1. Project Management

ADM2302 ~ Rim Jaber 1

PROJECT MANAGEMENTPROJECT MANAGEMENT


Learning ObjectivesUnderstand how to plan, monitor, and control projects

using PERT/CPM.Determine earliest start, earliest finish, latest start,

latest finish, and slack times for each activity.Understand impact of variability in activity times.Develop load charts to plan, monitor, and control use

of various resources during project.Use LP to find least cost solution to reduce total

project time, and solve LP models using Excel’s Solver.

Understand important role of software such as Microsoft Project in project management.


Introduction Every organization will take on a large and complex

project. Scheduling large projects is difficult challenge to most

managers when stakes are high. Millions of dollars in cost overruns have been wasted

due to poor project planning.Unnecessary delays have occurred due to poor

scheduling, and companies have gone bankrupt due to poor controls.

How can such problems be solved? Answers lie in popular decision modeling approach

known as project management.


Project Planning, Scheduling, and Controlling

Source: J. Heizer and B. Render. Operations Management. 6/e. Prentice Hall. 2001.


Project Planning, Project Planning, Scheduling, and Scheduling, and

ControllingControllingProject Planning1. Setting goals2. Defining the project3. Tying needs into timed project activities4. Organizing the team

Project Scheduling1. Tying resources to specific activities2. Relating activities to each other3. Updating and revising on regular basis

Project Controlling1. Monitoring resources, costs, quality and budgets2. Revising and changing plans3. Shifting resources to meet demands

Before Project

During Project


Software Packages in Project ManagementSoftware Packages in Project Management

• Managing large and complex projects has become easier due to availability of specialized project management software packages.

• Primavera (by Primavera Systems, Inc.), • Microsoft Project (by Microsoft Corp.), • MacProject (by Apple Computer Corp.), • Pertmaster (by Westminster Software, Inc.),• VisiSchedule (by Paladin Software Corp.), and • Time Line (by Symantec Corp.). • Microsoft Project 2000.


PROJECT SCHEDUELING PROJECT SCHEDUELING TECHNIQUES: CPM and PERT TECHNIQUES: CPM and PERT Network Techniques CPM: Critical Path Method PERT: Project Evaluation and Review

Technique


CPM vs. PERTCPM vs. PERT

Primary difference between PERT and CPM is how time needed for each activity in project is estimated.

CPM is a deterministic technique:It estimates completion time of each activity using a single

time estimate. PERT is a probabilistic technique:

each activity has three time estimates that are combined to determine expected activity completion time and its variance

Allows you to find the probability that the entire project will be completed at a given date.

9

Questions That May Be Questions That May Be Addressed by PERT and Addressed by PERT and

CPMCPM 1. When will the project be completed? 2. What are the critical activities or tasks in the project? 3. Which are the noncritical activities? 4. What is the probability that the project will be

completed by a specific date? 5. Is the project on schedule, ahead of schedule, or

behind schedule? 6. Is the project over or under the budgeted amount? 7. Are there enough resources available to finish the

project on time? 8. If the project must be finished in less than the

scheduled amount of time, what is the best way to accomplish this at least cost?


Six Steps Common toSix Steps Common toPERT and CPMPERT and CPM

1. Define the project and all of its significant activities or tasks.

2. Develop relationships among the activities. Determine the intermediate predecessors (activities or tasks that must be completed before the current activities can begin).

3. Draw the network connecting all of the activities. 4. Assign time and/or cost estimates to each activity 5. Compute the longest time path through the

network. This is called the critical path. 6. Use the network to help schedule, monitor, and

control the project.


General Foundry, Inc., a metalwork plant in Milwaukee, has long been trying to avoid the expense of installing air pollution control equipment. The local environment protection group has recently given the foundry 16 weeks to install a complex air filter system on its main smokestack. General Foundry was warned that it will be forced to close unless the device is installed in the allotted period. Lester Harky, the managing partner, wants to make sure that installation of the filtering system progresses smoothly and on time.

