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# Pert,cpm, resource allocation and gert

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### Pert,cpm, resource allocation and gert

1. 1. Symbiosis Institute of Management Studies (SIMS) Project Management PERT,CPM, Resource Allocation and GERT Manuja Goenka, E-12 Raj Jyoti Das-E-13 August 2013
2. 2. Tools for Scheduling • Two commonly used network methods for planning and scheduling are: 1. Program Evaluation and Review Techniques (PERT) 2. Critical path Method (CPM) *Both PERT & CPM are termed critical path methods
3. 3. History of PERT • Project Evaluation and Review Technique (PERT) – U S Navy (1958) for the POLARIS missile program – Multiple task time estimates (probabilistic nature)
4. 4. 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 (a) - the time the activity would take if things did not go well – most likely time (m ) - the consensus best estimate of the activity’s duration – optimistic time (b) - the time the activity would take if things did go well a + 4m + b Mean (expected time):te = Variance: V = 6 b- a 6 2
5. 5. Three Time Estimates of PERT PERT uses three time estimates to address uncertainty of project duration- •Optimistic •Most Likely •Pessimistic
6. 6. Mean or expected Time It is the time where there is 50-50 chances that the activity will be completed earlier or later than it. For this case :
7. 7. Variance Variance is measure of variability in the activity completion period. The larger V, the less reliable te
8. 8. The Expected Duration Of The Project The expected duration of the project (Te) is the sum of the expected activity times along the critical path Te = ∑ te Where te are expected times of the activities on the critical path
9. 9. The Variation In The Project Duration The variation in the project duration distribution is computed as the sum of the variances of the activity durations along the critical path: Vp = ∑ V Where V is the variance of critical path
10. 10. Near Critical Path Path (events) Te = ∑ te Vp = ∑ V 1-2-6-8 28** 6.34 1-7-8 20 17.00 1-2-5-7-8 Te=29* Vp=6.00 1-4-5-7-8 18 3.89 1-3-4-5-78 27** 12.00
11. 11. Probability of Finishing a Project Let us assume, Expected completion duration of a project = 29 weeks Variance of the project duration = 6 Then what will be the probability of finishing the project by 27 weeks can be calculated by the formula: Probability Therefore, Z=(27-29)/2.449 =-0.82 Prob. Of finishing the project by 27 weeks is app. 21% Z 0.207 27 darla/smbs/vit 29 Time 11
12. 12. History of Critical Path Method (CPM) • E I Du Pont de Nemours & Co. (1957) for construction of new chemical plant and maintenance shut-down • CPM is a “Deterministic” approach • CPM includes mathematical procedure for estimating the trade off between project duration and project cost • CPM emphasis on applying additional resources to particular key activities
13. 13. Time-Cost Relationship Normal Time, Tn: It is the time taken by an activity under normal work conditions Normal Cost, Cn: The cost incurred in doing an activity in normal time.
14. 14. Crashing An activity is said to be crashed when maximum effort is applied to finish that activity in the shortest possible time.
15. 15. Cost Slope • The cost slope shows by how much the cost of job would change if activities were speed up or slowed down. In this case, Cost Slope= (18-9)/(5-8) = \$3 K/week
16. 16. 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
17. 17. CPM calculation 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) 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
18. 18. Project Crashing • Crashing – reducing project time by expending additional resources • Crash time – an amount of time an activity is reduced • Crash cost – cost of reducing activity time • Goal – reduce project duration at minimum cost
19. 19. Time-Cost Relationship  Crashing costs increase as project duration decreases  Indirect costs increase as project duration increases  Reduce project length as long as crashing costs are less than indirect costs Time-Cost Tradeoff Total project cost Indirect cost Direct cost time
20. 20. Crashing Example 9 9 C 5 A 0 F 5 9 0 17 14 D 8 B 22 G E 8 22 7 5 17 Activi ty 17 Normal (Wks) Crush (Wks) 10 Tn Cn A 8 Tc Cost Slope (K\$) Cc 9 10 6 16 2 B 8 9 5 18 3 C 5 7 4 8 D 8 9 6 19 5 E 7 7 3 15 2 F 5 5 5 5 G 5 8 2 23 5 1 -
21. 21. 9 9 C 5 A 0 9 0 17 14 F 5 D 8 22 G B E 8 7 8 5 17 22 17 Critical Path A-D-G=22wks 10
22. 22. Types of Project Constraints • Technical or Logic Constraints – Constraints related to the networked sequence in which project activities must occur. • Physical Constraints – Activities that cannot occur in parallel or are affected by contractual or environmental conditions. • Resource Constraints – The absence, shortage, or unique interrelationship and interaction characteristics of resources that require a particular sequencing of project activities.
