Operational Research. Project Menagement Method by CPM/ PERT

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1 Operational Research Project Menagement Method by CPM/ PERT

2 Project definition A project is a series of activities directed to accomplishment of a desired objective. Plan your work first..then work your plan

3 Network analysis introduction Network analysis is the general name given to certain specific techniques which can be used for the planning, management and control of projects. One definition of a project: A project is a temporary endeavour undertaken to create a "unique" product or service

4 History CPM was developed by Du Pont and the emphasis was on the trade-off between the cost of the project and its overall completion time (e.g. for certain activities it may be possible to decrease their completion times by spending more money - how does this affect the overall completion time of the project?) PERT was developed by the US Navy for the planning and control of the Polaris missile program and the emphasis was on completing the program in the shortest possible time. In addition PERT had the ability to cope with uncertain activity completion times (e.g. for a particular activity the most likely completion time is 4 weeks but it could be anywhere between 3 weeks and 8 weeks).

5 CPM - Critical Path Method Definition: In CPM activities are shown as a network of precedence relationships using activity-on-node network construction Single estimate of activity time Deterministic activity times USED IN : Production management - for the jobs of repetitive in nature where the activity time estimates can be predicted with considerable certainty due to the existence of past experience.

6 PERT as a Project Evaluation & Review Techniques Definition: In PERT activities are shown as a network of precedence relationships using activity-on-arrow network construction Multiple time estimates Probabilistic activity times USED IN : Project management - for nonrepetitive jobs (research and development work), where the time and cost estimates tend to be quite uncertain. This technique uses probabilistic time estimates.

7 Gantt chart Advantages Gantt charts are quite commonly used. They provide an easy graphical representation of when activities (might) take place. Limitations Originated by H.L.Gantt in 1918 Do not clearly indicate details regarding the progress of activities. Do not give a clear indication of interrelation ship between the separate activities

8 CPM/PERT These deficiencies can be eliminated to a large extent by showing the interdependence of various activities by means of connecting arrows called network technique. Overtime CPM and PERT became one technique ADVANTAGES: Precedence relationships large projects more efficient

9 The Project Network 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. Nodes A node is represented by a circle - Indicate EVENT, a point in time where one or more activities start and/or finish.

10 Activity Slack Each event has two important times associated with it: - Earliest time, Te, which is a calendar time when a event can occur when all the predecessor events completed at the earliest possible times - Latest time, TL, which is the latest time the event can occur with out delaying the subsequent events and completion of project. Difference between the latest time and the earliest time of an event is the slack time for that event Positive slack: Slack is the amount of time an event can be delayed without delaying the project completion

11 Critical Path Is that the sequence of activities and events where there is no slack i.e.. Zero slack Longest path through a network Minimum project completion time

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

13 Questions Answered by CPM & PERT Completion date? On Schedule? Within Budget? Critical Activities? How can the project be finished early at the least cost?

14 CPM calculation 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

15 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

16 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

17 CPM analysis Draw the CPM network Analyze the paths through the network Determine the float for each activity Compute the activity s 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

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

19 CPM Example ES and EF Times a, f, 15 g, 17 h, 9 i, 6 b, d, 13 j, 12 c, e, 9

20 CPM Example ES and EF Times a, f, g, 17 h, i, 6 b, c, d, e, j, 12

21 CPM Example ES and EF Time a, b, 8 f, g, 17 h, i, d, 13 j, 12 c, e, Project s EF = 33

22 CPM Example LS and LF Times f, h, 9 a, b, c, g, d, e, i, j,

23 CPM Example LS and LF Times a, b, c, f, g, d, e, h, i, j,

24 CPM Example Float a, b, c, f, h, g, i, d, 13 j, e,

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

26 PERT PERT is based on the assumption that an activity s duration follows a probability distribution instead of being a single value Three time estimates are required to compute the parameters of an activity s 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 activity s duration optimistic time (t o ) - the time the activity would take if things did go well t Mean (expected time): t e = p + 4 t m + t o 6 Variance: V t = 2 = t p - t o 6 2

27 PERT analysis 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.

28 Limitations to CPM/PERT Clearly defined, independent and stable activities Specified precedence relationships Over emphasis on critical paths

29 Thank you for your attention

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