Critical Path Method
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This document provides information about critical path method (CPM) including: - An introduction to CPM and examples of projects where it can be applied. - The differences between CPM and PERT. - Key terms and definitions used in CPM like activity times, floats, and critical path. - An example of calculating event times, activity times, floats, and determining the critical path for a sample CPM network diagram.
Critical Path Method
- 1. Chapter –6 Critical Path Method (CPM) Course Code -CIE 403 Mr. Ramesh Nayaka, (M.Tech. –IIT Madras) Assistant Professor Department of Civil Engineering Manipal Institute of Technology, Manipal -576104 Karnataka, India
- 2. Content… •Introduction to CPM •Difference between CPM and PERT •Terms and Definitions •Calculation of Float •Critical Path
- 3. Introduction to CPM CPM network are usually used for repetitive type of projects, where fairly accurate estimates of time can be made for the activities of the project. The activities of these projects are characteristically subject to relatively small amount of variation. Hence CPM is not suitable for research and development type of projects. Examples from fairly diverse field where application of CPM can be made: Building a new bridge across river ganga, Constructing a multi-storeyed building, extension of a factory building, shifting a manufacturing unit to other site and manufacturing of a new car etc.
- 4. Difference between CPM and PERT CPM PERT Activity Oriented network Event oriented network The time estimatesare of a fair degree of accuracy Time estimates are not that accurate andthere is an uncertainty attached to it Follows deterministic approach Followsprobabilistic approach Cost is governingfactor Time is governing factor Project duration is so fixed such that the cost is minimum Assumed that cost is directly proportional to time so time is reduced maximum possible to enjoy least cost Critical path is thatpath which joins the critical activities Criticalpath is the path which joins the critical events
- 5. Terms and Definitions Activity Times Forward Passing : Earliest Start Time (EST) :earliest time by which an activity start EST = earliest event time of tail event = TEi Earliest Finish Time (EFT) : Earliest time by which an activity can be completed EFT = EST + tEij= TEi + tEij
- 6. Terms and Definitions Activity Times Backward Passing : Latest Finish Time (LFT) : latest time by which an activity can completed without delaying the completion of the project LFT = Latest Finish Time of head event = TLj Latest Start Time (LST) : latest time by which an activity can start without delaying the completion of the project LST = LFT -tEij= TLj -tEij
- 7. Terms and Definitions FLOATS Similar to slack in PERT Associated with activity times Denotes flexibility range within which the activity start and finish time may fluctuate without affecting the total duration of the project
- 8. Terms and Definitions TYPES OF FLOATS Total Float (FT) : timespan by which starting or finishing of an activity can be delayed without affecting the overall completion time of the project. It refers to the amount of time by which the completion of activity could be delayed beyond earliest expected completion time without affecting overall project duration time FT= LST –EST or LFT -EFT
- 9. Terms and Definitions TYPES OF FLOATS Free Float (FF) : duration by which an activity can be delayed without delaying any other succeeding activity. It refers to the amount of time by which the completion of an activity can be delayed beyond the earliest finish time without affecting the earliest start time of a subsequent succeeding activity. This float is concerned with the commencement of subsequent activity FF= FT–Sj , Sj= Slack of head event = TLj –TEj
- 10. Terms and Definitions TYPES OF FLOATS Independent Float (FID): It is excess time available if the preceding activity ends as late as possible and the succeeding activity starts as early as possible It is refers to that the amount of time by which the start of an activity can be delayed, without affecting earliest start time of any immediately following activities This float concerned with prior and subsequent activities FID= FF–Si Si = slack of tail event =TLi–TEi
- 11. Terms and Definitions TYPES OF FLOATS Interfering Float (FIT) : Another name for head event slack (Sj), it is the difference between total float and free float FIT= FT–FF = TLj –TEj = Sj Note : if the total float (FT) for any activity is zero then such activity is called critical activity Critical Activity : an activity is said to be critical, if a delay in its start cause a further delay in the completion of the entire project
- 12. Terms and Definitions Critical Path : The sequence of critical activities in a network which determines the duration of a project is called critical path. •It is the longest path in the network from the starting event to the ending event •For activities lies on critical path EST =LST , EFT = LFT and EST –EFT = LST –LFT Sub critical activity : When total float (FT ) is positive Critical Activity :When total float (FT ) is zero Super critical activity : When total float (FT ) is negative
- 13. Calculating Critical Path & Float for a Network Diagram Find out the length of all the paths in the network diagram The longest path is the critical path Float = EF –LF = ES -LS
- 14. Terms and Definitions Critical Path : The sequence of critical activities in a network which determines the duration of a project is called critical path. •It is the longest path in the network from the starting event to the ending event •For activities lies on critical path EST =LST , EFT = LFT and EST –EFT = LST –LFT Sub critical activity : When total float (FT ) is positive Critical Activity :When total float (FT ) is zero Super critical activity : When total float (FT ) is negative
- 15. Terms and Definitions Critical Path : The sequence of critical activities in a network which determines the duration of a project is called critical path. •It is the longest path in the network from the starting event to the ending event •For activities lies on critical path EST =LST , EFT = LFT and EST –EFT = LST –LFT Sub critical activity : When total float (FT ) is positive Critical Activity :When total float (FT ) is zero Super critical activity : When total float (FT ) is negative
- 16. CPM Analysis F 1 2 4 3 5 6 7 8 A B C D E H K J I 10 8 12 8 10 6 5 12 6 12 8 Aprojectconsistsof11activities,representedbythe networkshownbelowinfigureandalsothenormal durationsrequiredtoperformvariousactivitiesofthe projectaregiveninnetwork.Compute(a)Eventtimes (b)activitytimesandtotalfloat.Alsodetermine thecriticalpath.
- 17. a. Computation of Event times Event No. PredecessorSuccessorEventEvent12345678Earliest Expected Time (↓ )Latest occurrence Time ( ↑ ) tETETE (Max)tETLTL (Min)
- 18. b. Computation of activity times and floats Activity Duration Earliest (Units) Latest (Units) Total Float Free Float Independent Float (i -j) tEij EST EFT LST LFT FT FF FID 1 -2 1 -3 2 –5 2 –7 3–4 3–6 4–5 5 -6 5 -7 6 -7 7 -8
- 19. c. Location of Critical path •1-3 –4 –5 –6 –7 = 52 units F 1 2 4 3 5 6 7 8 A B C D E H K J I 10 8 12 8 10 6 5 12 6 12 8
- 20. Problem –2 F 1 2 4 3 5 6 7 8 A B G E D I L J 5 4 4 6 2 6 7 8 0 6 7 C K 3 Networkshownbelowinfigureandalsothenormaldurationsrequiredtoperformvariousactivitiesoftheprojectaregiveninnetwork.Compute(a)Eventtimes(b) activitytimes(c)totalfloatforeachactivityandestablishthecriticalpath.Alsodeterminethefreefloatandindependentfloat.
- 21. Problem –2 1 2 3 6 4 5 A B E D G H 3 5 3 1 14 4 C F 4 Networkshownbelowinfigureandalsothenormaldurationsrequiredtoperformvariousactivitiesoftheprojectaregiveninnetwork.Compute(a)Eventtimes(b) activitytimes(c)totalfloatforeachactivityandestablishthecriticalpath.Alsodeterminethefreefloatandindependentfloat. 6 1 I