PMI36 Scheduling

1

Agnese [email protected]

Project and Programme Management A and B

Scheduling

POLITECNICO DI MILANO

Project and Programme Management

Planning Tools

MILESTONESGANTT CHARTS

S CURVES

NETWORK DIAGRAMSSPACE-TIME DIAGRAMS

DATA TABLES

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Planning Tools

Precedence Chart

Gantt Chart

Resource scheduling

Res

ourc

es

Schedule



Gantt Chart

Jelena

Note

tool for planning and control, we can see start and end of overall project

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Gantt chart is a bar chart where project activities are presented as bars whose lengths are proportional to their estimated duration.

Gantt chart shows when project and each activity start and end based on a horizontal timescale

Steps:

• Activities have to be sequenced

• Each activity duration has to be estimated

• Gantt Chart can be drafted and refined


Gantt Chart


• Easy to assimilate and understand

• Activity progress is displayed very clearly and simply

• Activity float is easier to comprehend when shown on a barchart

• A schedule barchart is a prerequisite for forecasting procurement schedule, resource histogram and cash-flow statement

• Revised barchart is an excellent tool for planning and control

• A barchart can be used to communicate and disseminate schedule information

• A barchart is a key document for management decision making function


Gantt Chart Advantages

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• Suitable for projects made up of few acivites

Not (usually) suitable for multiple decision making

• It (usually) doesn’t show logic interrelationships between activites


Gantt Chart Shortcomings


Unlike the Gantt chart, the network diagrams show a systemic project representation. In this way they allow to define the project like the whole linked activities oriented to a unique objective.

In its simplest form only two items of information are required:

• List of activities

• Logic constraints (links), logical dependency or logical relationship between activites


Network Diagrams

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Here we can see critical part. We can see duration of each activity

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Network Diagrams

Project operative model

“What if” analysis


They allow to link together activities (or work package) making possible:

• Building of a logical model

• Building of a schedule model

• Verification of project feasibility

• Correctly allocation of activities resources

• Giving an inter-functional visibility

• Individualizing critical activities

• Simulation of impacts of time and cost variations or of possible problems and/or corrective actions


Network Diagrams Advantages

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In order to achieve reliable analysis it is necessary

• to consider a great amount of activities

• to use sophisticated logical links

It necessary to consider a great amount of data about:

• activities' attributes

• How the attributes change changing the activities

• The problems about data’s updating are increased by the methodanalyticity

• After each updating it is necessary to critically verify the results,analysing the development for the logical project concatenations

• The method does not allow to carry out “previsione a finire” on thebase of advancing data


Network Diagrams Disadvantages


A graph is a set of nodes linked by arrows. Their sequence defines a path.

If arrows of a graph have a direction, the graph is called oriented graph.


Graph

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•Without circuits

•With circuits

•With certain paths

•With uncertain paths

•With “AND nodes”

•With “OR nodes”

•With probabilistic node


Graph typologies

Activity A Activity B

Start A Case End A Case / Start B Case End B Case

Activity on arrow

Activity on node

Activity A

Activity A – Activity B connection

Activity B


FINISH TO START links

Dummy activities requested

The dummy activities are not characterized by duration or resources’ use. They only establish precedence constraints between the activities


AoA (Activity on Arrow) Networks

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Project has no life cycle.

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AoN (Activity on Nodes) Networks

• Each activity can have more than one ‘input’ and ‘output’ link

• Between two activities it is possible to have two different types of link

• Dummy activities (milestones) can be used



Link typologies

A B

A B

A B

A B

FINISH - START

START - START

FINISH - FINISH

START - FINISH (not much used)

FS

SS

FF

SF

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Note

milestones

Jelena

Note

Jelena

Typewriter

start together

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finish together

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Types of Graphs without circuits

Link types

Methods

Output(Durations)

Certain Durations Uncertain Durations

Deterministic Probabilistic

FS FSFS-FF-SS-SF

PDM PertCPM

If, for every link• Uncertain Paths• Uncertain Durations

Simulations



Link typologies

B1

A2A1

B2

A B

SS1

FF1

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critical part method

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Lead Time Tree

Production Lead Time Time

PLT Delivery Lead Time ?

