201:
151:
29:
2209:
283:: a PERT activity can be further decomposed into a set of sub-activities. For example, activity A1 can be decomposed into A1.1, A1.2 and A1.3. Sub-activities have all the properties of activities; in particular, a sub-activity has predecessor or successor events just like an activity. A sub-activity can be decomposed again into finer-grained sub-activities.
317:: the best estimate of the time required to accomplish an activity (te) or a path (TE), accounting for the fact that things don't always proceed as normal (the implication being that the expected time is the average time the task would require if the task were repeated on a number of occasions over an extended period of time).
277:: the actual performance of a task which consumes time and requires resources (such as labor, materials, space, machinery). It can be understood as representing the time, effort, and resources required to move from one event to another. A PERT activity cannot be performed until the predecessor event has occurred.
1711:
upon completion of the process, a far simpler mechanism involves computing the total of all activity durations. If an EF of more than the total is found, the computation should be terminated. It is worth saving the identities of the most recently visited dozen or so nodes to help identify the problem link.
1710:
Depending upon the capabilities of the data input phase of the critical path algorithm, it may be possible to create a loop, such as A -> B -> C -> A. This can cause simple algorithms to loop indefinitely. Although it is possible to "mark" nodes that have been visited, then clear the "marks"
1237:
In order to determine this information it is assumed that the activities and normal duration times are given. The first step is to determine the ES and EF. The ES is defined as the maximum EF of all predecessor activities, unless the activity in question is the first activity, for which the ES is
709:
others (there are two areas that need to be graded, but there are only enough bulldozers to do one). Additionally, the time estimates usually reflect the normal, non-rushed time. Many times, the time required to execute the task can be reduced for an additional cost or a reduction in the quality.
1780:
During project execution a real-life project will never execute exactly as it was planned due to uncertainty. This can be due to ambiguity resulting from subjective estimates that are prone to human errors or can be the result of variability arising from unexpected events or risks. The main reason
191:
of time and range of time necessary to complete each activity between two successive events. Such time expectations include estimates of "most likely time", "optimistic time", and "pessimistic time" for each activity. The technique is a management control tool that sizes up the outlook for meeting
82:
PERT is a method of analyzing the tasks involved in completing a project, especially the time needed to complete each task, and to identify the minimum time needed to complete the total project. It incorporates uncertainty by making it possible to schedule a project while not knowing precisely the
708:
The first step for scheduling the project is to determine the tasks that the project requires and the order in which they must be completed. The order may be easy to record for some tasks (e.g., when building a house, the land must be graded before the foundation can be laid) while difficult for
114:
PERT and CPM are complementary tools, because "CPM employs one time estimation and one cost estimation for each activity; PERT may utilize three time estimates (optimistic, expected, and pessimistic) and no costs for each activity. Although these are distinct differences, the term PERT is applied
1029:
is not specifically indicated on task 5 (d), though it can be observed on tasks 3 and 7 (b and f), (3) since weekends are indicated by a thin vertical line, and take up no additional space on the work calendar, bars on the Gantt chart are not longer or shorter when they do or don't carry over a
599:
654:: the longest possible continuous pathway taken from the initial event to the terminal event. It determines the total calendar time required for the project; and, therefore, any time delays along the critical path will delay the reaching of the terminal event by at least the same amount.
87:
of all the activities. It is more event-oriented than start- and completion-oriented, and is used more for projects where time is the major constraint rather than cost. It is applied to very large-scale, one-time, complex, non-routine infrastructure projects, as well as
192:
objectives on time; highlights danger signals requiring management decisions; reveals and defines both methodicalness and slack in the flow plan or the network of sequential activities that must be performed to meet objectives; compares current expectations with
1511:
to complete. To determine the path times, add the task durations for all available paths. Activities that have slack can be delayed without changing the overall time of the project. Slack is computed in one of two ways, slack = LF − EF
1546:
and the critical time is 19.51 work days. It is important to note that there can be more than one critical path (in a project more complex than this example) or that the critical path can change. For example, let's say that activities
469:
250:: a point that marks the start or completion of one or more activities. It consumes no time and uses no resources. When it marks the completion of one or more activities, it is not "reached" (does not occur) until
1006:
is the black lines connected to non-critical activities, (3) since
Saturday and Sunday are not work days and are thus excluded from the schedule, some bars on the Gantt chart are longer if they cut through a
1382:. The LF is defined as the minimum LS of all successor activities, unless the activity is the last activity, for which the LF equals the EF. The LS is the LF minus the task duration (LS = LF − duration).
