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**Project and Production Management**

Module 2 Project Planning Prof Arun Kanda & Prof S.G. Deshmukh, Department of Mechanical Engineering, Indian Institute of Technology, Delhi

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**Module 2 Project Planning**

1. Developing the Project Network Work Break Down Structure AOA & AON networks Basic Scheduling for AOA networks Critical Path Floats Basic Scheduling for AON networks Critical path 4. Scheduling Probabilistic Activities PERT assumptions Probability Statements 5. Illustrative Examples 6. Self Evaluation Quiz 7. Problems for Practice 8. Further exploration

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**FORMATION OF PROJECT TEAM**

Appointment of Project Manager Selection of Project team members Briefing meetings amongst team members Broad consensus about scope of work and time frame Development of work breakdown structure and allocation of responsibilities

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**WORK BREAKDOWN STRUCTURE**

A breakdown of the total project task into components to establish How work will be done? How people will be organized? How resources would be allocated? How progress would be monitored?

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**ALTERNATIVE WAYS TO BREAKDOWN WORK**

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**WORK BREAKDOWN STRUCTURE**

Project System I System II System N Subsystem Subsystem Subsystem Task Task Subtask Subtask Subtask Work package Work package

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**WORK BREAKDOWN STRUCTURE**

Hardware orientation (Identification of basic work packages) Agency orientation (Based on assignment of responsibility to different agencies) Function oriented (e.g Design, Procurement, Construction and Commissioning)

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**WORK BREAKDOWN STRUCTURE (Continued)**

Generally a WBS includes 6-7 levels. More or less may be needed for a situation. All paths on a WBS do not go down to the same level. WBS does not show sequencing of work. A WBS should be developed before scheduling and resource allocation are done.

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**WORK BREAKDOWN STRUCTURE (Continued)**

A WBS should be developed by individuals knowledgeable about the work. This means that levels will be developed by various groups and the the separate parts combined. Break down a project only to a level sufficient to produce an estimate of the required accuracy.

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**ILLUSTRATIVE WORK BREAKDOWN STRUCTURE**

Missile Guidance Rocket Launching Warhead control sys platform Ballistic Propulsion Re entry shell engine vehicle I Stage Solid fuel II Stage

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**MEANS OF PROJECT REPESENTATION**

Project name and description. List of jobs that constitute the project. Gantt or bar chart showing when activities take place. Project network showing activities, their dependencies and their relation to the whole. (A-O-A and A-O-N representations)

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**WHY USE PROJECT NETWORKS ?**

A convenient way to show activities and precedence in relation to the whole project. Basis of project planning: Responsibility allocation Definition of subcontracting units Role of different players Basic scheduling and establishment of work time tables

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**WHY USE PROJECT NETWORKS -II ?**

Critical path determination and selective management control Deterministic vs probabilistic activity times Resource planning for projects Project crashing with time cost tradeoffs Resource aggregation Resource levelling Limited resource allocation

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**WHY USE PROJECT NETWORKS - III ?**

Project implementation: Time table for implementation Monitoring and reporting progress Updation of schedules and resources Coordination of work with different agencies The project network is thus a common vehicle for planning, communicating and implementing the project right from inception.

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**EXAMPLE 1 Organizing a one day Seminar**

Generate the list of jobs to be done: 1) Decide date ,budget, venue for seminar. 2) Identify speakers, participants. 3) Contact and finalize speakers. 4) Print seminar brochure. 5) Mail brochures to tentative participants 6) Estimate number of participants.

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**Organizing a one day seminar**

7) Decide menu for lunch, tea & coffee 8) Arrange for catering 9) Arrange projection facilities at venue. 10) Receive guests at registration. 11) Conduct seminar as per brochure 12) See off guests.

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**EXAMPLE 1 Organizing a one day Seminar**

Activity Predecessors 1) Decide date ,budget, venue for seminar. -- 2) Identify speakers, participants 3) Contact and finalize speakers A2 4) Print seminar brochure A1, A3 5) Mail brochures to tentative participants A4 6) Estimate number of participants A5

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**Organizing a one day seminar**

Activity Predecessors 7) Decide menu for lunch, tea & coffee A6 8) Arrange for catering A1,A7 9) Arrange projection facilities at venue. A6 10) Receive guests at registration A8, A9 11) Conduct seminar as per brochure A8, A9, A10 12) See off guests A11

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**DRAWING THE PROJECT NETWORK (A-O-A)**

