Transcript activity time

Chapitre 6
Gestion de projets
Project management
Plan
•
Introduction
•
The characteristics of projects
•
The project manager
•
Planning and scheduling projects
•
The Gantt Chart
•
PERT and CPM
•
The Network
•
Critical Path Method (CPM)
•
PERT : probabilistic approach
•
Project compression: trade-offs between time and cost
•
Resource considerations
-2-
Intoduction
• Health care managers may work on projects that are
unique and nonroutine.
• Projects can be viewed as temporary endeavors
undertaken to create new products and services.
• Examples: moving to a new location by a certain date,
renovating an outpatient facility.
• Projects has considerable costs and involve a large number
of activities that must be carefully planned and coordinate.
• Project management is an approach for handling these
unique, one-time endeavors that have significant costs and
significant effect on the organisation’s operation.
• Planning and coordination are essential to complete
activities of the projects on time, within cost constraints,
and with high quality result.
-3-
Intoduction
• Most projects are expected to be complete with time, cost
and performance guidelines.
• Goals must be established and priorities set.
• Tasks must be identified and time estimates made.
• Resource requirements have to be projected?
• Budgets have to be prepared.
• Once under way, progress must be monitored.
-4-
The characteristics of projects
Project life cycle:
• Formulation and analysis: recognise the need of the project,
analyse the expected costs, benefits, and risks
• Planning: details of the projects, estimates of necessary
human resources, time and cost.
• Implementation: project undertaken, time and resources
consumed.
• Termination: reassign personnel and dealing with leftover
and excess materials and equipment.
-5-
The project manager
• Responsible for the organization and completion of the
project
• Communicate among the project team and coordinate
their activities
• Manage time and budget constraints
• Assess constantly the quality of the work done
• Set priorities among the tasks
• Ensure the activities being done in the necessary sequence
• Communicate with all relevant external players.
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Planning and scheduling projects
Project management tools:
•Gantt chart
•Program Evaluation and Review Techniques (PERT)
•Critical Path Method (CPM)
• Activities are project steps that consume resources and/or
time
• Crucial activities that requirement special attention to
ensure on-time completion of the project can be identified,
as well as how long others’ start can be delayed
-7-
The Gantt Chart
• Useful scheduling project activities at the planning stage,
and then monitoring them by comparing their actual
progress to planned progress.
Launching a new radiation oncology service
Precedence relation
Activity
Time
Activity
Predecessor
A.
Land acquisition
4 wk
A.
-
B.
Hire a radiation oncologist
16wk
B.
-
C.
Select contractor & develop a construction plan
8 wk
C.
A, B
D.
Build the facility
24 wk
D.
C
E.
Aquire equipment
28 wk
E.
C
F.
Hire technical staff
4 wk
F.
D,E
G.
Purchase & set up info syst. & software
8 wk
G.
D, E
H.
Testing of equipment
4 wk
H.
F, G
-8-
The Gantt Chart
Time in weeks
Activities
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
A
B
C
D
E
F
G
H
Advantage: simplicity
Disadvantages:
•cannot show the chronological relation among activities,
•cannot show how the delay of an activity impact the whole
project
-9-
PERT and CPM

Tools for planning and coordinating large projects

Project managers can



graph the project activities,

estimate the project duration,

identify the activities most critical to its on-time completion, and

calculate how long any activity can be delayed without delaying the project.
PERT and CPM developed independently in late 1950.

PERT by US government to speedup weapon development.

CPM by Du Pont & Remington Rand Co. To plan and coordinate
maintenance projects.
PERT considers the probabilistic nature and CPM mostly
derterministic.
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The Network

A network is a diagram of project activities and their precedence
relationships.

An activity represented by an arrow is called activity on arc
(AOA).

An activity can also be represented by a node and is called an
activity on node (AON).

Most project management computer program are desgined using
an AON network because of its simplicity.

A dummy arc with no time is needed to represent certain
precedence relations in AOA.

