1 project scheduling faculty of applied engineering and urban planning civil engineering department...

11

Project Scheduling

Faculty of Applied Engineering and Urban Planning

Civil Engineering Department

Week ( 6 + 7 )

Lec. ( 11 + 12 + 13 + 14 )

2nd Semester 2008/2009

UP Copyrights 2008

Const

ruct

ion P

roje

ct

Managem

ent

Eng: Eyad Haddad

22

CH4: Project SchedulingCH4: Project Scheduling

Construction Project management functions:Construction Project management functions:

Scheduling = Planning + TimeScheduling = Planning + Time

SchedulingScheduling is the determination of the timing of the activities comprising

the project to enable managers to execute the project in a timely manner.

1. Planningتخطيط

2. Organizationتنظيم

3. Supervisionمراقبه

4. Controlتحكم

1. Timeالوقت

2. Costالتكلفة

3. Qualityالجودة

4. Performanceاالنجاز

Scheduling

33

CH4: Project SchedulingCH4: Project Scheduling

The project scheduling is used for:

1. Knowing the activities timing and the project completion time.

2. Having resources available on site in the correct time.

3. Making correction actions if schedule shows that the plan will result in

late completion.

4. Assessing the value of penalties on project late completion.

5. Determining the project cash flow.

6. Evaluating the effect of change orders on the project completion time.

7. Determining the value of project delay and the responsible parties.

44

4.2 The Critical Path Method (CPM)4.2 The Critical Path Method (CPM)

The critical path can be defined as

the longest possible path through the "network" of project activities.

(CPM)(CPM) is the most widely technique used for scheduling, it calculates the

minimum completion time for a project along with the possible start and

finish times for the project activities.

55


The critical path itself represents the set or sequence of activities

which will take the longest time to complete.

The duration of the critical path is the sum of the activities'

durations along the path.

Duration of the critical path represents the minimum timeminimum time required

to complete a project.

Any delays along the critical path would delay the project.

More than one critical path may be among all the project activities,

so completion of the entire project could be delayed by delaying

activities along any one of the critical paths.

66


For example,

a project consisting of two activities performed in parallel that each

requires three days would have each activity critical for a completion in

three days.

Critical path scheduling assumes that a project has been divided into

activities of fixed duration and well defined predecessor relationships.

A predecessor relationship implies that one activity must come

before another in the schedule

77

The CPM is a systematic scheduling method for a project network and involves

four main steps:

1. A forward path to determine activities early-start timesearly-start times;

2. A backward path to determine activities late-finish timeslate-finish times;

3. Float calculations ( Free & Total ) float; and

4. Identifying critical activities.

88

4.3.1 Activity-on-node networks calculations

The objective of arrow network analysis is to compute each event in the

network its early and late timings. These times are defined as

Early event time (ET)Early event time (ET) is the earliest time at which an event can occur,

considering the duration of preceding activities.

Late event time (LT)Late event time (LT) Is the latest time at which an event can occur if the

project is to be completed on schedule.

i jx

ETj LTjETi LTi

dx

11 . .Forward PathForward Path::

ETj = ETi + dxETj = ETi + dx

99

11 . .Forward PathForward Path::

1 3

5

7

9 11

0

ProjectStart=0

Ad=3

C4

E5

B3

D

6 d2

d13

Es+d=EF

6

3+3=6

0+3=3

9

6+0=63+4=79+0=9

14

9+5=14

9

3+6=9

1A

ProjectStart=0

1A

1010

22 . .Backward PathBackward Path LS = LF – dLS = LF – d

1 3

5

7

9 11

0 0

3-3=0

A3

C4

E5

B3

D

6 d2

d13 3

9-4=5

6 9

9-0=9

9-6=3

9 9

14-5=9LF-d=LS

14 14

9 9

9-0=9

9-3=6

1111

3. Float Calculations:

First, let's tabulate the information we have as shown in next Table

One important aspect is Total-Float (TF) calculations, which determine the

flexibility of an activity to be delayed.