A A A A A A A A A12

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**DEVELOPING THE PROJECT NETWORK (A-O-N)**

A A A A A A8 A A A12 A A A10

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**EXAMPLE 2 Job Predecessors a -- b -- c -- d a,b e b,c a d b e c 4 3 2**

1 5 e c 4

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**EXAMPLE 3 Job Predecessors a -- b -- c -- d a,b e a,c f a,b,c 3 d b f**

c e 4

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**EXAMPLE 4 Job Predecessors a -- b a c a d a e b, c, d 3 b a c e**

d 4 DUMMIES FOR UNIQUENESS OF ACTIVITY REPRESENTATION

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EXAMPLE 5 S T DUMMIES FOR CREATION OF A SINGLE SOURCE AND SINK

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**THE ROLE OF DUMMIES IN PROJECT NETWORKS**

Role of Dummy I II III Network type A-O-A yes yes yes A-O-N no no yes I Correct representation of precedence logic II Uniqueness of activity representation III Creation of single source/ sink

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**EXAMPLE 6 Inconsistent Network**

A closed loop in a project network is a logical inconsistency.

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**EXAMPLE 7 REDUNDANCY (A-O-N)**

Job Predecessors a b a c d a, b, c e d f d b e d a *********** c f Redundancy a in the predecessor set for activity d could be removed thereby deleting arc a-d above

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**PREREQUISITES FOR A VALID PROJECT NETWORK**

NECESSARY REQUIREMENT The project network must not have any cycles or loops, since these represent logical inconsistencies in representation. DESIRABLE FEATURES The project network should have the minimum number of dummies and no redundancies since these unnecessarily clutter the network.

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**Basic Scheduling with A-O-A Networks**

PROJECT MANAGEMENT Basic Scheduling with A-O-A Networks

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**ALTERNATIVE PROJECT REPRESENTATIONS**

Activity on Arc (A-O-A) Arrow diagrams Event oriented networks Activity on Node (A-O-N) Precedence networks Activity oriented networks activity, a i j a

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**ACTIVITY DURATIONS Deterministic (as in CPM)**

when previous experience yields fairly accurate estimates of activity duration, eg construction activity, market surveys. Probabilistic (as in PERT) when there is uncertainty in times, as for instance in R&D activities, new activities being carried out for the first time.

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**TIME ESTIMATES Deterministic times Probabilistic times**

A single time estimate is used for each activity. This is taken from experts who have prior knowledge and experience of the activity. Probabilistic times Three time estimates (optimistic, most likely and pessimistic) are commonly used for each activity based on the consensus of the group.

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**EXAMPLE 1 Job Predecessors Duration (days) a -- 2 b -- 3 c a 1**

d a, b e d f d g c, e h c, e i f, g, h

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**PROJECT NETWORK FOR EXAMPLE 1 (A-O-A)**

h 4 1 a g 2 e 5 6 i b f 3 d 3 4 8

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**CRITICAL PATH The longest path in the network**

Lower bound on the project duration Selective control for management of project Can be determined by Enumeration of all paths in the network Event based computations (A-O-A networks) Activity based computations (A-O-N networks)

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**NODE NUMBERING FOR EXAMPLE 1 (A-O-A)**

c h 4 1 a g 2 e 5 6 i b f 3 d 3 4 8

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**PATH ENUMERATION Level 0 Level 1 Level 2 Level 3 Level 4 Level 5**

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**FORWARD PASS Initialization: Ej= Max (Ei+ tij) for all i before node j**

E1 = 0 (or the project start time S) (This applies to all source nodes) Ej= Max (Ei+ tij) for all i before node j ( Set B(j)) Ej j Ei tij B(j) i

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**FORWARD PASS EXAMPLE 1 (A-O-A)**

c h 2 6 5 4 1 a g 2 e 8 5 6 i 1 b f 3 d 3 7 3 4 4 8

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**BACKWARD PASS Initialization:**

Ln (or the latest occurrence of all ending nodes) = Project duration, T as determined in the forward pass Li = Min (Lj-tij) over all successor nodes j of the node i being investigated, (set A(i)) A(i) tij j i Lj Li

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**BACKWARD PASS EXAMPLE 1 (A-O-A)**

2 16 12 c h 2 6 5 4 1 21 a g 2 e 8 5 6 i 1 3 18 b 7 f 3 d 3 7 3 4 4 8

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**ACTIVITY SCHEDULE FROM EVENT TIMES**

