GIH6 Project Scheduling

8/13/2019 GIH6 Project Scheduling

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Chapitre 6

Gestion de projetsProject management


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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


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Intoduction

Health care managers may work on projects that areunique and nonroutine.

Projects can be viewed as temporary endeavorsundertaken 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 numberof activities that must be carefully planned and coordinate.

Project management is an approach for handling these

unique, one-time endeavors that have significant costs andsignificant effect on the organisations operation.

Planning and coordination are essential to completeactivities of the projects on time, within cost constraints,and with high quality result.


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Intoduction

Most projects are expected to be complete with time, costand 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.


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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 resourcesconsumed.

Termination:reassign personnel and dealing with leftover

and excess materials and equipment.


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The project manager

Responsible for the organization and completion of theproject

Communicate among the project team and coordinatetheir 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 chartProgram Evaluation and Review Techniques (PERT)


Activities are project steps that consume resources and/ortime

Crucial activities that requirement special attention toensure on-time completion of the project can be identified,as well as how long others start can be delayed


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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

Activity Time

A. Land acquisition 4 wk

B. Hire a radiation oncologist 16wk

C. Select contractor & develop a construction plan 8 wk

D. Build the facility 24 wk

E. Aquire equipment 28 wk

F. Hire technical staff 4 wk

G. Purchase & set up info syst. & software 8 wk

H. Testing of equipment 4 wk

Precedence relation

Activity Predecessor

A. -

B. -

C. A, B

D. CE. C

F. D,E

G. D, E

H. F, G


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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


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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

B C

Dummyactivity

A

B

C

Activity on arc

Nodes = beginning/end of

activities = events

Activity on node


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The netwok diagram shows the sequence in which activities must

be performed.

On AON networks, it is common to add a start nodepreceding

the first activities, and an end nodeto mark the completion.

Radiation oncology

serviceActivity Predecessor

A. -

B. -

C. A, B

D. C

E. C

F. D,E

G. D, E

H. F, G

Start

A

B

C

D

E

F

G

H End


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A pathis a sequence of activities from the start node to the end

node.

On AON networks, it is common to add a start nodepreceding

the first activities, and an end nodeto mark the completion.

Paths

ACDFH

ACDGH

ACEFH

ACEGH

BCDFH

BCDGH

BCEFH

BCEGH

Start

A

B

C

D

E

F

G

H End


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The length of a pathis the total time of activities on it.

The critical pathis the path with the longest time.

It defines the expected project duration.

All activities on the critical path are critical activities.

Path Lengths

ACDFH = 44

ACDGH = 48

ACEFH = 48

ACEGH = 52

BCDFH = 56

BCDGH = 60

BCEFH = 60

BCEGH = 64

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


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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

Activity name

ES

EF

LS

LF


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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).

Activityname

ES

EF

LS

LF

Start

A

B

C

D

E

F

G

H End

Activity Time

A. 4 wk

B. 16wk

C. 8 wk

D. 24 wkE. 28 wk

F. 4 wk

G. 8 wk

H. 4 wk


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Activityname

ES

EF

LS

LF

Start

A

B

C

D

E

F

G

H End

Activity Time

A. 4 wk

B. 16wk

C. 8 wk

D. 24 wk

E. 28 wk

F. 4 wkG. 8 wk

H. 4 wk

0

0

0

4

0

16

16

24

24

48

24

52

52

56

52

60

60

64

64

64


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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).

Activityname

ES

EF

LS

LF

Start

A

B

C

D

E

F

G

H End

Activity Time

A. 4 wk

B. 16wk

C. 8 wk

D. 24 wkE. 28 wk

F. 4 wk

G. 8 wk

H. 4 wk


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Activityname

ES

EF

LS

LF

Start

A

B

C

D

E

F

G

H End

Activity Time

A. 4 wk

B. 16wk

C. 8 wk

D. 24 wk

E. 28 wk

F. 4 wkG. 8 wk

H. 4 wk

0

0

12

16

0

16

16

24

28

52

24

52

56

60

52

60

60

64

64

64


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The allowable delay of an activity is called slack:

Slack = LS ES or

Slack = LF - EF


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Progrom Evaluation and Review Technique


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Progrom Evaluation and Review TechniquePERT : 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.


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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,

4

6e

o m pt

2

2

6

p os

which is similar to 3sestimation of Normal Law.


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Under the assumption of independent activity times, the completion time

of a path and its variance can be determined as follows:

path et t

2

path activitiespaths s 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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Probability of a path finishes before a specified time ts:

Path time , with s pathpath spath

t tP P t z zs

Where (z) is the standard Normal distribution.

Probability of a projet of N paths finishes before a specified time ts:

1 2...

Nproject path path pathP P P P

In practice, only paths that are significantfor the completion of theproject are considered.


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Path tpath spath z PpathACDFH

ACDGH

ACEFH

ACEGH

Significant paths

BCDFH

BCDGH

BCEFH

BCEGH

Act. o m p te sA. 2 4 8 4.33 1

B. 8 16 24 16 7.11

C. 4 8 16 8.67 4

D. 12 24 36 24 16

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

Project completed by 65, 66, 67, 70 weeks (proba = 0.32,0.44, 0.55, 0.81)


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Rflchir sur une mthode parsimulation pour lestimationde la probabilit de terminerun projet avant une datedonne.


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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.

Normal finishtime

Opt.compression

Maxcompression

Overhead &indirect costs

Direct compressioncost

Total cost (TC)


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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 thecritical 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 hasdecreased, perform steps 1-4 again. Otherwise stop because

the optimum compression time has been achieved.


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Example:

The indirect costs for design and

implementation of a new health info

syst project are 8000/day. Find the

optimal project scheduling.

Start A B

C

D

E

F

G

H EndI

Activity Normal time Compressed

time

Direct comp.

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

Optimal cost =1622000 for 200days.

j i ff i


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A linear programming approach

indirect0

min C

subject to, , precedes

0

i

N

end i i i

i

i i j

start

i i

s C Normal t

s t s i j i j

s

MAXcompression t Normal

R id i


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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.

R id ti


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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.

R id ti


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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.

Mthode srielle revoir.

R id ti


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Example: Consider the project network below. Activity times, in days, are givenin the figure.

a) Determine ES, EF, LS, LF of all activities, draw the Gantt chart based on ES, butindicate 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.

A B C D E F G H

6 1 5 9 10 6 4 3

A A A,B D C E,F

Activity

time

pred

R l di fil


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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 level ingis to reschedule noncritical slack in

order to smooth out the resource usage, which is often possible by

inspection.

R l di fil


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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

Res1

Res2



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Example: Consider the project network below. Activity times, in days, are givenin the figure.

a) Determine ES, EF, LS, LF of all activities, draw the Gantt chart based on ES, butindicate 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.

A B C D E F G H

6 1 5 9 10 6 4 3

A A A,B D C E,F

Activity

time

pred

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