Project Development Scheduling and Probability of Completion

Project DevelopmentScheduling and Probability of Completion

Learning Objectives

To define project Terminology To illustrate AOA and AON

diagrams To calculate Project Duration,

Critical Path, and slack To compute and interpret

probability of completing a project for a specific time

Project Networks

A flow chart that graphically depicts the sequence, interdependencies, and start and finish times of the project job plan of activities that is the critical path through the network.

Provides the basis for scheduling labor and equipment. Enhances communication among project participants. Provides an estimate of the project’s duration. Provides a basis for budgeting cash flow. Identifies activities that are critical. Highlights activities that are “critical” and can not be delayed. Help managers get and stay on plan.

Terminology

Activity (task): an element of the project that requires time.

Merge Activity: an activity that has two or more preceding activities on which it depends.

Parallel (Concurrent) Activities: Activities that can occur independently and, if desired, not at the same time.

A

C

DB

Terminology continued

Path: a sequence of connected, dependent activities.

Critical path: the longest path through the activity network that allows for the completion of all project-related activities;

C

A B D


Slack (or Float)

The amount of time an activity can be delayed after the start of a longer parallel activity or activities.

Total slack

The amount of time an activity can be delayed without delaying the entire project.


Event: a point in time when an activity is started or completed. It does not consume time.

Burst Activity: an activity that has more than one activity immediately following it (more than one dependency arrow flowing from it).

Two Approaches

Activity-on-Node (AON)

Uses a node to depict an activity.

Activity-on-Arrow (AOA)

Uses an arrow to depict an activity.

B

D

A C

CPM

Critical Path Method was developed by Dupont. It is a deterministic model where time estimates are accurate and do not vary. A project is made up of a sequence of activities or tasks that form a network representing a project

The path taking the longest time through this network of activities is called the "critical path". The critical path provides a wide range of scheduling information useful in managing a project. Critical Path Method (CPM) helps to identify the critical path(s) in the project networks. A network diagram is a graphic representation of the project and consists of directed arrows and nodes.

To create a workable network diagram a project must have:

well-defined jobs or tasks whose completion marks the end of the project;

independent jobs or tasks; and tasks that follow a given sequence.

Basic Rules to Follow in Developing Project Networks

1. Networks typically flow from left to right.

2. An activity cannot begin until all preceding connected activities are complete.

3. Arrows indicate precedence and flow and can cross over each other.

4. Each activity must have a unique identify number that is greater than any of its predecessor activities. (AOA)

5. Looping is not allowed.

6. Conditional statements are not allowed.

Illogical Loop

6–10FIGURE 6.10

Activity RelationshipsActivity RelationshipsActivity RelationshipActivity Relationship

AOA AON

Activity RelationshipsActivity RelationshipsS precedes T, which precedes U.S precedes T, which precedes U.

AOA AON

1 2S

3T

4U

S T U

Activity RelationshipsActivity RelationshipsS and T must be completed before U can be started.S and T must be completed before U can be started.

AOA AON

S

T

U

1

2

3T

S

4U

Activity RelationshipsActivity RelationshipsT and U cannot begin until S has been completed.T and U cannot begin until S has been completed.

AOA AON

T

U

S

3

4

1

T

U2S

Activity RelationshipsActivity RelationshipsU and V cannot begin until both S and T have been U and V cannot begin until both S and T have been completed. completed.

AOA AON

1

2

4

5

U

V

S

T 3

S

T

U

V

Activity RelationshipsActivity RelationshipsU cannot begin until both S and T have been U cannot begin until both S and T have been completed; V cannot begin until T has been completed; V cannot begin until T has been completed.completed.

AOA AON

S

T

U

V

1 3

DummyDummy

5

2 4 6

S U

T V

Activity RelationshipsActivity RelationshipsT and U cannot begin until S has been completed; V T and U cannot begin until S has been completed; V cannot begin until both T and U have been cannot begin until both T and U have been completed.completed.