LT2

LT1P1.1

A

A2

A1

P2.2

P2.1

P1.2 M1.2


Given an event i,

• EOTi Earliest Occurrence Time

• LOTi Latest Occurrence Time

Given an activity ik,

• ESTik Earliest Starting Time

• EFTik Earliest Finishing Time

• LSTik Latest Starting Time

• LFTik Latest Finishing Time

• tik Time (duration)

i = 0 indicates the start project node i = N indicates the end project node Ai = set of nodes x for which the xi arch exists and converges on i Bi = set of nodes y for which the iy arch exists and comes from i


Terminology and Definition

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earliest and latest start time

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Activity Duration

QUANTITY

PRODUCTIVITY

NEEDED RESOURCES

AVAILABLE RESOURCES

UNIT COST

ESTIMATED ACTIVITY DURATION

ESTIMATED ACTIVITY COST

• Resource Needed

• WBS

• Standard Productivity

• Corrective factors

• Standard Cost

Historical DB Experience

Planning Process

Accounting

Knowledge


The algorithm to calculate the network activities' dates is composed by two phases:

• Forward pass: earliest dates calculation

• Backward pass: latest dates calculation

Dates are scheduled in the two versions:• “earliest”: anticipate the activities that are not in the critical paths

to the earliest dates• “latest”: postpone the activities that are not in the critical paths to

the latest dates

CONVENTION:• activity start = unit of time start• activity end = unit of time end

FT = ST + d -1ST = FT – d -1


Network activities

d = FT – ST +1

Jelena

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duration

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Beginning from the start project node (node 0) end going towards the end project node all the earliest start and finish dates for each event/activity are computed


Forward Pass

EOT0 = 0

ESTik = EOTi + 1

EFTik = ESTik + tik - 1

EOTk = maxjAk (EFTjk)



Forward Pass Example

EF = ES + duration -1

16 2511 15

26 3011 20

1 10

ES EF

D 10B 5

E 5C 10

A 10

Att t

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It is necessary to consider the “end project” event (node N) and to set its maximal date (LOTN ) equal to the lowest date EOTN computed in the previous pass


Backwad Pass

LOTN = EOTN

LFTik = LOTk

LSTik = LFTik - tik + 1

EOTi = minlBi (LSTil) - 1



Backwad Pass Example

1 10

D 10

16 25

B 5

11 15

E 5

26 30

C 10

11 20

A 10

1 10

11 15 16 25

16 25 26 30

LS = LF – duration + 1

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From the resulting dates is possible to know:• Internal logic interrelationship • Activities durations

It is possible to assign to LOTN values (different from EOTN) imposed by external constraints to the network logic (contractual expiration date, etc.)

The following is established:• if degrees of freedom exist• where to share eventual negative TF


Forward and Backward Pass


From the data in the table draw:

• Precedence diagram

• Allocated resources profile

• Gantt chart

Assuming that there are infinite resources available and not temporal constraints


Exercise A

WP Precedence Duration res. per dayA / 8 4B / 6 4C / 7 5D A 5 4E A,B 6 10F E,C 9 9G D,E 4 2H G,F 2 2

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Through the comparison among earliest and latest dates – floatsexamination – it is possible to identify poject critical activities.

Types of floats:

• Total float

• Free float

• Independent float


Float



Float Graphic Representation

EOTi LOTi EOTk LOTK

SIik = EOTk - LOTi - tik

SLik = EOTk - EOTi - tik

STik = LOTk - EOTi - tikTotal float

Free float

Independent float

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Total float is the maximum range available to postpone or extend the execution for a single activity, without changing the project deadline

It is calculated using the following relationships:

It represents the maximum range available to reallocate the activities


Total Float

Stik = LFTik- EFTik = LFTik - (ESTik + tik - 1) =

= (LFTik - tik + 1) - ESTik = LSTik - ESTik =

= (LOTk - tik + 1) - EOTi - 1 = LOTk - EOTi - tik



Float Calculation Example

16 25

2516

11 15

1511

11 20

2516

1 10

101 0

A 10

ES EF

LFLS

00

5

26 30

3026 0

float

D 10B 5

C 10

A 10

E 5

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Not Critical Activities

Crtical Activities


Total Float in Critical and Not Critical Activities

duration

duration

float

floatEST

LFTLST

EFT

EST EFT

durationLST LFT

float = 0


Float available for the activity without postponing the earliest start date for the consecutive node (k)

Hypothesis: the starting node (i) is earliest realized.