Total Float (TF) = LF – EF

= LS – ES

.TFمالحظة : الواحد للنشاط يستخدم دوما

Free Float (FF) = ETj – ETi – d

or FF = smallest ES (of succeeding activities) – EF (of current activity)

.FFمالحظة : والالحق السابق للنشاطين يستخدم دوما

1212

3. Float Calculations:

Total Float (TF) = LF – EF

= LS – ES

.TFمالحظة : الواحد للنشاط يستخدم دوما


or FF = smallest ES (of succeeding activities) – EF (of current activity)

.FFمالحظة : والالحق السابق للنشاطين يستخدم دوما

i j

ES EF

A

LS LF

AOA

ES EF

ES EF

A

B

LS LF

LS LF

ES EF

A

LS LF

AON

TF

i j

ES EF

A

LS LF

AOA

i j

ES EF

B

LS LF

AOA

1313

Total Float (TF) = LF – EF = LS – ES


or FF = smallest ES (of succeeding activities) – EF (of current

activity)

ActivityDurationEarly Start

)ES(

Late Start

)LS(

Early Finish

)EF(

Late Finish

)LF(

Total Float

)TF(

CriticalActivity

AA3300003300YesYes

BB3333666933NoNo

CC4433557922NoNo

DD6633339900YesYes

EE559999141400YesYes

1414

4.3.2 Precedence Diagram Method (PDM):

Precedence Diagram Method (PDM) is the CPM scheduling method used for AON

networks and it follows the same four steps of the CPM for AOA method.

Forward PathForward Path

Forward path can proceed from one activity to the other; the process is as

follow .3 6

B(3)

3 7

C(4)

3 9

D(6)

0 3

A(3)

9 14

E(5)

Early start

Name (duration)

Early finish

Late start

Late finish

6,7,or 9

Fig. 4.8: Forward Path in PDM Analysis

1515

Backward PathBackward Path::

3 6

B(3)

3 7

C(4)

3 9

D(6)

0 3

A(3)

9 14

E(5)

Early start

Name (duration)

Early finish

Late start

Late finish

6,5 ,or 3

149

96

95

93

30

1616

FloatsFloats

Activity A7 days

Activity B13 days

Activity C4 days

Start CompletionProject duration = 24 days

CASE 1: All activities are critical: total float and free floats for all activities = 0

Activity A7 days

Activity B13 days

Activity C4 days

Start CompletionTotal Float = 5Free Float = 5

CASE 2: Activity sequence in which one activity has total and free float

Activity D8 days

Activity A7 days

Activity B13 days

Activity C4 days

Start Completion

Total Float of D = 5 Total Float of E = 5Free Float of D = 0 Free Float = 5

CASE 3: Activity sequence illustrating total and free float

Activity D5 days

Activity E3 days

1717

Floats - 2Floats - 2

Areas of shared float

Activity duration Total Float

Start Event Finish Event

TLi TEjTEi TLj

Activity duration Free Float

Activity duration Independent Float

1818

Float CalculationsFloat Calculations::

Total Float (TF) = LF – EF = LS – ES


Duration

3

3

4

65

ES

0

3

3

39

LF

3

9

9

914

LS

0

6

5

39

EF

3

6

7

914

TF

0

3

2

00

Activity

A

B

C

DE

Critical Act.

Yes

No

No

YesYes

1919

A3

B3

C5

D7

E4

F6

G4

I9

H6

J8

Fn

12 20

10 166 10

6 12

8 12

10 19

3 6

3 8

3 10

0 3

12 20

14 208 12

6 12

8 12

11 20

3 6

3 8

4 11

0 3

ActDur

ES EF

LS LF

TF/FF

PDM Calculations PDM Calculations (PDM = (PDM = PPrecedence recedence DDiagram iagram MMethod)ethod) ExampleExample

0/0

0/ 0

0/ 0

1/ 0

2/ 0

0/ 0

0/0

1/1

4/4

0/0

TF/FFTFi = LFi - EFi


or FF = smallest ES (of succeeding activities) – EF (of current

activity)

2020

PPrecedence recedence RRelationships - Lead & Lagelationships - Lead & Lag

FFij Lag time for a finish-to-finish relationship. (The succeeding activity finishes this amount of time after the completion of the preceding activity.)

SSij Lead time for a start-to-start relationship. (The preceding activity starts this much earlier than the start of the succeeding activity.)

FSij Lag time for a finish-to-finish relationship. (The succeeding activity starts this amount of time after the completion of the preceding activity.)

SFij Lead time for a start-to-finish relationship. (The preceding activity starts this much earlier than the completion of the succeeding activity.)