1378:, the project should take 19.51 work days to complete. The next step is to determine the late start (LS) and late finish (LF) of each activity. This will eventually show if there are activities that have
1690:
474:
187:
Through an electronic computer, the PERT technique processes data representing the major, finite accomplishments (events) essential to achieve end-objectives; the inter-dependence of those events; and
1208:
By itself, the network diagram pictured above does not give much more information than a Gantt chart; however, it can be expanded to display more information. The most common information shown is:
226:. The Work Breakdown Structure provides "a framework for complete networking, the Work Breakdown Structure was formally introduced as the first item of analysis in carrying out basic PERT/CPM."
1781:
that PERT may provide inaccurate information about the project completion time is due to this schedule uncertainty. This inaccuracy may be large enough to render such estimates as not helpful.
1145:
991:
1014:
626:
is a measure of the excess time and resources available to complete a task. It is the amount of time that a project task can be delayed without causing a delay in any subsequent tasks (
260:: an event that immediately precedes some other event without any other events intervening. An event can have multiple predecessor events and can be the predecessor of multiple events.
437:
376:
266:: an event that immediately follows some other event without any other intervening events. An event can have multiple successor events and can be the successor of multiple events.
1390:
is equal to the EF (19.51 work days) since it is the last activity in the project. Since the duration is zero, the LS is also 19.51 work days. This will be used as the LF for
1742:
PERT provides for potentially reduced project duration due to better understanding of dependencies leading to improved overlapping of activities and tasks where feasible.
1049:). Activity on node diagrams are generally easier to create and interpret. To create an AON diagram, it is recommended (but not required) to start with a node named
660:: An activity that has total float equal to zero. An activity with zero free float is not necessarily on the critical path since its path may not be the longest.
1592:
The activities on the critical path by definition have a slack of zero; however, it is always a good idea to check the math anyway when drawing by hand.
1788:, however, allowing for every possible disruption would be very slow and couldn't be accommodated by the baseline schedule. A second approach, termed
183:, Head of the Program Evaluation Branch, Special Projects Office, U.S. Navy, gave a detailed description of the main concepts of PERT. He explained:
305:: the maximum possible time required to accomplish an activity (p) or a path (P), assuming everything goes wrong (but excluding major catastrophes).
594:{\displaystyle {\begin{aligned}&\sigma _{te}={\frac {p-o}{6}}\\&\sigma _{TE}={\sqrt {\sum _{i=1}^{n}{\sigma _{te_{i}}}^{2}}}\end{aligned}}}
1784:
One possible method to maximize solution robustness is to include safety in the baseline schedule in order to absorb disruptions. This is called
1405:
is 19.51 work days. The duration (5.17 work days) is subtracted from the LF to get an LS of 14.34 work days. This will be used as the LF for
299:: the minimum possible time required to accomplish an activity (o) or a path (O), assuming everything proceeds better than is normally expected
1427:
is 14.34 work days. The duration (5.17 work days) is subtracted from the LF to get an LS of 9.17 work days. This will be used as the LF for
1416:
is 19.51 work days. The duration (4.5 work days) is subtracted from the LF to get an LS of 15.01 work days. This will be used as the LF for
196:
completion dates and computes the probability for meeting scheduled dates; and simulates the effects of options for decision— before decision.
673:
must be completed in order to allow sufficient time for the activities that must elapse before a specific PERT event reaches completion.
124:
1041:
A network diagram can be created by hand or by using diagram software. There are two types of network diagrams, activity on arrow (
127:
to support the U.S. Navy's
Polaris nuclear submarine project. It found applications throughout industry. An early example is the
1993:
2249:
2244:
135:
which used PERT from 1965 until the opening of the 1968 Games. This project model was the first of its kind, a revival for the
2147:
2128:
2106:
2087:
311:: the best estimate of the time required to accomplish an activity (m) or a path (M), assuming everything proceeds as normal.
123:
PERT was developed primarily to simplify the planning and scheduling of large and complex projects. It was developed for the
2025:
cited in: Stauber, B. Ralph; Douty, Harry M.; Fazar, Willard; Jordan, Richard H.; Weinfeld, William; and Manvel, Allen D.;
165:
but by 1959 was renamed. It had been made public in 1958 in two publications of the U.S. Department of the Navy, entitled
1246:
is zero since it is the first activity. Since the duration is zero, the EF is also zero. This EF is used as the ES for
1764:
The network charts tend to be large and unwieldy, requiring several pages to print and requiring specially-sized paper.
