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Network analysis is the general name given to certain specific techniques which can be used for the planning, management and control of projects. Use of nodes and arrows:- Arrows An arrow leads from tail to head directionally Indicate ACTIVITY, a time consuming effort that is required to perform a part of the work.

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NODE:- A node is represented by a circle - Indicate EVENT, a point in time where one or more activities start and/or finish. Activity:- – A task or a certain amount of work required in the project – Requires time to complete – Represented by an arrow Dummy Activity:- – Indicates only precedence relationships – Does not require any time of effort.

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Event:- Signals the beginning or ending of an activity Designates a point in time Represented by a circle (node) Network:- Shows the sequential relationships among activities using nodes and arrows Activity-on-node (AON):- nodes represent activities, and arrows show precedence relationships Activity-on-arrow (AOA):- arrows represent activities and nodes are events for points in time

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SITUATIONS IN NETWORK DIAGRAM:- A B C A must finish before either B or C can start. Both A and B must finish before C can start. Both A and B must finish before either of C or D can start. A must finish before B can start both A and C must finish before D can start. C A B A B C D A C Dummy B D

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illustration of network analysis of a minor redesign of a product and its associated packaging. The key question is: How long will it take to complete this project ?

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Path A connected sequence of activities leading from the starting event to the ending event Critical Path The longest path (time); determines the project duration Critical Activities All of the activities that make up the critical path.

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Forward Pass:- Earliest Start Time (ES) earliest time an activity can start ES = maximum EF of immediate predecessors Earliest finish time (EF) earliest time an activity can finish earliest start time plus activity time EF= ES+t

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Backward Pass:- Latest Start Time (LS) Latest time an activity can start without delaying critical path time LS= LF - t Latest finish time (LF) latest time an activity can be completed without delaying critical path time LS = minimum LS of immediate predecessors

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Draw the CPM network Analyze the paths through the network Determine the float for each activity Compute the activitys float float = LS - ES = LF - EF Float is the maximum amount of time that this activity can be delay in its completion before it becomes a critical activity, i.e., delays completion of the project Find the critical path is that the sequence of activities and events where there is no slack i.e.. Zero slack Longest path through a network Find the project duration is minimum project completion time

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CPM Network:- a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12

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ES and EF Times:- a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 06 08 05

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ES and EF Times:- a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 0 0 0 6 8 5 621 623 821 514

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ES and EF Times:- a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 06 08 05 621 30 623 29 821 514 2133 Projects EF = 33 Projects EF = 33

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LS and LF Times:- a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 00 05 0 06 0 08 00 621 00 30 24 0 236 33 21 0 8 0 00 145 0 21 3327 2923 3321 33

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LS and LF Times:- a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 06 410 8 0 0 218 8 127 50 145 8 1824 621 3321 3321 6 2733 2923 33 30 24 21 2710 23

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FLOAT:- a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12 410 06 0 6 23 2710 21 6 8 8 127 5 2112 145 03 4 3327 2923 924 0 0 21 33 3 3 24 3021 04 7 0 80 80 7

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Critical Path:- a, 6 f, 15 b, 8 c, 5 e, 9 d, 13 g, 17 h, 9 i, 6 j, 12

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PERT is based on the assumption that an activitys duration follows a probability distribution instead of being a single value Three time estimates are required to compute the parameters of an activitys duration distribution: pessimistic time (t p ) - the time the activity would take if things did not go well most likely time (t m ) - the consensus best estimate of the activitys duration optimistic time (t o ) - the time the activity would take if things did go well t e = a+4m+b 6

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Draw the network. Analyze the paths through the network and find the critical path. The length of the critical path is the mean of the project duration probability distribution which is assumed to be normal The standard deviation of the project duration probability distribution is computed by adding the variances of the critical activities (all of the activities that make up the critical path) and taking the square root of that sum Probability computations can now be made using the normal distribution table.

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Determine probability that project is completed within specified time Z = where = t p = project mean time = project standard mean time x = (proposed ) specified time x -

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= t p Time x Z Probability

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Useful at many stages of project management Mathematically simple Give critical path and slack time Provide project documentation Useful in monitoring costs

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How long will the entire project take to be completed? What are the risks involved? Which are the critical activities or tasks in the project which could delay the entire project if they were not completed on time? Is the project on schedule, behind schedule or ahead of schedule? If the project has to be finished earlier than planned, what is the best way to do this at the least cost?

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Parallel paths-identifying a single path is difficult when there are parallel paths with similar duration. Time consuming-critics note that it takes too much time to identify all activities and inter-relate them to get multiple projects paths. First time projects-CPM is not suitable if projects cannot be broken down into discrete activities with known completion times.

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PRESENTED BY:- BHUPENDRA SINGH SHEKHAWAT ANKIT VINOD AGRAWAL BHANU MATHUR AMIT SINGAL AKANSHA CHOUDHARY KAMAL KANT AKASH GARG MOHIT SHARMA ANKIT BAJORIA MAYANK AGRAWAL

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