2121

PRECEDENCE LOGICPRECEDENCE LOGIC1. Preceding Activities. السابقة الفعاليات

Which activities must be finished before this activity may begin ?

What is the time lag? (finish to start.)

Which activities must be started before this activity may begin?

What is the lead time (start to start.)

Which activities must be finished before this activity may be completed?

What is the lag time? (Finish to finish)

Which activities must be started before this activity is completed?

What is the lead time ? (start to finish.)

R. RUSTOMR. RUSTOM 2222

Follow: PRECEDENCE LOGICFollow: PRECEDENCE LOGIC

2. Succeeding Activities الالحقة الفعاليات

Which activities can begin after the finish of this activity?

What is the time lag? (finish to start.)

Which activities can begin after the start of this activity?

What is the lead time? ( Start to start )

Which activities can be completed after the finish of this activity?

What is the lag time? (Finish to finish.)

Which activities can finish after the start of this activity? What is the lead time? (Start to finish.)

3. Concurrent Activities.

Which activities can be carried out at the same time?

(Start to start equals zero, that is, SS = 0 in this case.)

2323

Lead/Lag RelationshipsLead/Lag Relationships

ES DESC. EF ES DESC. EF

FF ij

FS ij

SS ij

SF ij

Forward Pass

Backward Pass

i Dij Dj

LS DESC. LF LS DESC. LF

FF jk

FS jk

SS jk

SF jk

j Djk Dk

2424

PDM Activity Diagramming MethodsPDM Activity Diagramming Methods

Activity No.

Duration RESP.

Star

t Sid

e

Fini

sh S

ide

METHOD 1METHOD 1METHOD 1METHOD 1

Activity No.

Duration RESP.

Star

t Sid

e

Fini

sh S

ide


DESCRIPTION DESCRIPTION

ES

LS

EF

LF

Activity No.

LS LF

Star

t Sid

e

Fini

sh S

ide


Activity No.

Star

t Sid

e

Fini

sh S

ide


DESCRIPTION DESCRIPTION

ES

LS

EF

LF

DUR TF

ES EFDuration RESP.

2525

Logical Relationships of PDMLogical Relationships of PDM

12

FINISH - TO - STARTFINISH - TO - STARTFINISH - TO - STARTFINISH - TO - START

Layout & Excavate

2 GO

12Install exterior

Conduit & piping

5 EL

20

FINISH - TO - FINISHFINISH - TO - FINISHFINISH - TO - FINISHFINISH - TO - FINISH

Install fuel tanks

2 GO

12Install exterior

Conduit & piping

5 EL

10

Contract Award

2 GO

10

Layout & Excavate

2 GO

START - TO - FINISHSTART - TO - FINISHSTART - TO - FINISHSTART - TO - FINISH

12

Layout & Excavate

2 GO

18

Install fuel tanks

2 ME

START - TO - STARTSTART - TO - STARTSTART - TO - STARTSTART - TO - START

12

Layout & Excavate

2 GO

12Install exterior

Conduit & piping

5 EL

Relationship with LagRelationship with LagRelationship with LagRelationship with Lag

1

PDM Calculation ProcedurePDM Calculation Procedure(Assumes no splitting of activity is allowed)(Assumes no splitting of activity is allowed)

F O R W A R D P A T H

S t e p 1

jiji

jiji

iji

iji

j

DSFES

DFFEF

SSES

FSEF

MaxES

1

S t e p 2

jjj DESEF

2727

Follow PDM Calculation ProcedureFollow PDM Calculation Procedure

B A C K W A R D P A T H

S t e p 1

iijj

iijj

ijj

ijj

i

DSFLF

DSSLS

FFLF

FSLS

alTimeTer

MinLF

min

S t e p 2

iii DLFLS

2828

Calculation of Total Float and Free FloatCalculation of Total Float and Free Float