23. 23. The Resource Problem • Resources and Priorities – Project network times are not a schedule until resources have been assigned. • The implicit assumption is that resources will be available in the required amounts when needed. • Adding new projects requires making realistic judgments of resource availability and project durations. • Resource-Constrained Scheduling – Resource leveling (or smoothing) involves attempting to even out demands on resources by using slack (delaying noncritical activities) to manage resource utilization.
24. 24. Kinds of Resource Constraints • People • Materials • Equipment • Working Capital
25. 25. Classification of A Scheduling Problem • Time Constrained Project – A project that must be completed by an imposed date. • Time is fixed, resources are flexible: additional resources are required to ensure project meets schedule. • Resource Constrained Project – A project in which the level of resources available cannot be exceeded. • Resources are fixed, time is flexible: inadequate resources will delay the project.
26. 26. Example : • Without resource constraints relatively easy • With resource constraints very complex: when jobs share resources with limited availability, these jobs cannot be processed simultaneously Jobs p(j) R(1,j) R(2,j) 1 8 2 3 2 4 1 0 3 6 3 4 4 4 1 0 5 4 2 3 Resource Available R1 4 R2 8 1 4 2 5 3 27
27. 27. S 'j  earliest possible starting time of job j C 'j  earliest possible completion time of job j C ''  latest possible completion time of job j j slack j  C ''  p j  S 'j j 28
28. 28. Resource constraints • Suppose jobs require a resource: Job p(j) Predecessors S' C'' R(1,j) 1 2 0 3 3 2 3 0 3 1 3 1 0 6 2 4 4 1,2 3 7 2 5 2 2,3 3 8 3 6 1 4 7 8 3 6 5 3 4 3 2 5 2 1 resource requirements 1 6 4 1 2 3 4 5 6 7 8 29
29. 29. Resource constraints (cont.) • Suppose R 1  4 : 6 5 4 3 2 2 1 1 3 1 2 5 4 3 4 5 6 7 6 8 9 10 Cmax increases by 2 30
30. 30. Resource-Constrained Project Scheduling Problem (RCPSP) • • • • • • n jobs j=1,…,n N resources i=1,…,N Rk:availability of resource k pj: duration of job j Rkj:requirement of resource k for job j Pj: (immediate) predecessors of job j 31
31. 31. RCPSP • Goal: minimize makespan: Cmax  max C j • Restrictions: ' j – no job may start before T=0 – precedence relations – finite resource capacity 32
32. 32. RCPSP example Job p(j) P(j) S' C'' R(1,j) R(2,j) 1 2 - 0 3 3 2 2 3 - 0 3 1 1 3 1 - 0 6 2 1 4 4 1,2 3 7 2 1 5 2 2,3 3 8 3 2 6 1 4 7 8 3 1 4 R1  4 2 2 1 0 2 2 R2  2 4 3 2 1 0 6 5 3 4 2 6 8 4 4 10 6 6 8 5 10 12 33
33. 33. Loading And Leveling • Loading- amount of a resource necessary to conduct a project – Depends on the requirements of individual activities. – Changes throughout a project • Resource Leveling- process of scheduling activities so that the amount of a certain required resource is balanced throughout the resource.
34. 34. Multiproject Resource Schedules • Multiproject Scheduling Problems – Overall project slippage • Delay on one project create delays for other projects – Inefficient resource application • The peaks and valleys of resource demands create scheduling problems and delays for projects. – Resource bottlenecks • Shortages of critical resources required for multiple projects cause delays and schedule extensions.
35. 35. Multiproject Resource Schedules • Managing Multiproject Scheduling – Create project offices or departments to oversee the scheduling of resources across projects. – Use a project priority queuing system: first come, first served for resources. – Centralize project management: treat all projects as a part of a “megaproject.” – Outsource projects to reduce the number of projects handled internally.
36. 36. Limitations of PERT/CPM • All immediate predecessor activities must be completed before a given activity can be started. • No activity can be repeated and no “looping back” • Duration time for an activity is restricted to Beta Distribution PERT and a single estimate in CPM. • Critical Path is always considered the longest. • There is only one terminal event and the only way to reach it is by completing all activities in the project
37. 37. GERT • A network analysis technique used in project management. • It allows probabilistic treatment of both network logic and activity duration estimated. • The technique was first described in 1966 by Dr. Alan B. Pritsker of Purdue University and WW Happ. • Compared to other techniques, GERT is an only rarely used scheduling technique.
38. 38. Contd.. • Utilizes probabilistic and branching nodes • It represents the node will be reached if any m of its p immediate predecessors are completed. m n p
39. 39. Contd.. • It represents a probabilistic output where any of q outputs are possible • Each branch has an assigned probability • When no probability is given, the probability is assumed to be one for each branch. 1 2 q
40. 40. Example
41. 41. Thank YOu