Ej Ei tij j i Lj Li Early start of activity ij = ES(ij) = Ei Early finish of activity ij= EFij = ES(ij)+ tij FORWARD PASS Late finish of activity ij = LF(ij) = Lj Late start of activity ij = LS(ij) = LF(ij) -tij BACKWARD PASS

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**EARLY & LATE SCHEDULE FOR EXAMPLE 1**

Job duration ES EF LS LF TF a b c d e f g h i

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**GANTT CHART SHOWING ACTIVITY SCHEDULE**

b ^^^^^^ c d ^^^^^^^^^ e ^^^^^^^^^^^^^ f g ^^^^^^^^^^^^^^^^ h i ^^^^^^^^

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**CRITICAL PATH EXAMPLE 1 (A-O-A)**

2 16 12 c h 2 6 5 4 1 21 a 12 3 18 g 2 e 8 5 6 i 1 3 18 b 7 f 3 21 d 3 7 3 4 4 8 7 18 3

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**EVENT SLACKS Ei Ej tij i j Li Lj Ei Li Ej Lj Slack on node i = Li - Ei**

Slack on node j = Lj - Ej

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**ACTIVITY FLOATS Ei Ej tij Li Lj Ei Li Ej Lj**

Total float = F1(ij) = Lj-Ei -tij Safety float = F2(ij) = Lj- Li-tij Free float = F3(ij) = Ej -Ei -tij Independent float = F4(ij) = Max (0, Ej -Li- tij)

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**FLOAT COMPUTATIONS Ei Ej tij Li Lj**

Total float = LS - ES = LF-EF of activity Safety float = Total float - Slack on preceding node Free float = Total float - Slack on succeeding node Independent float = Max (0, Total float - Slack on preceding and succeeding nodes)

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**FLOATS FOR EXAMPLE 1 Job Total Safety Free Independent a 1 1 0 0**

c d e f g h i

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**INTERPRETATION OF FLOATS**

An activity , in general, has both predecessors and successors. Each of the four kinds of float depends on how these accommodate the activity. Predecessors Successors activity

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**FLOAT INTERPRETATION SUCCESSORS Early Late Early Free Total**

PREDECESSORS Independent Safety Late

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**ANOMALIES ACTIVITY h FLOATS Total Safety Free Ind. 2 2 2 2 2 0 2 0**

18 12 h 5 7 4 12 18 h 5 7 4 12 18 h 5 7 4 12 18 h 5 7 4 18 12

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**Basic Scheduling with A-O-N Networks**

PROJECT MANAGEMENT Basic Scheduling with A-O-N Networks

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**ALTERNATIVE PROJECT REPRESENTATIONS**

Activity on Arc (A-O-A) Arrow diagrams Event oriented networks Activity on Node (A-O-N) Precedence networks Activity oriented networks activity, a i j a

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**SCHEDULING WITH A-O-N NETWORKS**

Basic scheduling computations can be done on both A-O-A or A-O-N networks. A-O-N networks are simpler to draw, though they lack intuitive work flow interpretation of A-O-A networks. There are no float anomalies in A-O-N networks. A-O-N networks are becoming more popular, in computer packages, Lead easily to PDM with expanded precedence relations FS , FF, SS, SF.

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**EXAMPLE Job Predecessors Duration (days) a -- 2 b -- 3 c a 1 d a, b 4**

f d g c, e h c, e i f, g, h

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**PROJECT NETWORK EXAMPLE (A-O-N)**

2 1 a c 6 g 4 4 5 i 3 d h e 3 b 8 f

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**FORWARD PASS (A-O-N Networks)**

Initialization: Early start(ES) for all beginning activities = 0 (or the start date, S for the project) Early finish (EF) for activity = ES+ duration ES(j)= Max (EF all predecessors) ES/EF ES/ EF ES/EF i1 j ES/EF i2 ip

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**FORWARD PASS FOR EXAMPLE**

2 1 a c 6 g 4 4 5 i 3 d h e 3 b 8 f

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**BACKWARD PASS (A-O-N Networks)**

Initialization Project duration,T = Max (EF of ending jobs). LF(all ending jobs) =T LS = LF- Duration LF = Min (LS of successors) LS/LF LS/LF LS/LF LS/LF

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**BACKWARD PASS FOR EXAMPLE**

2 / 3 0 / 2 12 / 18 2 1 a c 6 g 3 / 7 18 / 21 7 / 12 12 / 16 4 4 5 i 3 0 / 3 d h e 3 b 7 / 15 8 f