The following relationships are assumed:

It is always true: SLik ≤ STik


Free Float

Slik = EOTk - EFTik = EOTk - (ESTik + tik -1) =

= EOTk - EOTi - tik

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Acceptable delay for an activity with the hypothesis that the starting date is the latest start date and the finish activities (consecutive activity starting) must be realized at the earliest start date. The independent float does not influence previous and consecutive activities.

It is calculated with the following relationship:

It always results SIik ≤ SLik ≤ STik


Independent Float

SIik = EOTk - LOTi - tik


NET “not earlier than”

(forward pass)

NLT “not later than”

(backward pass)

ON

(forward e backward pass)


Temporal Constraints on Nodes

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It is the activities chain characterized by the maximal comprehensiveduration or by the minimal float

A delay for any activity belonging to the Critical Path implies a delayfor the whole project.

In order to reduce the whole project duration (10-20%) it is necessaryto operate on the critical path’s activities.

If EOTN = LOTN TF=0

If there are temporal constraints on the nodes the critical path could not be the path with the maximal duration.


Critical Path


If you need to accelerate the schedule, do it by fast-tracking andcrashing.

Watch out! Accelerating the schedule may increase the number ofcritical activities. (from 10 percent to 40-50 percent of activities willresult critical).

Sprinkle major milestones over your CPM chart. It helps you seewoods (milestones) and trees (activities).

Color-code activities performed by various resource providers inorder to identify their interfaces and provide their coordination.

Develop template CPM charts. Then, use them consistently todevelop the schedule for new projects.


CPM tips

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• It considers the time/costs trade-off

“normal” duration/cost

“crashed” duration/cost

• It tries to reduce the project duration to the least necessary expense

find the critical path

compact the critical path activities beginning from the least expensive

repeat the process until dC/dT < dBenefits/dT


Cost Critical Path Method (CPM)

Estimated Duration

HR Allocated1 2 3 4


You are the PM of the above described project. Suppose that the customer would give a prize of “40” for every unitary reduction of delivery times. What would you decide to do?


Cost CPM Example

ACTIVITY PRED. NORMAL TIME

NORMAL COST

CRASHED TIME

CRASHED COST dC/dT

A - 3 30 2 40 10

B A 2 30 1 65 35

C A 2 60 / / /

D A 3 60 2 75 15

E B 3 30 2 45 15

F C 1 30 / / /

G D 1 60 / / /

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Cost CPM Example

Activity A

Activity B

Activity C

Activity D

Activity E

Activity F

Activity G

Project Duration = 6Project Cost = 235Marginal Cost = 15Marginal Revenue = 40Profit = 25Critical activities: A, B, E and A, D, G

D e B are both candidate for crashing

Activity Pred.

Early

StartEarly Finish

Late

Start

Late

Finish dC/dT

A - 0 3 0 3 na

B A 3 5 3 5 35

C A 3 5 5 7 /

D A 3 6 4 7 15

E B 5 8 5 8 na

F C 5 6 7 8 /

G D 6 7 7 8 /



Cost CPM Example

Activity A

Activity B

Activity C

Activity D

Activity E

Activity F

Activity G

Project Duration = 5Project Cost = 285Marginal Cost = 50Marginal Reveneu = 40Profit = -10Critical Activities: A, B, E; A, D, G and A, C, F

0 1 2 3 4 5 6 7 8 9 10

The profit is negative, we refuse to crash B and D

Activity Pred.

Early

StartEarly Finish

Late

Start

Late

Finish dC/dT

A - 0 3 0 3 na

B A 3 5 3 5 na

C A 3 5 5 7 /

D A 3 6 4 7 na

E B 5 8 5 8 na

F C 5 6 7 8 /

G D 6 7 7 8 /

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Cost CPM Example

Activity A

Activity B

Activity C

Activity D

Activity E

Activity F

Activity G

Project duration= 8Project Cost= 210Critical Activities A, B, E

0 1 2 3 4 5 6 7 8 9 10

A is the candidate for crashing

Activity Pred.