When the project begins the building of the internal components for the device, and the modifications that are necessary for the floor and roof can be started. The construction of the collection stack can begin once the internal components are completed. Pouring the new concrete floor and installation of the frame can be completed as soon as the internal components are completed and the roof and floor have been modified. Once the collection stack has been constructed, the high-temperature burner can be built, and the installation of the pollution control system activity can begin. The air pollution device can be installed after the high-temperature burner has been built, the concrete floor has been poured, and the frame has been installed. Finally, after the control system, and pollution device have been installed, the system can be inspected and tested.

General Foundry ExampleGeneral Foundry Example


General Foundry Example General Foundry Example (Cont’d)(Cont’d)

1. Define all project activities.

2. Determine the intermediate predecessors (activities/tasks that must be completed before the current activities can begin).

3. Draw the corresponding network.


General Foundry Example: General Foundry Example: Activity, Immediate Activity, Immediate Predecessor, TimePredecessor, Time

Activity Description Immediate Predecessor Time (weeks)

ABCDEFGH

Build internal componentsModify roof and floorConstruct collection stackPour concrete and install frameBuild high temperature burnerInstall control systemInstall air pollution deviceInspection and testing

AA,BCCD, EF,G

23244352


Network FundamentalsNetwork Fundamentals

Network: A graphical display of project that contains the activities and shows the precedence relationships among the activities.

Activity: A time consuming job or task that is a key subpart of the whole project. Number of activities in project will depend:

On nature and scope of project. On level of detail with which project manager

monitors and controls project.


Drawing Project NetworkThere are two approaches for drawing project network --

Activity on Node (AON), and Activity on Arc (AOA).

Although both approaches are popular in practice, many

project management software packages, including

Microsoft Project 2000, use AON networks.

Focus is on AON network:The nodes of the network represent the activities.The arcs (the line with arrows) represent/show the precedence

relationships among the activities.

16

Some Network Construction RulesSome Network Construction Rules If activity A precedes activity B, activity A must

be completed before starting activity B.Each network has only one start and only one

termination point. If there are two activities or more that do not have any

predecessors, then include a dummy activity called Start.

In case of two activities or more with no successors, all arrows must meet at the same Finish-of-project node. Include a dummy activity called Finish

Dummy activity does not really exist and takes up zero time and resources.

Two or more activities cannot share both the same start and end event (AOA)Dummy activities may be needed in AOA networks to

show all precedence relationships


Network for General Foundry, Network for General Foundry, Inc.--Activity on Node (AON)Inc.--Activity on Node (AON)

s

A C

DB

H f

G

E

F


Network for General Foundry, Network for General Foundry, Inc.--Activity on Node (AON)Inc.--Activity on Node (AON)

s

A C

DB

H f

G

E

F

2

3

2

4

4

3

5

20 0


Network for General Foundry, Network for General Foundry, Inc.--Activity on Arc(AOA)Inc.--Activity on Arc(AOA)

1

2 4

53

6

(Build Internal Components) (Construct

Collection Stack)

(Modify Roof and Floor)

(Pour Concrete and

Install Frame)

(Install Control System)

(Install PollutionDevice)

7

(Inspect andTest) (Build

Burner)

A

B

D

C

E

F

GH


Network for General Network for General Foundry, Inc. (AOA)Foundry, Inc. (AOA)

1

2 4

53

6 7

A

B

D

C

E

F

GH

t = 2

t = 4

t = 3

t = 2

t = 3

t = 5

t = 2t = 4Dummy

Activity


Once project network has been drawn to show all activities and precedence relationships, determine project schedule.

Determining The Project Schedule


Critical PathCritical PathDefinition

The critical path is the longest time path route through the network.

To find out just how long the project will take, perform critical path analysis for network:

Find the Critical Path

How to find the Critical Path?Determine: ES, EF, LS, LF, and slack time.


What is ES and EF?What is ES and EF?

Earliest Start Time (ES): Earliest time at which an activity can start, assuming all predecessors have been completed.All predecessors activities must be completed

before an activity can be started

Earliest Finish Time (EF): Earliest time at which an activity can be finished.


Compute ES and EF for Compute ES and EF for each Activityeach Activity

EF = ES + t

= Earliest start time + activity timeES : make a forward Pass through the

network.