1053:. This "activity" has a duration of zero (0). Then you draw each activity that does not have a predecessor activity (
2166:
1817:
2274:
2269:
1726:
1321:
is 9.17. The duration (5.17 work days) is added to the ES to get an EF of 14.34. This EF is used as the ES for
1290:
is four. The duration (6.33 work days) is added to the ES to get an EF of 10.33. This EF is used as the ES for
188:
2189:
33:
382:
1261:
is zero. The duration (4 work days) is added to the ES to get an EF of four. This EF is used as the ES for
1121:
as a predecessor activity, so an arrow is drawn connecting the activities. Likewise, an arrow is drawn from
193:
84:
1442:
is 15.01 work days. The duration (6.33 work days) is subtracted from the LF to get an LS of 8.68 work days.
328:
2264:
2259:
2254:
2213:
1767:
The lack of a timeframe on most PERT/CPM charts makes it harder to show status, although colours can help,
1456:
is 9.17 work days. The duration (5.33 work days) is subtracted from the LF to get an LS of 3.84 work days.
2279:
2239:
1887:
1449:
is 9.17 work days. The duration (5.17 work days) is subtracted from the LF to get an LS of 4 work days.
1822:
1504:
1379:
1231:
1026:
1003:
622:
618:
1745:
The large amount of project data can be organized and presented in diagram for use in decision making.
1977:
1837:
1758:
There can be potentially hundreds or thousands of activities and individual dependency relationships.
1046:
175:
56:
1807:
1730:
1203:
A node like this one can be used to display the activity name, duration, ES, EF, LS, LF, and slack.
1042:
223:
1589:
are milestones and by definition have no duration, therefore they can have no slack (0 work days).
1475:
is 4 work days. The duration (4 work days) is subtracted from the LF to get an LS of 0 work days.
2229:
1857:
1792:, defines a procedure to react to disruptions that cannot be absorbed by the baseline schedule.
741:
is complete). Additionally, each task has three time estimates: the optimistic time estimate (
1571:
is reduced to 15.34 work days, which is slightly less than the time of the new critical path,
2055:
1375:
136:
20:
2159:
Schedule, Cost, and Profit
Control with PERT - A Comprehensive Guide for Program Management
1698:
1578:
Assuming these scenarios do not happen, the slack for each activity can now be determined.
1500:
1153:
1061:
in this example) and connect them with an arrow from start to each node. Next, since both
1036:
1022:
999:
695:
687:
650:
200:
128:
71:
8:
1739:
PERT facilitates identification of early start, late start, and slack for each activity.
613:
PERT supplies a number of tools for management with determination of concepts, such as:
2178:
1847:
67:
52:
2234:
2185:
2162:
2143:
2124:
2102:
2083:
1812:
1689:
1516:
slack = LS − ES. Activities that are on the critical path have a slack of zero (0).
1149:
995:
1667:
can be delayed almost 4 work days without delaying the project. Likewise, activity
150:
2180:
The
Polaris System Development: Bureaucratic and Programmatic Success in Government
2140:
Project
Management ToolBox: Tools and Techniques for the Practicing Project Manager
1852:
1802:
2008:
1339:
is 14.34. The duration (5.17 work days) is added to the ES to get an EF of 19.51.
219:
with about 150 publications on PERT and CPM, all published between 1958 and 1968.
1842:
1694:
1332:
is 10.33. The duration (4.5 work days) is added to the ES to get an EF of 14.83.
1964:; "Application of a Technique for Research and Development Program Evaluation",
1283:
is four. The duration (5.17 work days) is added to the ES to get an EF of 9.17.
1276:
is zero. The duration (5.33 work days) is added to the ES to get an EF of 5.33.
2121:
Project
Management: A Systems Approach to Planning, Scheduling, and Controlling
2116:
1494:
1370:
is a milestone (and therefore has a duration of zero), so the EF is also 19.51.
1144:
1137:, it is recommended (but again not required) to connect them to a node labeled
2223:
2022:
1961:
180:
1736:
PERT facilitates identification of the critical path and makes this visible.