Early

StartEarly Finish

Late

Start

Late

Finish dC/dT

A - 0 3 0 3 10

B A 3 5 3 5 35

C A 3 5 5 7 /

D A 3 6 4 7 15

E B 5 8 5 8 15

F C 5 6 7 8 /

G D 6 7 7 8 /



Cost CPM Example

Activity A

Activity B

Activity C

Activity D

Activity E

Activity F

Activity G

Project Duration = 7Project Cost = 220Marginal Cost = 10Marginal Revenue= 40Profit = 30Critical Activities A, B, E

0 1 2 3 4 5 6 7 8 9 10

E is the candidate for crashing

Activity Pred.

Early

StartEarly Finish

Late

Start

Late

Finish dC/dT

A - 0 3 0 3 na

B A 3 5 3 5 35

C A 3 5 5 7 /

D A 3 6 4 7 15

E B 5 8 5 8 15

F C 5 6 7 8 /

G D 6 7 7 8 /

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Link Between Activities – Representation Methods

SFij

FFij

FSij

SSij

a)

b)

c)

d)


• SSij Start to Start

Minimal number of units of time that must be past from the previous activity’s start to allow the successive activity to start

• FFij Finish to Finish

Minimal number of units of time required to complete the successive activity after the previous activity’s completion.

• FSij Finish to Start

Minimal number of units of time that must be past from the previous activity’s completion to allow the successive activity to start

• SFij Start to Finish

Minimal number of units of time that must be past from the previous activity’s start to the successive activity’s completion


Link Between Activities – Representation Methods

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Precedence Diagram

DA = 5

DB = 10

FF15

SS2

ES = 3 EF = 20

[11]


It is necessary to consider the constraint relative to the considered activity’ predecessors (Start e Finish)

In case of many predecessors it is necessary to consider the maximaldate


Precedence Diagrams - Forward Pass

FSij ESj = EFi + lag + 1

SSij ESj = ESi + lag

FFij EFj = EFi + lag

SFij EFj = ESi + lag - 1

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Precedence Diagrams - Forward Pass - Example

A

171

20

190

B

158

30

187

C

180

20

199

D

187

10

196

E

177

40

216

F

182

25

206

I

192

30

226

Activity Duration

ES EF

FS = 0

FS = 0

SS = 10

SS = 5

FF = 10

FF = 18




ES (I/A) = 190 + 0 + 1 = 191

ES (I/B) = 187 + 0 + 1 = 188

ES (I/C) = 180 + 10 = 190

ES (I/D) = 187 + 5 = 192

EF (I) = 192 + 30 - 1 = 221

EF (I/E) = 216 + 10 = 226

EF (I/F) = 206 + 18 = 224

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In general:

EF = ES + d -1

In presence of external predecessors for its finish (FF and SF), it is possible

having incongruities.•

Activities Splitting



A109

20128

B95

40143

A109

20128

B195

25119

B2129

15143

FF = 15

(134)

(9)


It is necessary to consider the constraint relative to the considered activity’ successors (Start e Finish)

In case of many predecessors it is necessary to consider the minimal date


Precedence Diagrams – Backward Pass

FSij LFj = LSi - lag - 1

SSij LSj = LSi - lag

FFij LFj = LFi - lag

SFij LSj = LFi - lag - 1

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Precedence Diagrams - Backward Pass - Example

172

40

A133

20152

B143

30

C100 139

E105

20124

F118

30147

FS = 0

FS = 5

FF = 10

SS = 10

SS = 15

I95

30129

Activity Duration

LS LF




LF (I/A) = 133 - 0 - 1 = 132

LF (I/B) = 143 - 5 - 1 = 137

LF (I/C) = 139 -10 = 129

LS (I) = 129 - 30 +1 = 100

LS (I/E) = 105 - 10 = 95

LS (I/F) = 118 -15 = 103

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In general:

LS = LF - d -1

In presence of external predecessors for its start (FS and SS), it is possible

having incongruities.

Activities’ s Splitting



A203

30237

B213

30242

A2218

20237

B213

30242

A1203

10212

SS = 10

(208)

(5)

PMI36 Scheduling

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