AOA AON

1 2 4

3

S T5

V

UDummyDummy

S T V

U

St. Adolf’s HospitalSt. Adolf’s Hospital

ImmediateImmediateActivityActivity DescriptionDescription Predecessor(s)Predecessor(s) ResponsibilityResponsibility

AASelect administrative and medical staff.Select administrative and medical staff.BBSelect site and do site survey.Select site and do site survey.CCSelect equipment.Select equipment.DDPrepare final construction plans and layout.Prepare final construction plans and layout.EEBring utilities to the site.Bring utilities to the site.FFInterview applicants and fill positions inInterview applicants and fill positions in

nursing, support staff, maintenance, nursing, support staff, maintenance, and security.and security.

GGPurchase and take delivery of equipment.Purchase and take delivery of equipment.HHConstruct the hospital.Construct the hospital.IIDevelop an information system.Develop an information system.JJInstall the equipment.Install the equipment.KKTrain nurses and support staff.Train nurses and support staff.



AASelect administrative and medical staff.Select administrative and medical staff. ——JohnsonJohnsonBBSelect site and do site survey.Select site and do site survey. ——TaylorTaylorCCSelect equipment.Select equipment. AAAdamsAdamsDDPrepare final construction plans and layout.Prepare final construction plans and layout. BBTaylorTaylorEEBring utilities to the site.Bring utilities to the site. BBBurtonBurtonFFInterview applicants and fill positions inInterview applicants and fill positions in AAJohnsonJohnson


GGPurchase and take delivery of equipment.Purchase and take delivery of equipment. CCAdamsAdamsHHConstruct the hospital.Construct the hospital. DDTaylorTaylorIIDevelop an information system.Develop an information system. AASimmonsSimmonsJJInstall the equipment.Install the equipment. E,G,HE,G,HAdamsAdamsKKTrain nurses and support staff.Train nurses and support staff. F,I,JF,I,JJohnsonJohnson






Example 8.1Example 8.1

























































































































Network Computation Process

Forward Pass—Earliest Times How soon can the activity start? (early start—ES) How soon can the activity finish? (early finish—EF) How soon can the project finish? (expected time—ET)

Backward Pass—Latest Times How late can the activity start? (late start—LS) How late can the activity finish? (late finish—LF) Which activities represent the critical path? How long can activity be delayed? (slack or float—

SL)

6–41

Forward Pass Computation Add activity times along each path in the network (ES + Duration

= EF).

Carry the early finish (EF) to the next activity where it becomes its early start (ES) unless…

The next succeeding activity is a merge activity, in which case the largest EF of all preceding activities is selected.

6–42


Forward Forward Pass:Pass:Earliest Earliest StartStart&&Earliest Earliest FinishFinish

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

I

15

F

10

FinishStart

Backward Pass Computation

Subtract activity times along each path in the network (LF - Duration = LS).

Carry the late start (LS) to the next activity where it becomes its late finish (LF) unless

The next succeeding activity is a burst activity, in which case the smallest LF of all preceding activities is selected.

6–44


A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

BackwarBackward Pass:d Pass:Latest Latest StartStartandandLatest Latest Finish Finish TimesTimes

FinishStart

Determining Free Slack (or Float)

Free Slack (or Float) Is the amount of time an activity can be

delayed after the start of a longer parallel activity or activities.

Is how long an activity can exceed its early finish date without affecting early start dates of any successor(s).

Allows flexibility in scheduling scarce resources.

Sensitivity The likelihood the original critical path(s) will

change once the project is initiated. The critical path is the network path(s) that

has (have) the least slack in common.

6–46

Special

Laddering

Activities are broken into segments so the following activity can begin sooner and not delay the work.

Lags

The minimum amount of time a dependent activity must be delayed to begin or end.

Hammock

Probability of completion

Probability of Completing the Project

The equation below is used to compute the “Z” value found in statistical tables (Z = number of standard deviations from the mean), which, in turn, tells the probability of completing the project in the time specified.









Optimistic Likely Pessimistic Expected VarianceActivity (a) (m) (b) Time (te ) (2 )

Time Estimates (wk) Activity Statistics

A 11 12 13B 7 8 15C 5 10 15D 8 9 16E 14 25 30F 6 9 18G 25 36 41H 35 40 45I 10 13 28J 1 2 15K 5 6 7


2 = (variances of activities) z = Ts – TE

2

2 =

z =

Probabilities

Critical Path =

T = TE =

Z Values and Probabilities

7–53

Z Ta

ble


Any questions?

Documents

Project Development Scheduling and Probability of Completion