1678:
can be delayed 4.68 work days without delaying the project (alternatively,
1013:
990:
664:
216:
95:
PERT offers a management tool, which relies "on arrow and node diagrams of
1729:(precedence relationships) between the work breakdown structure (commonly
222:
For the subdivision of work units in PERT another tool was developed: the
1827:
1555:
take their pessimistic (b) times to complete instead of their expected (T
1238:
zero (0). The EF is the ES plus the task duration (EF = ES + duration).
1073:
as a predecessor activity, their nodes are drawn with arrows coming from
982:
243:, with connections to its known predecessor events and successor events.
1037:
Next step, creating network diagram by hand or by using diagram software
733:) while others cannot be done until their predecessor task is complete (
2026:
1563:
and the critical time is 22 work days. On the other hand, if activity
1659:
has an LF of 19.51 and an EF of 14.83, so the slack is 4.68 work days.
1652:
has an LF of 15.01 and an EF of 10.33, so the slack is 4.68 work days.
1886:
Kelley, James E.; Walker, Morgan R.; Sayer, John S. (February 1989).
212:
28:
1645:
has an LF of 9.17 and an EF of 5.33, so the slack is 3.84 work days.
450: : the variability of the time for accomplishing an activity (σ
292:
PERT defines four types of time required to accomplish an activity:
1018:
132:
111:
or nodes that indicate each completed phase of the total project."
1862:
1748:
PERT can provide a probability of completing before a given time.
173:
both primarily written by
Charles F. Clark. In a 1959 article in
140:
60:
270:
Besides events, PERT also tracks activities and sub-activities:
2208:
144:
89:
1948:, Council of Planning Librarians, Monticello (IL), 1968, p. 1
2077:
1495:
Next step, determination of critical path and possible slack
254:
of the activities leading to that event have been completed.
1832:
1960:
Malcolm, Donald G.; Roseboom, John H.; Clark, Charles E.;
167:
Program
Evaluation Research Task, Summary Report, Phase 1.
66:
PERT was originally developed by
Charles E. Clark for the
2010:
Program
Evaluation Research Task, Summary Report, Phase 2
1995:
Program Evaluation Research Task, Summary Report, Phase 1
717:
In the following example there are seven tasks, labeled
211:
Ten years after the introduction of PERT, the American
32:
PERT network chart for a seven-month project with five
1482:
is the minimum LS of its successor activities. Since
1463:
is the minimum LS of its successor activities. Since
147:'s CPM was invented at roughly the same time as PERT.
1923:
1921:
1919:
1917:
1915:
1913:
472:
385:
331:
139:
of Frederick Taylor and later refined by Henry Ford (
70:
in 1958; it is commonly used in conjunction with the
1968:, vol. 7, no. 5, September–October 1959, pp. 646–669
1775:
1761:
PERT is not easy to scale down for smaller projects.
2080:
A Guide to the Project Management Body of Knowledge
2013:, Government Printing Office, Washington (DC), 1958
1998:, Government Printing Office, Washington (DC), 1958
1490:
has an LS of 3.84 work days, the LS is 0 work days.
2177:
1910:
1567:can be reduced to one work day, the path time for
1346:is the greatest EF of its predecessor activities (
1301:is the greatest EF of its predecessor activities (
593:
431:
370:
239:In a PERT diagram, the main building block is the
55:, which was designed to analyze and represent the
1885:
1129:. Since there are no activities that come after
691:: performing more critical activities in parallel
36:(10 through 50) and six activities (A through F).
2221:
1725:PERT chart explicitly defines and makes visible
1507:. The critical path is the path that takes the
115:increasingly to all critical path scheduling."
2082:(5th ed.). Project Management Institute.
1714:
745:), the most likely or normal time estimate (
699:: Shortening duration of critical activities
1956:
1954:
981:Once this step is complete, one can draw a
19:"PERT" redirects here. For other uses, see
16:Statistical tool used in project management
2016:
1693:A completed network diagram created using
74:(CPM), which was also introduced in 1958.
2137:
2096:
1940:
1938:
1936:
1881:
1879:
2175:
2099:Project Management: Tools and Trade-offs
1951:
1888:"The Origins of CPM: a personal history"
1688:
1471:has an LS of 8.68 work days, the LF for
1143:
1012:
989:
725:. Some tasks can be done concurrently (
432:{\displaystyle TE=\sum _{i=1}^{n}te_{i}}
234:
199:
149:
27:
2115:
2044:Program Evaluation and Review Technique
1927:
2222:
2156:
1933:
1876:
1771:, specific colour for completed nodes.
