We can now determine the float, or slack, for each activity as well as the overall critical path. Again, float informs us of the amount of time an activity can be delayed and still not delay the overall project. Activity float is found through using one of two equations: LF - EF = Float or LS - ES = Float. Consider activity E with 12 weeks of float. Assume the worst-case scenario, in which the activity is unexpectedly delayed 10 weeks, starting on week 20 instead of the planned week 10. What are the implications of this delay on the overall project? None. With 12 weeks of float for activity E, a delay of 10 weeks will not affect the overall length of the project or delay its completion. What would happen if the activity were delayed by 14 weeks? The ES, instead of 10, is now 24. Adding activity duration (6 weeks), the new EF is 30. Take a look at the network shown in Figure 9.20 to see the impact of this delay. Because activity H is a merge point for activities E, F, and G, the largest EF value is the ES for the final node. The new largest EF is 30 in activity E. Therefore, the new node EF = ES + Dur, or 30 + 2 = 32. The effect of overusing available slack delays the project by 2 weeks. One other important point to remember about activity float is that it is determined as a result of performing the forward and backward passes through the network Show
Sets found in the same folderPresentation on theme: "PERT and CPM."— Presentation transcript: 1 PERT and CPM 2 Contents PERT/CPM Network
3 Rules of Network Construction
4 Network Activity Imm. Pred. Activity Imm. Pred. A - B C D A, B E F G
5 Network E H I B F J C G A L D K 4 2 5 1 6 9 3 7 8 Activity Imm. Pred.
6 Critical Path Critical path refers to the longest path of a given project
network Duration of a project is given by the length of the critical path Activities on a critical path are called critical activities while remaining activities are non-critical A project can have more than one critical path as well Critical activities are so called because their timely completion is critical to the completion of the project in time Critical activities can not be delayed while non-critical activities have some
cushion available 7 Critical Path: Example: 8 9 Critical Path (…continued)
10 Floats Total float is the amount of time by which an activity may be delayed without delaying the project completion Caution:
interpret total floats of activities carefully - all can not be used independently Free float is that part of total float which can be used without affecting floats of the succeeding activities The part of total float which is not free is called interfering float Independent float is the amount of time which can be used without affecting the head and the tail events Total Float ≥ Free Float ≥ Independent Float
11 Calculation of Floats Total float 12 Floats Calculation i - j t ES EF LS LF TF IF FF lnF 1-2 2 9 11 1-3 7 13 Resource Analysis and Allocation
14 Crashing Involves use of additional resources with a view to reduce the project duration Crashing increases direct cost of doing activities but reduces overhead, which is usually a
function of time It may also help to reap any benefits of early completion It needs information on cost of reduction of every activity per unit of time In crashing, always consider the critical path and choose the activity that can be crashed at least cost In case of multiple critical paths, all of them should be considered for crashing simultaneously Time-cost schedule is prepared to get information on normal time and the cost,
the minimum time to complete project and the cost, and optimal duration of the project 15 Resource Leveling Resource leveling refers to scheduling the activities of a project in such a manner that the requirement of resources may be leveled to the extent possible without delaying the completion of the
project To begin with every activity is scheduled at the earliest and the requirement of the resource involved is assessed on a daily basis Since the activities are scheduled on early days, the demand for the resource, say labour, is likely to be large in earlier days of the project and small in the later days
16 Resource Leveling (…continued) 17
PERT Uses three time estimates for every activity: optimistic (a), most likely (m) and pessimistic (b) They are used to obtain expected times and their variances Expected time = (a+4×m+b)/6; and Variance = [(b – a )/6]2 Obtain critical path using expected times and identify critical activities Add variances for critical activities to get variance for completion time and find its square root to get
standard deviation With expected duration and standard deviation, calculate probabilities of project completion using normal distribution 18 PERT (Example) The owner of a chain of fast-food restaurants is considering a new computer system for accounting and inventory control. A computer company sent the
following information about the system installation: Activity Immediate Predecessor Most Optimistic Most likely Most Pessimistic A - 4 6 8 B 5 7 15 C 12 D 20 25 E 10 18 26 F
9 16 G H D,F 1 2 3 I G,H 19 20
PERT Calculations Critical activities: A B E G I
21 PERT Calculations (…continued)
22 PERT/Cost A modification of PERT which allows planning, monitoring and controlling of project cost and duration Budgeting process
allows to determine how much money is to be spent every time unit (week/month) over planned duration of project Budgets are prepared on the basis of earliest and latest start times of activities Comparisons are made continuously between the actual costs and budgeted amounts Comparisons are also made between percentage of work done and percentage of budgeted amount spent: if former is smaller than the later, we have budget overrun
23 Multiple Choice Questions
24 Multiple Choice Questions
25 Multiple Choice Questions 26 Multiple Choice Questions 27 Multiple Choice Questions 28 Multiple Choice Questions 29 Multiple Choice Questions 30
Multiple Choice Questions
31 Multiple Choice Questions 32 Multiple Choice Questions 33 Multiple Choice Questions
34 Multiple Choice Questions 35 Multiple Choice Questions
36 Multiple Choice Questions 37 Multiple Choice Questions 38 Thank You
What burst event?Burst event – When more than one activity leaves an event such an event is known as burst event. 3. Merge and Burst event – An activity may be merge and burst event at the same time as with respect to some activities it can be a merge event and with respect to some other activities it may be a burst event. 3.
Is that event where more than one activity ends?b) Burst Event: When more than one activity leaves an event is known as burst event.
What do you mean by single event which represent the joint start of more than one activities?If an event represents the joint initiation of more than one activity, it is called a burst event. The activities can be further classified into the following three categories : 1. Predecessor activity. An activity which must be completed before one or more other activities start is known as predecessor activity.
Which of the following shows that when more than two activities ends at one event a burst B dummy C merge d none of these?If so many activities, (two or more) are ending at one node, it is called merge event. If so many activities two or more than two are starting from one node, it is called burst event.
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