==>the earliest start time is the time when all the activities ending at the node have been completed

==> ES =Max{ EF of all immediate predecessors}


General Foundry’s Earliest Start General Foundry’s Earliest Start (ES) and Earliest Finish (EF) (ES) and Earliest Finish (EF)

Times--AONTimes--AON

s

A C

DB

H f

G

E

F

2

3

2

4

4

3

5

20 0

ESEF

ESEF

ESEF

ESEF

ESEF

ESEF

ESEF

ESEF

ESEF

ESEF


What is LS and LF?What is LS and LF?

Latest Start Time (LS): Latest time at which an activity can start so as to not delay completion time of entire project.

Latest Finish Time (LF): Latest time by which an activity has to finish so as to not delay the completion time of entire project.


Compute LS and LF for each Compute LS and LF for each activityactivity

For each activity, determine its LF value, followed by its LS value.

LS = LF - t= Latest Finish time - activity time.

LF : make a backward pass through the network (begins with last

activity in project)==> computed by making sure that the project will not be delayed for any activity

LF = Min{ LS of all immediate following activities}


General Foundry’s Latest General Foundry’s Latest Start (LS) and Latest Finish Start (LS) and Latest Finish

(LF) Times(LF) Times--AON--AON

s

A C

DB

H f

G

E

F

2

3

2

4

4

3

5

20 0

LSLF

LSLF

LSLF

LSLF

LSLF

LSLF

LSLF

LSLF

LSLF

LSLF


General Foundry’s ES,LS,EF General Foundry’s ES,LS,EF and LFand LF--AON--AON

s

A C

DB

H f

G

E

F

2

3

2

4

4

3

5

20 0

S=(0 ,0)F=(0,0)

S= ( 0,0)F= ( 2,2)

S=( 2,2)F=( 4,4)

S= (4 ,10)F=(7 ,13)

S= ( 13,13)F=( 15,15)

S=( 0,1)F=(3 ,4)

S=(3 ,4)F=(7,8)

S=( 8,8)F= (13 ,13)

S= ( 15,15)F=( 15,15)

S=(4 ,4)F=( 8,8)


Results of CPM: Results of CPM: Activities Along Critical Activities Along Critical

PathPath

General Foundry’s Schedule and Slack Times

OnCriticalPath?

Slack(LS - ES)

LatestStart (LS)

EarliestFinish (EF)

EarliestStart (ES)Activity

ABCDEFGH

0023448

13

234787

1315

01244

108

13

01010600

YesNoYesNoYesNoYesYes

LatestFinish (LF)

24488

131315


s

A C

DB

H f

G

E

F

2

3

2

4

4

3

5

20 0

Results of CPM: Activities Results of CPM: Activities Along Critical Path (cont’d.)--Along Critical Path (cont’d.)--

AONAON

General Foundry’s Critical Path (A - C - E - G - H)


Multiple Critical PathsIn General Foundry’s case, there was just a single

critical path.

Can project have multiple critical paths?

Answer is yes.

For example, what if time required for activity B had

been estimated as 4 weeks, instead of 3 weeks?

Due to this change, earliest and latest times for

activities B and D would have to be revised.


Project Evaluation and Review Project Evaluation and Review Technique (PERT)Technique (PERT)

An alternative to CPM

Uses Probabilistic activities times

Same step as taken for the CPM Network Except:

on the fourth step instead of assuming a single time estimate we determine three time estimates for each activity: m, a, and b


Three Time Estimates in PERT Optimistic time (a)= time an activity will take if

everything goes as planned.

Pessimistic time (b) = time an activity will take

assuming very unfavorable conditions.

Most likely time (m) = most realistic estimate of

time required to complete an activity.


Beta Probability Beta Probability Distribution with Three Distribution with Three

Time EstimatesTime Estimates

Pro

bab

ilit

y

OptimisticTime(a)

MostLikelyTime(m)

PessimisticTime(b)

Activity Time

Probability of1 in 100

(b) Occuring

Probability of1 in 100

(a) Occuring


Expected Time and Variability To find expected activity time, t, beta distribution weights

three time estimates as follows:

• t = (a + 4m + b) / 6 Most likely time (m) is given four times weight as optimistic time (a)

and pessimistic time (b)

To compute dispersion or variance of activity completion

time, use formula:

• Variance = [ (b - a) / 6 ] 2

Standard deviation of activity completion time is square root

of variance.

