短持续时间(亦称乐观估计时间)； bi 为 i 工作最长持续时间(亦称悲观估计时间) ； ci 为 i 工作正常持续时间，可由施工定额估算。 其中，ai 和 bi 两种工作的持续时间一般由统计方法进行估算。 三时估算法把非肯定型问题转化为肯定型问题来计算，用概率论的观点分析，其偏差仍不可避免，但趋向总是有明显的参考价值，当然，这并不排斥每个估计都尽可能做到可能精确的程度。为了进行时间的偏差分析(即分布的离散程度 )，可用方差估算：
5、式中：2i 为 i 工作的方差。 标准差 网络计划按规定日期完成的概率，可通过下面的公式和查函数表求得。 式中： Q 为网络计划规定的完工日期或目标时间； M 为关键线路上各项工作平均持续时间的总和； 为关键线路的标准差； 为概率系数。 PERT 网络分析法的工作步骤 开发一个 PERT 网络要求管理者确定完成项目所需的所有关键活动，按照活动之间的依赖关系排列它们之间的先后次序，以及估计完成每项活动的时间。这些工作可以归纳为5 个步骤。 1、确定完成项目必须进行的每一项有意义的活动，完成每项活动都产生事件或结果； 2、确定活动完成的先后次序； 3、绘制活动流程从起点到终点的图形，明确表示出每项
6、活动及其它活动的关系，用圆圈表示事件，用箭线表示活动，结果得到一幅箭线流程图，我们称之为 PERT 网络； 4、估计和计算每项活动的完成时间； 5、借助包含活动时间估计的网络图，管理者能够制定出包括每项活动开始和结束日期的全部项目的日程计划。在关键路线上没有松弛时间，沿关键路线的任何延迟都直接延迟整个项目的完成期限。 案例分析 下面举一个例子来说明。假定你要负责一座办公楼的施工过程，你必须决定建这座办公楼需要多长时间。下表概括了主要事件和你对完成每项活动所需时间的估计。 建筑办公楼的 PERT 网络 完成这栋办公楼将需要 50 周的时间，这个时间是通过追踪网络的关键路线计算出来的。该网络的关键
7、路线为：A-B-C-D-G-H-J-K，沿此路线的任何事件完成时间的延迟，都将延迟整个项目的完成时间。 PERT 网络技术的作用 1、标识出项目的关键路径，以明确项目活动的重点，便于优化对项目活动的资源分配； 2、当管理者想计划缩短项目完成时间，节省成本时，就要把考虑的重点放在关键路径上； 3、在资源分配发生矛盾时，可适当调动非关键路径上活动的资源去支持关键路径上的活动，以最有效地保证项目的完成进度； 4、采用 PERT 网络分析法所获结果的质量很大程度上取决于事先对活动事件的预测，若能对各项活动的先后次序和完成时间都能有较为准确的预测，则通过 PERT 网络的分析法可大大缩短项目完成的时间。
8、 相关阅读 CPM( 关键路径 法) 和 PERT 是 50 年代后期几乎同时出现的两种计划方法。随着科学技术和生产的迅速发展，出现了许多庞大而复杂的科研和工程项日，它们工序繁多，协作面 广，常常需要动用大量人力、物力、财力。因此，如何合理而有效地把它们组织起来，使之相互协调，在有限资源下，以最短的时间和最低费用，最好地完成整个项 目就成为一个突出的重要问题。CPM 和 PERT 就是在这种背景下出现的。这两种计划方法是分别独立发展起来的，但其基本原理是一致的，即用网络图来表达项 目中各项活动的进度和它们之间的相互关系，并在此基础上，进行网络分析，计算网络中各项时间多数，确定关键活动与关键路线
9、，利用时差不断地调整与优化网 络，以求得最短周期。然后，还可将成本与资源问题考虑进去，以求得综合优化的项目计划方案。因这两种方法都是通过网络图和相应的计算来反映整个项目的全 貌，所以又叫做网络计划技术。 此外，后来还陆续提出了一些新的网络技术，如 GERT（Graphical Evaluation and Review Technique，图示评审技术），VERT（Venture Evaluation and Review Technique，风险评审技术）等。应该采用哪一种进度计划方法，主要应考虑下列因素： 项目的规模大小。很显然，小项目应采用简单的进度计划方法，大项目为了保证按期按质达到项
10、目目标，就需考虑用较复杂的进度计划方法。 项目的复杂程度。这里应该注意到，项目的规模并不一定总是与项目的复杂程度成正比。例如修一条公路，规模虽然不小，但并不太复杂，可以用较简单的进度计 划方法。而研制一个小型的电子仪器，要很复杂的步骤和很多专业知识，可能就需要较复杂的进度计划方法。 项目的紧急性。在项目急需进行，特别是在开始阶段，需要对各项工作发布指示，以便尽早开始工作，此时，如果用很长时间去编制进度计划，就会延误时间。 对项目细节掌握的程度。如果在开始阶段项目的细节无法解明，CPM 和 PERT 法就无法应用。 总进度是否由一、两项关键事项所决定。如果项目进行过程中有一、两项活动需要花费很长
11、时间，而这期间可把其他准备工作都安排好，那么对其他工作就不必编 制详细复杂的进度计划了。 有无相应的技术力量和设备。例如，没有计算机，CPM 和 PERT 进度计划方法有时就难以应用。而如果没有受过良好训练的合格的技术人员，也无法胜任用复杂的方法编制进度计划。 此外，根据情况不同，还需考虑客户的要求，能够用在进度计划上的预算等因素。到底采用哪一种方法来编制进度计划，要全面考虑以上各个因素。Using PERT/CPM to determine variability in project completion timeThe Program Evaluation and Review Tech
12、nique (PERT) and the Critical Path Method (CPM) are widely recognized as valuable tools in the field of project management. PERT was developed in the 1950s to deal with the unprecedented management needs of the Polaris missile project. CPM, on the other hand, was developed primarily for industrial p
13、rojects involving well-known activity times. The best features of PERT and CPM have been combined into a single technique, known as PERT/CPM, that enables project managers to schedule projects with a good deal of efficiency. The reliability of the technique depends heavily, however, on the accuracy
14、of the estimated activity times. The PERT/CPM technique Creating a project network diagramThe first step is to prepare a list of the activities that make up the project and identify the predecessor activities of each project activity. A predecessor activity is one that must be completed before the a
15、ctivity of which it is a predecessor can be started. When all the estimates have been compiled, a project network diagram representing the flow of project activities is created. The following is a typical project network diagram. Since several activity paths can be identified from start to finish in
16、 a typical project, there will be a path that takes the longest time to complete. This path is known as the “critical path“. Clearly the completion time of the project is dependent on the time taken to complete the critical path. In the example above the activities that make up the critical path - t
17、he critical activities comprising activities A, D, G, and K - are colored in green. Estimating activity timesThe completion time for each activity is estimated. This entails assessing the number of work periods and the period of calendar time likely to be required to complete the activity. Activity
18、time estimation can involve several techniques. One such technique is expert judgment. It is carried out by an individual or group with relevant specialized knowledge or training, and is generally guided by historical information relating to previous projects. A useful variant of expert judgment is
19、analogous estimating (also known as top-down estimating). This technique is most commonly used in projects for which little detailed information is currently available. It bases activity time estimates on the duration of previous similar “analogous“ activities. Another estimation technique is simula
20、tion. This involves the use of a computerized approximation algorithm, such as Monte Carlo analysis, that estimates project activity times using different sets of initial assumptions. PERT/CPM with uncertain activity timesOptimistic time, modal time, and pessimistic timeActivity time estimation can