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**EARLY & LATE SCHEDULE FOR EXAMPLE**

Job duration ES EF LS LF TF a b c d e f g h i

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**CRITICAL PATH FOR EXAMPLE**

2 / 3 0 / 2 12 / 18 2 1 a c 6 g 1 / 3 12 /18 11 / 12 3 / 7 18 / 21 7 / 12 12 / 16 4 4 5 i 3 0 / 3 d h e 3 b 3 / 7 7 / 12 18 /21 14 / 18 7 / 15 0 / 3 8 f 10 / 18

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**CRITICAL PATH FOR EXAMPLE**

2 1 a c 6 g 4 4 5 i 3 d h e 3 b 8 f

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**GANTT CHART SHOWING ACTIVITY SCHEDULE**

a *** ] b ^^^^^^ c ** ] d ^^^^^^^^^ e ^^^^^^^^^^^^^ f ****************** ] g ^^^^^^^^^^^^^^^ h ********** ] i ^^^^^^^^^

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**INTERPRETATION OF FLOATS**

An activity , in general, has both predecessors and successors. Each of the four kinds of float depends on how these accommodate the activity. Predecessors Successors activity

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**FLOAT INTERPRETATION SUCCESSORS Early Late Early Free Total**

PREDECESSORS Late Independent Safety

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**COMPUTATION OF FLOATS ES/EF i1 k1 LS/LF ES/EF ES/EF i2 k2 j LS/LF**

im kn LS/LF Slack on preceding node= Max (LF of predecessors) -ES Slack on succeeding node = LF- Min (ES of successors) (in the corresponding A-O-A representation)

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**FLOATS FOR EXAMPLE Job Total Safety Free Independent a 1 1 0 0**

c d e f g h i

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**FLOAT COMPUTATIONS FOR ACTIVITY a**

Total Float = LS - ES = LF - EF =1 Safety float = Total Float - [Max (LF of predecessors)-ES] = (0 - 0) = 1 Free float = Total Float -[LF -Min(ES of successors)] = (3-2) = 0 Independent float = Total float - both the latter terms = 1 - (0+1) = 0 0 / 2 2 / 3 c a 3 / 7 1 / 3 d

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**FLOAT COMPUTATIONS FOR ACTIVITY c**

Total Float = LS - ES = LF - EF =9 Safety float = Total Float - [Max (LF of predecessors)-ES] = (3 -2) = 8 Free float = Total Float -[LF -Min(ES of successors)] = (12-12) = 9 Independent float = Total float - both the latter terms = 9 - (1+0) = 8 12 / 18 2 / 3 c g a 11 / 12 1 / 3 12 / 16 h

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**FLOAT COMPUTATIONS FOR ACTIVITY f**

Total Float = LS - ES = LF - EF =3 Safety float = Total Float - [Max (LF of predecessors)-ES] = (7 -7) = 3 Free float = Total Float -[LF -Min(ES of successors)] = ( ) = 3 Independent float = Total float - both the latter terms = 3 - (0+0) = 3 18 / 21 7 / 15 d f i 10 / 18 3 / 7

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**FLOAT COMPUTATIONS FOR ACTIVITY h**

Total Float = LS - ES = LF - EF =2 Safety float = Total Float - [Max (LF of predecessors)-ES] = ( ) = 2 Free float = Total Float -[LF -Min(ES of successors)] = ( ) = 2 Independent float = Total float - both the latter terms = 2 - (0+0) = 2 c 18 / 21 12 / 16 11 / 12 e h i 14 / 18 7 / 12

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**PRECEDENCE DIAGRAMMMING METHODS**

Generalized precedence relations Start to Start (SS) Finish to Finish (FF) Start to Finish (SF) Finish to Start (FS) Permit partial or complete overlap of activities

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START TO START LAG (SS) v1 v2 u1 u2

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**FINISH TO FINISH LAG (FF)**

v1 v2 u1 u2

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**START TO FINISH LAG (SF)**

v1 v2 u1 u2

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**FINISH TO START LAG (FS)**

v u

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**PDM EXAMPLE COMPUTATIONS**

SF 4 SS 3 FS 4 B 8 D 6 FS 0 FF 5 FS 0 A 10 E 12 F 14 G 2 SS 3 SS 2 FF 5 C 20 FF 2 SS 10

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**Project Scheduling with Probabilistic Activity Times**

PROJECT MANAGEMENT Project Scheduling with Probabilistic Activity Times

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**UNCERTAIN ACTIVITY DURATIONS**