• Standard deviation = Variance = (b - a) / 6

37

Time Estimates (in weeks) Time Estimates (in weeks) for General Foundry, Inc. for General Foundry, Inc.

(Table 13.2)(Table 13.2)t =

a + 4m + b

6Variance =

b - a

6( )

2

ActivityOptimistic

aMost

Probable- mPessimistic

bExpected Time

t = [(a + 4m + b)/6]Variance[(b - a)/6]2

A

B

C

D

E

F

G

H

1

2

1

2

1

1

3

1

2

3

2

4

4

2

4

2

3

4

3

6

7

9

11

3

2

3

2

4

4

3

5

2

3 - 16( ) 4

36=2

4 - 26( ) 4

36=2

3 - 16( ) 4

36=2

6 - 26( ) 16

36=2

7 - 16( ) 36

36=2

9 - 16( ) 64

36=2

11 - 36( ) 64

36=2

3 - 16( ) 4

36=2

Total 25 weeks


s

A C

DB

H f

G

E

F

2

3

2

4

4

3

5

20 0

General Foundry’s Critical Path (A - C - E - G - H)

Results of PERT: Results of PERT: Activities Activities

Along Critical PathAlong Critical Path

Activities Along Critical Path


PERT Time EstimatesPERT Time Estimates

ActivityOptimistic

(a)

MostProbable

(m)Pessimistic

(b)Expected

Time Variance


PERT WorksheetPERT WorksheetActivity Expected

TimeES EF LF Slack Critical?


The Expected Project The Expected Project Completion Time Completion Time

tp = Sum of the expected (mean) time of all the activities on the critical path.


The project VarianceThe project Variance

PERT uses variance of critical path activities to help determine variance of overall project.

Project variance computed by summing variances of critical activities:• Project variance = (variances of activities on critical path)

Variance of activities are: A is 0.11, C is 0.11, E is 1.00, G is 1.78, and H is 0.11. Total project variance and project standard deviation are computed

as follows:• Project variance (P

2) = 0.11 + 0.11 + 1.00 + 1.78 + 0.11 = 3.11 weeks2

• Project standard deviation (P) = (Project variance) = (3.11) = 1.76 weeks


Probability of Completing Project on Time

• How can information be used to answer questions regarding probability of finishing project on time?

• PERT makes two more assumptions: (1) total project completion times follow normal probability distribution; and (2) activity times are statistically independent.

• Normal curve implies there is 50% chance project completion time will be less than 15 weeks, and 50% chance it will exceed 15 weeks.

General Foundry, Inc.

44

Probability of General Foundry’s Probability of General Foundry’s Meeting the Deadline of 16 weeksMeeting the Deadline of 16 weeks

Z = Due Date - Expected Completion Date

σp= 16 - 15

1.76= 0.57

.57 Standard Deviations

16Weeks

15Weeks

Time

Probability(T <= 16 Weeks)is 71.6%

Compute « Standardized Data Values”: the number of standard deviations (Z) a value is from the mean, then refer to the normal table to find the probability


Meeting 16-week Deadline

• Z = (due date - expected date of completion) / P

• = (16 weeks - 15 weeks) / 1.76 weeks = 0.57 • Referring to Normal Table in Appendix A, there is 71.6%

chance pollution control equipment can be put in place in 16 weeks or less.



Determining Project Completion Time for

Given Confidence Level Project completion time follows normal probability

distribution with mean of 15 weeks and standard deviation of 1.76 weeks.

Find due date deadline for 99% chance of project completion.

Determine Z value corresponding to 99%. In Normal Table in Appendix A, identify a Z value of 2.33

as closest to a 0.99 probability.

Due Date = Expected completion time + Z x P

= 15 + 2.33 x 1.76 = 19.1 weeks


Determining Project Completion Time for

Given Confidence Level

• Due Date = Expected completion time + Z x P

= 15 + 2.33 x 1.76 = 19.1 weeks



Project CrashingProject Crashing


Project Crashing • Project manager may be faced with either (or both) situations:

(1) the project is behind schedule, and/or

(2) the scheduled project completion time has been moved forward.