Total Float

iii EFLFTF Free Float

iijj

iijj

iijj

iijj

ESSFEF

EFFFEF

ESSSES

EFFSES

2929

A10

B7

C10

D10

E4

F3

G10

H15

I7

K5

L5

J3

M6

N8

SS5

FS2

FF2

SS5

FF1

FS5

FS3

SF7

SS2

SS10, FF2

FS2

SS3

FF2, SS1

FS1

FF0

1 11

6 13

11 21

11 21

7 11

15 18

21 31

16 31

16 23

23 28

28 33

11 14

31 37

38 46

38 46

ESi + SSij1 +5 = 6

EFi + FFi - Di11 + 0 - 4

FS0

FS0

EFi + FSij13 + 2

ESi + SFij - Dj15 + 7 -5

EFi + FFij - Dj28 + 2 - 8

ESi + SSij 23 + 1

EFi + FFij-Dj 13 + 2 -10

FS0ESi +SSij11 + 5

EFi + FFij - Dj21 + 1 - 7

EFi + FSij11 +5

ESi + SSij21 + 2

ESi + SSij16 + 10

EFi + FFij - Dj31 + 2 - 5

EFi+FSij23 + 2

FS0

EFi + FSij14 + 3

ESi+SSij28+3

EFij+FSij37+1

FORWARD PASS

3030

A10

B7

C10

D10

E4

F3

G10

H15

I7

K5

L5

J3

M6

N8

SS5

FS2

FF2

SS5

FF1

FS5

FS3

SF7

SS2

SS10, FF2

FS2

SS3

FF2, SS1

FS1

FF0

38 46

38 4631 37

31 37

23 28

37 42

28 33

28 33

11 14

25 28

15 18

35 38

21 31

35 45

16 31

16 3116 23

19 26

6 13

26 3311 21

11 21

11 21

15 25

7 11

11 14

1 11

1 11

LFj - FFij46 - 2

LSj - SSj - Di38 - 1 + 5

LSj - FSij38 - 1

LSj - SSij + Di31 - 3 + 5

LSj - FSij31 - 3

LFj - Sfij + Di42 - 7 + 3

LSj - SSij + Di 37 - 2 + 10

LFi - FFij33 - 2

LSj - SSij + Di28 - 10 + 15

LSj - FSij28 - 2

LSj - FSij19 - 5

LFj - FFij26 - 1

LSj - SSij + Di 16 - 5 + 10

FS0

LSj - FSij35 - 2

LSj - SSij + Di26 - 5 + 10

SF0

SF0

SF0

LFj - FFij45 - 2

BACKWARD PASS

3131

A10

B7

C10

D10

E4

F3

aG10

H15

I7

K5

L5

J3

M6

N8

SS5

FS2

FF2

SS5

FF1

FS5

FS3

SF7

SS2

SS10, FF2

FS2

SS3

FF2, SS1

FS1

FF0

38 46

38 4631 37

31 37

28 33

28 33

11 14

25 28

23 28

37 42

15 18

35 38

21 31

35 45

16 31

16 31

16 23

19 26

6 13

26 33

11 21

11 21

11 21

15 25

7 11

11 14

1 11

1 11

ESj - SSij - ESi6-5-1

ESj - FSij - EFi15 - 2-13

ESj - Sfij - ESi28 - 7 - 15 ESj - SSij - ESi

38 - 1 - 23

EFj - FFij - EFi46 - 2 - 28

ESj - FSij - EFi38 - 1 - 37

ESj - FSij - EFi31 - 3 - 14

ESj - FSij - EFi11 - 0 - 11

ESj - FFij -EFi11 - 0 - 11

EFj - FFij - EFi31 - 2 - 13

ESj - SSij - ESi16 - 5 - 11

ESj - FSij -EFi21 - 0 - 21

FS0

ESj - FFij - EFi23 - 1 - 21

ESj - FSij - EFi16 - 5 - 11

FS0

ESj - SSij - ESi23 - 2 - 21

ESj - FSij - EFi28 - 2 - 23

EFj - FFij - EFi33 - 2 - 31

ESj - SSij - ESi28 - 10 - 16

ESj - SSij - ESi31 - 3 28

0/0

20/0

0/0

4/1

3/0

20/0

14/0

0/0

3/3

14/14

0/0

14/14

0/0

0/0FS0

FS0

ESj - FSij - ESj11 - 0 - 1

ESj - FSij - Efi11 - 0 - 11

TF/FFTFi = LFi - EFi

3232

4.4 Time-Scaled Diagrams:Time-scaled diagrams are used extensively in the construction industry. Such diagrams enable one to determine immediately which activities are scheduled to proceed at any point in time . to monitor field progress. it can be used to determine resources need. The time scale used in time-scaled diagrams can be either the calendar dates or the working periods (ordinary dates), or using both at the same time.Its disadvantage is that it needs a great effort to be modified or updated. Also, it can not be used torepresent overlapping activities.