21、involve several techniques The PERT/CPM technique takes uncertainties into account Many projects, such as research and development projects, involve uncertain activity dates. The PERT/CPM technique takes these uncertainties into account to determine the probability of completing the project by a cer
22、tain date. It does this by using three estimates for each activity - the optimistic time (a), the modal - “most probable“ - time (m), and the pessimistic time (b). The optimistic time is the minimum activity time if the activity progresses under optimum conditions. The most probable time is an estim
23、ate of the duration of the activity under normal conditions. The pessimistic time is the longest activity time envisaged if significant problems are encountered. Suppose that you are the project manager of a certain project for which you have identified activities A, D, G, and K as the critical acti
24、vities. You have established estimates of the optimistic time, the modal time, and the pessimistic time for each of these activities as follows: Critical path activity Optimistic (days) Modal (days) Pessimistic (days)A 5 8 17D 5 8 23G 3 6 9K 5 8 11 Lets see how you deal use PERT/CPM to deal with thi
25、s scenario. Finding the expected time and the varianceThe following expression is used to calculate a weighted average known as the expected time (t) for each activity: So you calculate the expected time for each critical activity to produce the following results: Critical path activity Expected tim
26、e (days)A 9D 10G 6K 8You can use the expected times to draw up a project network diagram and create a project schedule. By identifying the critical path you can determine the expected time of completion of the entire project - this is the sum of the expected times of the critical activities. In this
27、 example the expected time of the project is 33 days. Variance of critical activities and total varianceThe variance ( 2) - the dispersion of activity time values - of each of the critical activity times is given by the following expression: As the expression clearly indicates, your estimates of the
28、 optimistic time and the pessimistic time have a very significant bearing on the variance of any given activity. In this example the variances of the projects critical activities are as follows: Critical path activity Variance 2A 4D 9G 1K 1Variances in critical activity times automatically affect th
29、e time of completion of the entire project, either upwards or downwards. The assumption is that the variance of the project completion time equals the sum of the variances of the critical activities. That is: This assumption is correct if all the activity times are independent of each other, but is
30、decreasingly useful as an approximation as activity times become more mutually dependent. In this example, the total variance of the project is calculated to be 15 days. The standard deviation () of the project completion time is simply the square root of the project completion time variance. So the
31、 standard deviation in this example is 3.87. Probability of meeting a project completion dateNow you can investigate the probability of the project being completed on a particular date. For example, suppose penalties will begin to accrue if it takes you more than 40 days to complete the project. You
32、r critical path indicates a project completion time of 33 days. So you need to determine the probability of the project taking 7 days longer than the time indicated by the critical path. You do this by calculating the z value - the normal probability distribution - of the scenario in which the proje
33、ct takes 40 days. The following expression yields the z value: Here T is the project completion time you are investigating - 40 days - and TC is the project completion time indicated by the critical path - 33 days. So the expression becomes Using a table of areas for the standard normal distribution
34、, this z value yields an area for the standard normal distribution of 0.9649. So your initial estimates predict a 96% probability of your project being completed on or before the 40-day milestone when penalties begin to take effect. Lets investigate the probability of the project being completed in
35、30 days. This yields a z-value expression of The table of areas for the standard normal distribution yields an area of 0.2206. So there is a 22% probability of the project being completed 3 days earlier than the estimated critical path time. Now lets look at the probability of the project being comp
36、leted within the range 29-37 days - 4 days before and after the estimated critical path completion date. Our technique produces a probability of 15% that the project will be completed in 29 days or sooner and a probability of 85% that it will be completed in 37 days or sooner. So there is a 70% probability that the project will be completed in the range 29-37 days.