• Some or all of remaining activities need to be expedited to finish project by desired due date.

• Process to shorten duration of project in lowest cost possible is called project crashing.

• Choose which activities to crash, and by how much to ensure:

– Amount by which activity is crashed is permissible.

– Shortened activity durations enable one to finish project by due date and

– Total cost of crashing is as small as possible.

50

Crashing Project - Hand Calculations

Four Steps of Project Crashing1. Compute crash cost per week for all activities in

network. If crash costs are assumed to be linear over time, following formula may be used: Crash cost per period = (Crash cost - Normal cost)

(Normal time -Crash time) 2. Using current activity times, find critical path(s) in project

network. Identify the critical activities.

3. If there is only one critical path, then select activity on critical path that: (a) can still be crashed, and (b) has smallest crash cost per period. Crash this activity by one period.


Crashing Project - Hand CalculationsIf there is more than one critical path, then select one

activity from each critical path such that: (a) each

selected activity can still be crashed, and (b) total crash

cost per period of all selected activities is smallest.

Crash each activity by one period each.

4. Update all activity times.

If desired due date has been reached, stop.

If not, return to Step 2.


Crash and Normal Crash and Normal Times and CostsTimes and Costs

$34,000

$33,000

$32,000

$31,000

$30,000

ActivityCost

CrashCost

NormalCost

Crash Time Normal Time

Time (Weeks)

Crash Cost/Week =

1 2 3

Crash Cost - Normal CostNormal Time - Crash Time

$34,000 - $30,0003 - 1

=

= $4,0002 Weeks

= $2,000/Week

Normal

Crash


Project CrashingProject Crashing

CriticalPath?CrashCrashNormalActivity

ABCDEFGH

23244352

11132221

$23,000 $34,000 $27,000 $49,000 $58,000 $30,500 $86,000 $19,000

$1,000 $2,000 $1,000 $1,000 $1,000 $500 $2,000 $3,000

Normal

$22,000 $30,000 $26,000 $48,000 $56,000 $30,000 $80,000 $16,000

Time (Weeks) Cost ($)Crash Costper Week

YesNoYesNoYesNoYesYes


A Linear Programming Model A Linear Programming Model for Crashing Decisionsfor Crashing Decisions

Use Linear programming to determine which activities to crash and how much they should be crashed

Decision VariablesXfin= the finish time of the projectXi = the earliest start time for activity iYi = the amount of time activity i is crashed

i = A, B, C, D,E, F, G, H


Objective functionMinimize Crash Cost =

ConstraintsCrash Time Constraints (maximum allowable crashing

time for each activity)

Project Completion ConstraintXfin <= 13

Constraints Describing the Network: Precedence Constraints. (ES of an activity)>= (EF of the Immediate Predecessor activity)

EF = ES + t If ES the earliest start time for an activity is known, the effect of crashing a

particular activity will be to reduce the t and hence EF, the earliest finish time


Precedence Constraints

Duration of activity i may be reduced by Yi. If activity A starts the earliest at XA, then the earliest finish (EF) is at (XA+2-YA). Earliest start time of activity C (namely, XC) can be no earlier than (XA+2-YA). XA =0

XB = 0XC XA + 2 - YA (precedence AC)

XD XA + 2 – YA (precedence AD) XD XB + 3 - YB (precedence BD) XE XC + 2 - YC (precedence CE) XF XC + 2 - YC (precedence CF) XG XD + 4 - YD (precedence DG) XG XE + 4 - YE (precedence EG) XH XF + 3 - YF (precedence FH) XH XG + 5 – YG (precedence GH) Xfin XH + 2 – YH (precedence HFin)

All Xi and Yi 0 (non-negativity)



Managing Project Costs

Steps of the Budgeting ProcessSteps of the Budgeting Process • Identify all costs with each of the activities.

Then add these costs together to get one estimated cost or budget for each activity.

• If you are dealing with a large project, several activities may be combined into larger work packages. A work package is simply a logical collection of activities. Since the Genaral Foundry project we have been discussing is small, one activity will be a work package.


Steps of the Budgeting ProcessSteps of the Budgeting Process

3. Convert the budget cost per activity into a cost per time period. To do this, we assume that the cost of completing any activity is spent at a uniform rate over time.