A3

C4

B3

D6

E5

3

2

Time-scaled diagram

1 2 3 4 5 6 7 8 9 10 11 12 13 14

3333

The TF for activity A equals the smallest of the sum of the floats along all paths from the end of activity A to the end of the project. The float on path ABE = 3, path ACE = 2 and path ADE = 0, then the TF of activity A = 0. The calculations are shown in Table 4.2.

Table 4.2 Time-scaled diagram calculations

3434

4.54.5 Schedule PresentationSchedule Presentation::

After the AOA and AON calculations are made, it is important to present their results in a format that is clear and understandable to all the parties involved in the project. The simplest form is the Bar chart or Gantt chart, named after the person who first used it. A bar chart is a time versus activity chart in which activities are plotted using their early or late times .

a) Early bar chat

b) Late bar chart

3535

The bar chart representationThe bar chart representation::

It shows various details. Float times of activities, critical activities can be shown in a different color, or bold borders, as shown in Figure 4.12. The bar chart can also be used for accumulating total daily resources and / or costs, as shown at the bottom part of Figure 6.13. In this figure, the numbers on each activity represent the number of labors needed.

Figure 4.13: Using bar chart to accumulate resources

3636

4.6 Criticisms to Network Techniques:4.6 Criticisms to Network Techniques:

1- Assume all required resources are available: The CPM calculations do not incorporate resources into their formulation. Also, as they deal with activity durations only, it can result in large resource fluctuations. Dealing with limited resources and resource leveling, therefore, has to be done separately after the analysis.

2- Ignore project deadline: The formulations of CPM and PDM methods do not incorporate مندمجةغير a deadline duration to constrain project duration.

3- Ignore project costs: Since CPM and PDM methods deal mainly with activities durations, they do not deal with any aspects related to minimize project cost.

4- Use deterministic durations: The basic assumption in CPM and PDM formulations is that activity durations are deterministic. In reality, however, activity durations take certain probability distribution that reflect the effect of project conditions on resource productivity and the level of uncertainty involved in the project.

3737

4.74.7 Solved ExamplesSolved Examples

Example 3.1Example 3.1For the project data in Table 4.3, answer the following questions:

a) Draw an AOA network of the project?

b) Perform forward path and backward path calculations c) What is the effect of delaying activity D by 3 days?

3838

Solution:

a, b

0

1A

2

3

5 6

0

2

4

2 2

8 8

14 14 16 16

9 11

B

6

E

6

C

3 F

3

G

21D

8,or10

14,or122,or 8

9,or 5

c) Total float of activity D = LF – ES – d = 11 – 8 – 1 = 2.

3939

Example 3.2Example 3.2Perform PDM calculations for the small project below and determine activity times. Durations are shown on the activities.

4040

Solution:

1 5

B(4)

1 5

5 6

D(1)

5 6

6 7

G(1)

6 7

7 14

J(7)

7 14

14 16

L(2)

14 16

1 2

C(1)

6 7

2 4

E(2)

7 9

4 5

H(1)

9 10

2 4

F(2)

8 10

5 9

K(4)

10 14

0 1

A(1)

0 1

7 9

I(2)

12 14

7or85or4

9or9or14

1or6

12or7

4141

Example 3.3Example 3.3For the activities listed in the table below, draw the time-scaled diagram and mark the critical path. Determine the completion time for the project. Tabulate activities times and floats.

4242

Solution:

4343

Example 3.4Example 3.4Perform PDM calculations for the small AoN network shown here. Pay special attention to the different relationships and the lag times shown on them.

Solution:

0 3

A(3)

0 3

2 5

B(3)

4 7

3 7

C(4)

3 7

3 9

D(6)

4 10

7 12

E(5)

7 12

SS2

FF2

8

5 or 7 or 2=9-2-5

12-2=10

4 or 3 or 5=4-2+3

4444

Exercise 4Exercise 4

4545

Exercise 4 Exercise 4 (Cont.)(Cont.)

4646


4747


4848


4949


5050


1 project scheduling faculty of applied engineering and urban planning civil engineering department...

Documents

project network

network of project activities

project completion time

critical activities

entire project

project late completion

critical path scheduling

forward path