Both are used in practice. Representation of one can be
transformed into that of another.
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The Network
Activity
Predecessor
A.
-
B.
-
C.
A, B
A
Dummy
activity
A
B
C
C
Activity on arc
B
Activity on node
Nodes = beginning/end of
activities = events
- 12 -
Critical Path Method (CPM)

The netwok diagram shows the sequence in which activities must
be performed.

On AON networks, it is common to add a start node preceding
the first activities, and an end node to mark the completion.
Radiation oncology
service
Activity
Predecessor
A.
-
B.
-
C.
A, B
D.
C
E.
C
F.
D,E
G.
D, E
H.
F, G
A
D
F
C
Start
B
H
E
End
G
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Critical Path Method (CPM)

A path is a sequence of activities from the start node to the end
node.

On AON networks, it is common to add a start node preceding
the first activities, and an end node to mark the completion.
Paths
ACDFH
ACDGH
ACEFH
ACEGH
A
F
C
Start
BCDFH
BCDGH
BCEFH
BCEGH
D
B
H
E
End
G
- 14 -
Critical Path Method (CPM)

The length of a path is the total time of activities on it.

The critical path is the path with the longest time.

It defines the expected project duration.

All activities on the critical path are critical activities.
Activity
Time
A.
4 wk
B.
16wk
C.
8 wk
D.
24 wk
E.
28 wk
F.
4 wk
G.
8 wk
H.
4 wk
Path Lengths
ACDFH = 44
ACDGH = 48
ACEFH = 48
ACEGH = 52
BCDFH = 56
BCDGH = 60
BCEFH = 60
BCEGH = 64
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Critical Path Method (CPM)

CPM algorithm determines the following pieces of information:

ES: the earliest time an activity can start

LS: the latest time the activity can start and not delay the project

EF: the earliest time the activity can finish

LF: the latest time the activity can finish and not delay the project
ES
LS
Activity name
EF
LF
- 16 -
Critical Path Method (CPM)
Computing ES and EF times:

EF = ES + activity time (t)

The earliest start time (ES) of an activity is equal to the largest EF
of its entering arrow (i.e. its predecessors).
ES
Activity Time
A.
4 wk
B.
16wk
C.
8 wk
D.
24 wk
E.
28 wk
F.
4 wk
G.
8 wk
H.
4 wk
LS
Activity
EF nameLF
A
D
F
C
Start
B
H
E
End
G
- 17 -
Critical Path Method (CPM)
Activity Time
A.
4 wk
B.
16wk
C.
8 wk
D.
24 wk
E.
28 wk
F.
4 wk
G.
8 wk
ES
H.
LS
Activity
EF nameLF
0
4 wk
A
4
0
24
48
16
Start
0
24
0
16
B
D
52
F
56
60
C
64
24
52
E
52
H
64
End
64
G
60
- 18 -
Critical Path Method (CPM)
Computing LS and LF times:

LS = LF - activity time (t)

The latest finish time (LF) of an activity is equal to the smallest
LS of its outgoing arrow (i.e. its successors).
ES
Activity Time
A.
4 wk
B.
16wk
C.
8 wk
D.
24 wk
E.
28 wk
F.
4 wk
G.
8 wk
H.
4 wk
LS
Activity
EF nameLF
A
D
F
C
Start
B
H
E
End
G
- 19 -
Critical Path Method (CPM)
Activity Time
A.
4 wk
B.
16wk
C.
8 wk
D.
24 wk
E.
28 wk
F.
4 wk
G.
8 wk
H.
4 wk
ES
LS
Activity
EF nameLF
A
D
16
0
Start
12
C
0
B
0
16
28
52
F
56
60
16
H
24
E
24
52
G
64
60
End
64
64
52
60
- 20 -
Critical Path Method (CPM)
The allowable delay of an activity is called slack:

Slack = LS – ES or

Slack = LF - EF
- 21 -
Critical Path Method (CPM)
0
A
4
0
24
48
16
Start
0
24
0
16
56
24
12
52
E
C
B
0
16
64
Activity
Slack
Critical
A.
12
No
B.
0
Yes
C.
0
Yes
D.
4
No
E.
0
Yes
F.
4
No
56
G.
0
Yes
60
H.
0
Yes
H
End
64
G
60
D
16
0
60
64
52
0
F
C
B
A
Start
52
D
28
52
F
16
H
24
E
24
52
G
64
60
End
64
64
52
60
- 22 -
Progrom Evaluation and Review Technique
PERT : probabilistic approach
When activity duration cannot be estimated with certainty, PERT
uses three time estimates:

Optimistic time (o): length of time required under the best conditions

Pessimistic time (p): length of time required under the worst
conditions

Most likely time (m): the most probable length of time required.
Care should be taken to make the estimates as realistic as
possible.
- 23 -
PERT : probabilistic approach

These estimates can be used to find the average or expected time of
each activity te, and the variance, s2.

Based on a beta distribution,
te 
s
2
o  4m  p
6
 po


 6 
2
which is similar to 3s estimation of Normal Law.
- 24 -
PERT : probabilistic approach

Under the assumption of independent activity times, the completion time
of a path and its variance can be determined as follows:
t path 
s path 
t
e
 s path activities
2
In PERT,
•completion time of a path is assumed to be Normally distributed
•completion times of different paths are assumed independent
Simulation is now used for more realistic project evaluation &
optimization.
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PERT : probabilistic approach

Probability of a path finishes before a specified time ts:
Ppath  P  P ath tim e  t s     z  , w ith z 
t s  t path
s
path
Where (z) is the standard Normal distribution.

Probability of a projet of N paths finishes before a specified time ts:
Pp ro ject  Pp a th1 Pp a th2 ... Pp a th N

In practice, only paths that are significant for the completion of the
project are considered.
- 26 -
PERT : probabilistic approach
s2
Act.
o
m p
te
A.
2
4
4.33
B.
8
16 24
16
C.
4
8
8.67
D.
12 24 36
24
E.
16 28 36
27.33 11.11
F.
2
4
12
5
2.78
G.
4
8
12
8
1.78
H.
2
4
6
4
0.44
8
16
1
7.11
4
16
Path
tpath spath
ACDFH
ACDGH
ACEFH
ACEGH
z
Ppath
Significant paths
BCDFH
BCDGH
BCEFH
BCEGH
Project completed by 65, 66, 67, 70 weeks (proba = 0.32,
0.44, 0.55, 0.81)
- 27 -
PERT : probabilistic approach
Réfléchir sur une méthode par
simulation pour l’estimation
de la probabilité de terminer
un projet avant une date
donnée.
- 28 -
Project compression: trade-offs between time and cost

Most activities can be speed up by more budget and more
manpower.

In general, there is need of trade-off between direct compression
cost and indirect overhead cost.
Total cost (TC)
Overhead &
indirect costs
Direct compression
cost
Max
compression
Opt.
compression
Normal finish
time
- 29 -
Project compression: trade-offs between time and cost
A general algorithm for project compression
1.
Compute path lengths and identify the critical path
2.
Rank the activities on the critical path according to their
compression costs
3.
Shorten the activity with the least compression cost and the
critical path
4.
Calculate the total costs
5.
Compare the total cost of the current compressed time to that
of the previous compression time; if the total cost has
decreased, perform steps 1-4 again. Otherwise stop because
the optimum compression time has been achieved.
- 30 -
Project compression: trade-offs between time and cost
Example:
The indirect costs for design and
implementation of a new health info
syst project are 8000€/day. Find the
optimal project scheduling.
C
F
Start
A
B
Activity
Normal time Compressed Direct comp.
time
Cost/day (in
000)
A
20
19
11
B
75
74
8
C
42
40
6
D
45
44
10
E
28
26
7
F
21
18
20
G
40
40
0
H
20
19
18
I
20
19
20
D
H
E
I
End
Optimal cost =
1622000 for 200
days.
G
- 31 -
Project compression: trade-offs between time and cost
A linear programming approach
N
m in C indirect s end 
 C  N orm al
i
i
 ti 
i0
subject to
s i  t i  s j ,  i , j i precedes j
s start  0
M A X com pression i  t i  N orm al i
- 32 -
Resource considerations

Determining optimal schedules for complex project networks
subject to resource limitations is an extremely difficult
combinatorial problem.