1093:is drawn with arrows coming from both
749:), and the pessimistic time estimate (
371:{\displaystyle te={\frac {o+4m+p}{6}}}
2078:Project Management Institute (2013).
1946:PERT and CPM: a selected bibliography
1898:(2). Project Management Institute: 18
1686:can be delayed 2.34 work days each).
215:Maribeth Brennan compiled a selected
2060:Handbook of Business Administration,
2033:, 13(2): 9–12 (April 1959), pp. 9–12
1978:1968 Winter Olympics official report
1980:, p. 49. Accessed 1 November 2010.
1559:) times. The critical path is now
1089:as predecessor activities, so node
608:
13:
2069:
1499:The next step is to determine the
14:
2291:
2201:
1818:Critical chain project management
1776:Uncertainty in project scheduling
1705:
757:) is computed using the formula (
703:
683:can follow a specific PERT event.
634:). Positive slack would indicate
163:Program Evaluation Research Task,
125:U.S. Navy Special Projects Office
2207:
2027:"Federal Statistical Activities"
1752:
1148:A network diagram created using
642:; and zero slack would indicate
638:; negative slack would indicate
51:) is a statistical tool used in
2049:
1113:have been completed. Activity
679:: the earliest time by which a
107:or work necessary to reach the
59:involved in completing a given
45:evaluation and review technique
2036:
2001:
1992:U.S. Department of the Navy,
1986:
1971:
1362:has an EF of 19.51, the ES of
229:
1:
2250:Schedule (project management)
2245:Project management techniques
2138:Milosevic, Dragan Z. (2003).
2007:U.S. Department of the Navy,
1869:
1719:
1486:has an LS of 0 work days and
1467:has an LS of 4 work days and
1317:has an EF of 9.17, the ES of
205:PERT Guide for Management Use
2184:. Harvard University Press.
2176:Sapolsky, Harvey M. (1971).
1017:A Gantt chart created using
994:A Gantt chart created using
7:
1795:
1503:and if any activities have
155:PERT Summary Report Phase 2
77:
10:
2296:
2157:Miller, Robert W. (1963).
1823:Float (project management)
1715:As project scheduling tool
1221:The early finish time (EF)
1215:The expected duration time
712:
448:standard deviation of time
118:
18:
2031:The American Statistician
1838:Precedence diagram method
1227:The late finish time (LF)
1218:The early start time (ES)
1180:
783:
780:
777:
774:
176:The American Statistician
161:Initially PERT stood for
2123:(10th ed.). Wiley.
1808:Arrow diagramming method
1224:The late start time (LS)
1105:cannot begin until both
1045:) and activity on node (
1025:is highlighted, (2) the
630:) or the whole project (
224:Work Breakdown Structure
2101:(3rd ed.). Wiley.
2097:Klastorin, Ted (2003).
1982:(in English and French)
1858:Triangular distribution
1358:has an EF of 14.83 and
753:). The expected time (
287:
103:: arrows represent the
2275:Engineering management
2270:Management cybernetics
2056:Maynard, Harold Bright
1702:
1313:has an EF of 5.33 and
1157:
1031:
1008:
985:or a network diagram.
696:crashing critical path
669:: the time by which a
595:
555:
433:
415:
372:
208:
198:
158:
37:
1692:
1542:The critical path is
1534:The duration of path
1527:The duration of path
1520:The duration of path
1147:
1016:
998:(MSP). Note (1) the
993:
596:
535:
434:
395:
373:
235:Events and activities
203:
185:
153:
137:scientific management
31:
21:PERT (disambiguation)
2216:at Wikimedia Commons
1786:proactive scheduling
1663:Therefore, activity
470:
383:
329:
129:1968 Winter Olympics
72:Critical Path Method
2265:Operations research
2260:Booz Allen Hamilton
2255:Systems engineering
1966:Operations Research
1944:Brennan, Maribeth;
1790:reactive scheduling
1636:= 19.51 − 19.51 = 0
1625:= 14.34 − 14.34 = 0
1575:(15.67 work days).
1538:is 15.67 work days.
1531:is 19.51 work days.
1524:is 14.83 work days.
