Pert,cpm, resource allocation and gert
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Pert,cpm, resource allocation and gert

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Pert,cpm, resource allocation and gert Pert,cpm, resource allocation and gert Presentation Transcript

  • 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
  • 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
  • History of PERT • Project Evaluation and Review Technique (PERT) – U S Navy (1958) for the POLARIS missile program – Multiple task time estimates (probabilistic nature)
  • 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
  • Three Time Estimates of PERT PERT uses three time estimates to address uncertainty of project duration- •Optimistic •Most Likely •Pessimistic
  • 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 :
  • Variance Variance is measure of variability in the activity completion period. The larger V, the less reliable te
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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.
  • Crashing An activity is said to be crashed when maximum effort is applied to finish that activity in the shortest possible time.
  • 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) = $3 K/week
  • CPM calculation • Path – A connected sequence of activities leading from the starting event to the ending event • Critical Path – The longest path (time); determines the project duration • Critical Activities – All of the activities that make up the critical path
  • CPM calculation Forward Pass • Earliest Start Time (ES) – earliest time an activity can start – ES = maximum EF of immediate predecessors • Earliest finish time (EF) – earliest time an activity can finish – earliest start time plus activity time (EF= ES + t) Backward Pass Latest Start Time (LS) Latest time an activity can start without delaying critical path time LS= LF - t Latest finish time (LF) latest time an activity can be completed without delaying critical path time LS = minimum LS of immediate predecessors
  • Project Crashing • Crashing – reducing project time by expending additional resources • Crash time – an amount of time an activity is reduced • Crash cost – cost of reducing activity time • Goal – reduce project duration at minimum cost
  • Time-Cost Relationship  Crashing costs increase as project duration decreases  Indirect costs increase as project duration increases  Reduce project length as long as crashing costs are less than indirect costs Time-Cost Tradeoff Total project cost Indirect cost Direct cost time
  • Crashing Example 9 9 C 5 A 0 F 5 9 0 17 14 D 8 B 22 G E 8 22 7 5 17 Activi ty 17 Normal (Wks) Crush (Wks) 10 Tn Cn A 8 Tc Cost Slope (K$) 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 -
  • 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
  • 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.
  • 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.
  • Kinds of Resource Constraints • People • Materials • Equipment • Working Capital
  • 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.
  • 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
  • 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
  • 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
  • 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
  • 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
  • RCPSP • Goal: minimize makespan: Cmax  max C j • Restrictions: ' j – no job may start before T=0 – precedence relations – finite resource capacity 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
  • 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.
  • 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.
  • 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.
  • 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
  • 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.
  • 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
  • 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
  • Example
  • Thank YOu