A project may require a variety of different resources.

Heuristic methods are generally used to modify schedules
obtained by more conventional means.
- 33 -
Resource considerations

In general, the inclusion of resource constraints has the following
effects:

The total amount of scheduled slack is reduced

The critical path may be altered. Further, the zero-slack activities
may not necessarily lie along one or more continuous paths

Earliest and latest start schedules may not be unique. They
depend on the rules that are used to resolve resource limitations.
- 34 -
Resource considerations

Most heuristic methods involve ranking the activities according
to some criterion and resolveing resource conflicts according to
the sequence of the ranking.

Examples of ranking rules include:

Minimum job slack

(minimum) Latest finishing times

Greatest resource demand (priority to bottleneck activities)

Greatest resource utilization (select combination of activities that results in
the maxi resource utilisation in any scheduling interval)

The first two methods tend to be the best performers.

Méthode sérielle à revoir.
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Resource considerations

Example: Consider the project network below. Activity times, in days, are given
in the figure.
a)
Determine ES, EF, LS, LF of all activities, draw the Gantt chart based on ES, but
indicate the activity slack. How long is the project?
b)
A critical piece of equipment is required in order to complete the following
activities (A, B, C, D, G, H). Determine a feasible schedule for the project assuming
that non of these activities can be done simultaneously.
c)
Two resources, R1 and R2, are used for each activity. Assume that these are both
consummable resources with daily requirements as follows (A, 4R1, 0R2), (B, 8, 6),
(C, 10, 9), (D, 18, 4), (E, 12, 3), (F, 5, 12), (G, 3, 2), (H, 0, 6). Determine resource
loading profiles based on the schedule found in part b).
d)
Based on the results of part c), determine the cumulative amounts of resources R1
and R2 consumed if the schedule found in part b) is used.
Activity
A
B
C
D
E
F
G
H
time
6
1
5
9
10
6
4
3
A
A
A,B
D
C
E,F
pred
- 36 -
Resource loading profiles

A loading profile is a representation over time of the resources needed.

As long as the requirements associated with each activity are known,
one can easily obtain the resulting loading profiles of all required
resources.

Resources can be either consumable (cash, fuels) or nonconsummable
(manpower).

A desirable feature of loading profiles is that they be as smooth as
possible.

Large variations in resource requirements make planning difficult and
may result in exceeding resource availability at some time.

The idea behind resource leveling is to reschedule noncritical slack in
order to smooth out the resource usage, which is often possible by
inspection.
- 37 -
Resource loading profiles
Activities
4
8
12
16
20 24
28
32
36
40
44
48
52
56
60
64
A
B
C
D
E
F
G
H
Res
1
Res
2
- 38 -
Resource considerations

Example: Consider the project network below. Activity times, in days, are given
in the figure.
a)
Determine ES, EF, LS, LF of all activities, draw the Gantt chart based on ES, but
indicate the activity slack. How long is the project?
b)
A critical piece of equipment is required in order to complete the following
activities (A, B, C, D, G, H). Determine a feasible schedule for the project assuming
that non of these activities can be done simultaneously.
c)
Two resources, R1 and R2, are used for each activity. Assume that these are both
consummable resources with daily requirements as follows (A, 4R1, 0R2), (B, 8, 6),
(C, 10, 9), (D, 18, 4), (E, 12, 3), (F, 5, 12), (G, 3, 2), (H, 0, 6). Determine resource
loading profiles based on the schedule found in part b).
d)
Based on the results of part c), determine the cumulative amounts of resources R1
and R2 consumed if the schedule found in part b) is used.
Activity
A
B
C
D
E
F
G
H
time
6
1
5
9
10
6
4
3
A
A
A,B
D
C
E,F
pred
- 39 -