1002:is in red, (2) the
737:cannot begin until
2280:Management science
2240:Evaluation methods
2042:Cook, Desmond L.;
1892:Project Management
1848:Project management
1703:
1158:
1101:, signifying that
1032:
1009:
591:
589:
429:
368:
209:
159:
68:United States Navy
53:project management
38:
2212:Media related to
2149:978-0-471-20822-8
2130:978-0-470-27870-3
2108:978-0-471-41384-4
2089:978-1-935589-67-9
1813:PERT distribution
1614:= 9.17 − 9.17 = 0
1376:unforeseen events
1212:The activity name
1200:
1199:
1152:(MSP). Note the
1150:Microsoft Project
996:Microsoft Project
979:
978:
671:predecessor event
658:critical activity
636:ahead of schedule
585:
510:
366:
281:PERT sub-activity
258:predecessor event
2287:
2211:
2195:
2183:
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1969:
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1931:
1925:
1908:
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1883:
1853:Project planning
1803:Activity diagram
1163:
1162:
1021:. Note (1) the
772:
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609:Management tools
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309:most likely time
303:pessimistic time
2295:
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2289:
2288:
2286:
2285:
2284:
2220:
2219:
2204:
2199:
2198:
2192:
2169:
2161:. McGraw-Hill.
2150:
2131:
2117:Kerzner, Harold
2109:
2090:
2072:
2070:Further reading
2067:
2066:
2054:
2050:
2041:
2037:
2021:
2017:
2006:
2002:
1991:
1987:
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1972:
1959:
1952:
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1911:
1901:
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1877:
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1867:
1843:Project network
1798:
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1722:
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1708:
1695:Microsoft Visio
1635:
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1204:
1201:
1195:
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1167:
1081:is listed with
1039:
781:Time estimates
715:
706:
681:successor event
640:behind schedule
611:
588:
587:
579:
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297:optimistic time
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264:successor event
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17:
12:
11:
5:
2293:
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2230:Network theory
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2202:External links
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15:
9:
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2046:, 1966, p. 12
2045:
2039:
2032:
2028:
2024:
2023:Willard Fazar
2019:
2012:
2011:
2004:
1997:
1996:
1989:
1979:
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1967:
1963:
1957:
1955:
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1941:
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1753:Disadvantages
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1699:critical path
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1501:critical path
1489:
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688:fast tracking
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315:expected time
313:
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2018:
2009:
2003:
1994:
1988:
1973:
1965:
1945:
1928:Kerzner 2009
1900:. Retrieved
1895:
1891:
1789:
1785:
1783:
1779:
1768:
1727:dependencies
1709:
1697:. Note the
1683:
1679:
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1374:Barring any
1373:
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1329:
1322:
1318:
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1122:
1118:
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1098:
1094:
1090:
1086:
1082:
1078:
1077:. Activity
1074:
1070:
1066:
1062:
1058:
1054:
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961:
956:
937:
932:
913:
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904:
885:
880:
861:
856:
834:
812:
804:
797:
790:
778:Predecessor
766:
762:
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754:
750:
746:
742:
738:
734:
730:
726:
722:
718:
716:
707:
694:
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649:
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631:
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612:
447:
314:
308:
302:
296:
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217:bibliography
210:
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186:
174:
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166:
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154:
122:
113:
108:
104:
100:
96:
94:
83:details and
81:
65:
48:
44:
41:
39:
25:
2214:PERT charts
2062:1967, p. 17
1828:Gantt chart
1733:) elements.
1603:= 4 − 4 = 0
1478:The LF for
1459:The LF for
1452:The LF for
1445:The LF for
1438:The LF for
1423:The LF for
1412:The LF for
1401:The LF for
1386:The LF for
1366:is 19.51.
1342:The ES for
1335:The ES for
1328:The ES for
1297:The ES for
1286:The ES for
1279:The ES for
1272:The ES for
1257:The ES for
1242:The ES for
983:Gantt chart
644:on schedule
632:total float
230:Terminology
207:, June 1963
2224:Categories
2191:0674682254
1870:References
1720:Advantages
1701:is in red.
1354:). Since
1309:). Since
1181:Task Name
1156:is in red.
628:free float
248:PERT event
105:activities
97:activities
92:projects.
34:milestones
2142:. Wiley.
1674:activity
1655:Activity
1648:Activity
1641:Activity
1171:Duration
775:Activity
560:σ
537:∑
519:σ
501:−
480:σ
397:∑
213:librarian
194:scheduled
189:estimates
85:durations
2235:Diagrams
2119:(2009).