For each activity in the project three time estimates are obtained Optimistic time, a Most likely time, m Pessimistic time, b

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**PERT TIME ESTIMATES Mean of activity duration = (a + 4m + b) / 6**

Variance of activity duration = { (b - a) / 6}2 Standard deviation of activity duration = Sq. root of variance = (b - a ) / 6

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**BETA DISTRIBUTION f(t) = K(t-a)c (b - t)d , a <= t <=b**

a m b f(t) = K(t-a)c (b - t)d , a <= t <=b = 0, otherwise [ a,b are the location parameters c,d are the shape parameters ]

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WHY CHOOSE BETA ? The beta distribution is bounded on both sides with non-negative intercepts. It is a uni-modal distribution. Permits flexibility of shapes by suitable choice of location and shape parameters. Intuitive appeal. Easy approximations to mean and variance.

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**OTHER POSSIBLE DISTRIBUTIONS**

UNIFORM TRIANGULAR EXPONENTIAL NORMAL DISCRETE OTHERS ...

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**UNIFORM DISTRIBUTION 1/ (b-a) a b Mean = (a + b) / 2**

Variance = (b - a)2 / 12

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**TRIANGULAR DISTRIBUTION**

2/ (b-a) a m b Mean = (a + m + b) / 3 Variance = {(b -a)2 + (b - m)2 + (m -a)2}/36 = (a2 + m2 + b2 - am - ab - mb)/18

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**EXPONENTIAL DISTRIBUTION**

m f(t) = me -mt Mean = 1/m Variance = 1/m2

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NORMAL DISTRIBUTION N (mu, sigma 2) mu Mean = mu Variance = sigma 2

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**DISCRETE DISTRIBUTION**

p2 pn p1 p3 - - - t t t tn Mean = p1 t1 + p2 t pn tn Variance = p1 t12 + p2 t pn tn2 - (Mean) 2

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**BASIC PERT PROCEDURE - I**

Compute mean and variance of all jobs. Conduct forward and backward pass on the project network with expected times of all activities. Identify the Critical Path. Obtain variance of critical path by adding variance of activities.

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**BASIC PERT PROCEDURE - II**

Obtain the distribution of the Project Duration. Make probability statements about the project Chances of meeting the target date. Probability of exceeding a given ceiling date. Probability that the project duration is confined to an interval of time.

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**AN EXAMPLE Job Predecessors Time estimates Mean Variance a m b**

A B C A D A E A F B,C G D,F H D,F I E,H

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**SAMPLE NETWORK (A-O-A)**

2 5 A 8.33 I 4.33 D 7.66 1 H 4 6 6 C 8 B G 6.33 15.33 F 4 3 6

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**FORWARD & BACKWARD PASS**

E 2 5 A 8.33 I 4.33 D 7.66 1 H 4 6 6 C 8 B G 6.33 15.33 F 4 3 6

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CRITICAL PATH 4.33 20.33 E 2 5 A 8.33 I 24 4.33 31.66 4.33 D 7.66 1 H 4 6 6 C 8 B G 31.66 16.33 10.33 6.33 15.33 F 4 3 6 10.33 16.33

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**DISTRIBUTION OF THE PROJECT DURATION**

Project duration follows a Normal Distribution with Mean = Variance = 6 = (2.45)2

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**CONFIDENCE INTERVALS Chances that the project is completed within**

mean +/- 1 sigma 68% ( ) mean +/- 2 sigma 95% ( ) mean +/_ 3 sigma 99% ( )

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**PROBABILITY STATEMENTS - I**

Probability of meeting a Target Date, say 36 days Z (Standard normal deviate) = ( )/2.45 = 4.34/2.45 = 1.77 Area from normal tables =

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**PROBABILITY STATEMENTS - II**

Probability of exceeding a ceiling, say 28 days Z (Standard normal deviate) = ( )/2.45 = -3.66/2.45 = Area from normal tables =

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**PROBABILITY STATEMENTS - III**

Probability of duration lying in an interval, say 28 to 36 days Area from normal tables = =

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**STANDARD PERT ASSUMPTIONS**

1. The activities are independent 2 The critical path contains a large no. of activities so that we can invoke the Central Limit Theorem. 3 .All activities not on the critical path are ignored. 4. Activity times follow a Beta distribution. 5. The mean and variance of the activities are given by (a+4m+b)/6 and [(b-a)/6]2.

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