– If budgeted cost for given activity is $48,000 and activity's expected time is four weeks, budgeted cost per week is $12,000 (= $48,000/4 weeks).

4. Using the earliest and latest start times, find out how much money should be spent during each week or month to finish the project by the date desired.


PERT and Budgeting: Activity PERT and Budgeting: Activity Cost for General Foundry, Inc.Cost for General Foundry, Inc.

BudgetedCost per

Week

TotalBudgeted

Cost

LatestStart (LS)

EarliestStart (ES)Activity

ABCDEFGH

0023448

13

01244

108

13

$22,000 $30,000 $26,000 $48,000 $56,000 $30,000 $80,000 $16,000

$11,000 $10,000 $13,000 $12,000 $14,000 $10,000 $16,000 $ 8,000

ExpectedTime, t

23244352

Total $308,000


PERT and BudgetingPERT and Budgeting

Using the earliest start time, we can find the exact weeks during which the budget for each activity should be spent. These weekly amount can be summed for all the activities to arrive at the weekly budget for the entire project.


Budget Cost ($1000)for General Foundry Budget Cost ($1000)for General Foundry Inc., Using Earliest Start TimesInc., Using Earliest Start Times

Activity

ABCDEFGH

11110

2121

4

1312

2590

21110

2142

3

1013

2365

6

121410

36162

5

121410

36126

7

121410

36198

9

16

16228

8

14

14212

11

16

16260

10

16

16244

13

16

16292

12

16

16276

14

8

8300

15

8

8308

Total2230264856308016

Total to dateTotal/Week

Week

308


PERT and BudgetingPERT and Budgeting

Another budget can be computed using the latest start time. This budget will delay the expenditure of funds until the last possible moment.


Budget Cost ($1000)for General Foundry Budget Cost ($1000)for General Foundry Inc., Using Latest TimesInc., Using Latest Times

Activity

ABCDEFGH

111

1111

4

1013

2378

21110

2132

3

1013

2355

6

1214

26130

5

1214

26104

7

1214

26156

9

16

16198

8

1214

26182

11

1016

26240

10

16

16214

13

1016

26292

12

1016

26266

14

8

8300

15

8

8308

Total2230264856308016

Total to dateTotal/Week

Week

308


Budget Ranges for General Budget Ranges for General Foundry, Inc.Foundry, Inc.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

$300,000

$250,000

$200,000

$150,000

$100,000

$50,000

$0

TotalBudgetedCost

Weeks

Budget UsingEarliest Start

Times, ES

Budget UsingLatest StartTimes, LS


Budget Ranges for General Budget Ranges for General Foundry, Inc.Foundry, Inc.

Lester Harky can use any budget between the feasible ranges and still complete the air pollution project on time.

Budget shown in the previous figure are normally developed before the project is started. Then as the project is being completed, funds expended should be monitored and controlled.

Purpose of monitoring and controlling project costs is to ensure project is progressing on schedule and cost overruns kept to minimum.


Monitoring and Controlling Monitoring and Controlling Projects CostsProjects Costs

Is the Project on Schedule and within the budget?Value of work completed =

(percent of work completed)*(total activity budget)Activity difference =

actual cost –value of work completed

Activity difference <= 0 cost underrun

Activity difference >= 0 Cost overrun


Monitoring and Controlling budget Monitoring and Controlling budget Cost (week 6)Cost (week 6)

ActivityDifference

($)

TotalBudgeted

Cost

Percent ofCompletion

Actual Cost($)Activity

ABCDEFGH

20,00036,00026,0006,000

20,0004,000

00

10010010010202000

$22,000 $30,000 $26,000 $48,000 $56,000 $30,000 $80,000 $16,000

-2,000 6,000

0 1,200 8,800 -2,000

0 0

Value of WorkCompleted

($)

22,00030,00026,0004,800

11,2006,000

00

Total 100,000 112,000 12,000

Overrun


Monitoring and Controlling Monitoring and Controlling budget Costbudget Cost

Question: The value of work completed is on

$100,000, and the actual cost of the project to date is $112,000. How do these costs compare to the budget cost for week 6?

1. Project Management

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