1902:20 March
1796:See also
1030:weekend.
1019:OmniPlan
1007:weekend.
796:Normal (
721:through
677:lag time
171:Phase 2.
133:Grenoble
78:Overview
42:program
1863:PRINCE2
1509:longest
1196:finish
1176:finish
803:Pess. (
769:) ÷ 6.
713:Example
141:Fordism
119:History
90:R&D
61:project
2188:
2165:
2146:
2127:
2105:
2086:
1587:finish
1388:finish
1368:Finish
1364:finish
1344:finish
1191:Slack
1188:Start
1168:Start
1139:finish
789:Opt. (
157:, 1958
145:DuPont
109:events
101:events
1583:Start
1505:slack
1480:start
1380:slack
1244:start
1232:slack
1174:Early
1166:Early
1069:list
1051:start
1027:slack
1004:slack
975:5.17
951:4.50
927:5.17
899:6.33
875:5.17
851:5.33
829:4.00
623:slack
619:float
241:event
57:tasks
2186:ISBN
2163:ISBN
2144:ISBN
2125:ISBN
2103:ISBN
2084:ISBN
1904:2024
1833:GERT
1769:e.g.
1682:and
1632:– EF
1621:– EF
1610:– EF
1599:– EF
1585:and
1569:aceg
1551:and
1544:aceg
1529:aceg
1431:and
1394:and
1350:and
1305:and
1265:and
1250:and
1230:The
1194:Late
1186:Late
1117:has
1109:and
1097:and
1085:and
1065:and
1057:and
729:and
667:time
665:lead
288:Time
169:and
99:and
49:PERT
40:The
1731:WBS
1573:beg
1561:adf
1536:beg
1522:adf
1133:or
1125:to
1047:AON
1043:AOA
896:10
761:+ 4
621:or
252:all
143:).
131:in
2226::
2058:,
2029:,
1953:^
1935:^
1912:^
1894:.
1890:.
1878:^
1672:or
1628:LF
1617:LF
1606:LF
1595:LF
1514:or
1141:.
972:8
969:5
966:3
948:8
945:4
942:3
924:7
921:5
918:4
912:,
893:6
890:4
872:7
869:5
866:4
848:9
845:5
842:3
839:—
826:6
823:4
820:2
817:—
807:)
800:)
793:)
765:+
755:te
456:TE
452:te
179:,
63:.
2194:.
2171:.
2152:.
2133:.
2111:.
2092:.
1930:.
1906:.
1896:3
1684:f
1680:d
1676:f
1669:d
1665:b
1657:f
1650:d
1643:b
1634:g
1630:g
1623:e
1619:e
1612:c
1608:c
1601:a
1597:a
1565:c
1557:E
1553:f
1549:d
1488:b
1484:a
1473:a
1469:d
1465:c
1461:a
1454:b
1447:c
1440:d
1435:.
1433:c
1429:b
1425:e
1420:.
1418:d
1414:f
1409:.
1407:e
1403:g
1398:.
1396:g
1392:f
1360:g
1356:f
1352:g
1348:f
1337:g
1330:f
1325:.
1323:g
1319:e
1315:c
1311:b
1307:c
1303:b
1299:e
1294:.
1292:f
1288:d
1281:c
1274:b
1269:.
1267:d
1263:c
1259:a
1254:.
1252:b
1248:a
1135:g
1131:f
1127:g
1123:e
1119:d
1115:f
1111:c
1107:b
1103:e
1099:c
1095:b
1091:e
1087:c
1083:b
1079:e
1075:a
1071:a
1067:d
1063:c
1059:b
1055:a
962:E
957:G
938:D
933:F
914:C
910:B
905:E
886:A
881:D
862:A
857:C
835:B
813:A
805:p
798:m
791:o
767:p
763:m
759:o
751:p
747:m
743:o
739:A
735:C
731:B
727:A
723:G
719:A
646:.
581:2
572:i
568:e
564:t
552:n
547:1
544:=
541:i
531:=
526:E
523:T
508:6
504:o
498:p
492:=
487:e
484:t
458:)
425:i
421:e
417:t
412:n
407:1
404:=
401:i
393:=
390:E
387:T
364:6
360:p
357:+
354:m
351:4
348:+
345:o
339:=
336:e
333:t
47:(
23:.
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