Project Management

MD707 Operations Management

Professor Joy Field

Definition of a Project

A project is an interrelated set of activities that has a definite starting and ending point within a limited time frame and results in a unique product or service.

Examples of projects include building construction, introducing a new product, and software development.

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Some Terminology …

Activity The smallest unit of work effort consuming both time and resources

that the project manager can schedule and control

Precedence relationship A sequencing constraint between interrelated activities by which one

activity cannot start until a preceding activity has been completed

Schedule A plan that sets priorities, determines start and finish times, and

allocates resources to accomplish the activities

 

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Project Management Approaches

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Predictive(e.g. CPM, waterfall, stage

gate)

Adaptive(e.g. agile)

Activities Low uncertainty High uncertainty

Precedence relationships Low uncertainty High uncertainty

Activity duration Low or high uncertainty High uncertainty

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Project Management Using Network Models

Describe the project Define project activities Determine precedence relationships

Diagram the network Nodes (circles) and arcs (arrows) Activity-on-node (AON) network - Nodes are activities and arcs

show precedence relationships

First two steps:

Project Management ExampleSt. John’s Hospital

Activity DescriptionImmediate

Predecessor(s)A Select administrative and medical staff. ---

B Select site and do site survey. ---

C Select equipment. A

D Prepare final construction plans and layout. B

E Bring utilities to the site. B

F Interview applicants and fill positions in nursing, support staff, maintenance, and security.

A

G Purchase and take delivery of equipment. C

H Construct the hospital. D

I Develop an information system. A

J Install the equipment. E, G, H

K Train nurses and support staff. F, I, J6

AON Network for St. John’s Hospital Project

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Start

A

G

D H

E

C

F

I

B

K

J

Finish

Determining the Critical Path

Activity Time (weeks) Path Length (weeks)

A 12

B 9 A-F-K 28

C 10

D 10 A-I-K 33

E 24

F 10 A-C-G-J-K 67

G 35

H 40 B-D-H-J-K 69*

I 15

J 4 B-E-J-K 43

K 6

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*critical path = longest path through the network

Network Time Calculations

Earliest finish time (EF) for an activity EF = ES + t

   Earliest start time (ES) for an activity

ES = Max [EF times of all immediately preceding activities]   Latest start time (LS) for an activity

LS = LF – t   Latest finish time (LF) for an activity

LF = Min[LS times for all immediately following activities]

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Calculating Activity Slacks

Activity LF EF Slack

A 14 12 2

B 9 9 0

C 24 22 2

D 19 19 0

E 59 33 26

F 63 22 41

G 59 57 2

H 59 59 0

I 63 27 36

J 63 63 0

K 69 69 0

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Activity slack: LS-ES or LF-EF, Critical path in bold

Calculating Time Estimates

Optimistic time ( ) Shortest time during which an activity can be completed

  Most likely time ( )

Best estimate of average time

  Pessimistic time ( )

Longest time an activity can take

  Activity’s expected time ( ) and variance ( ) with beta

distribution

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Calculating Probabilistic EstimatesSt. John’s Hospital Example

ActivityOptimistic

( )Most likely

( )Pessimistic

( )Expected time ( )

Variance ( )

A 11 12 13

B 7 8 15

C 5 10 15 10 2.78

D 8 9 16 10 1.78

E 14 25 30 24 7.11

F 6 9 18 10 4.00

G 25 36 41 35 7.11

H 36 40 45 40 2.78

I 10 13 28 15 9.00

J 1 2 15 4 5.44

K 5 6 7 6 0.11

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Time estimates (weeks)

Analyzing Probabilities

Probabilities can be assessed using the z-transformation formula

Assuming the activity times are independent, the path standard deviation is the square root of the sum of the activity time variances.

To determine the probability of completing a project in a specified amount of time Calculate the probability of each of the paths being completed in that

amount of time based on the value of z. For any value of z that is greater than 3, the probability that the corresponding path will be completed in that amount of time can be considered to be 100%.

If all paths are independent, then the probability of completing a project in the specified amount of time is the product of the individual path probabilities.

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deviation standardPath

meanPath - timeSpecifiedz

Hospital Project Completion Time Probabilities

PathProbability of

completion in 72 weeks

A-F-K (72 – 28)/2.05 = 21.5 100%A-I-K (72 – 33)/3.04 = 12.8 100%

A-C-G-J-K (72 – 67)/3.94 = 1.27 90%B-D-H-J-K (72 – 69)/3.45 = 0.87 81%

B-E-J-K (72 – 43)/3.80 = 7.6 100%

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How likely is it that the hospital project will be completed in 72 weeks?

Analyzing Costs in a Project

Direct costs and time Normal time Normal cost Crash time Crash cost

Cost assumptions Linear costs per unit of time (The problems in your textbook do

not necessarily make this assumption.)

Indirect costs and penalty costs

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Determining the Minimum-Cost Schedule

Step 1 Determine the project’s critical path(s).

Step 2 Find the least expensive activity or activities on the critical path(s) to

crash. Step 3

Reduce the time for this activity until the first of (a) it cannot be further reduced, (b) another path becomes critical, or (c) the increase in direct costs exceeds the savings that result from shortening the project. If more than one path is critical, the time for an activity on each path may have to be reduced simultaneously.

Step 4 Repeat this procedure until the increase in direct costs is less than the

savings generated by shortening the project.

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Direct Cost and Time Data for Hospital Project

ActivityNormal

time(wks)

Normal cost($K)

Crash time(wks)

Crash cost($K)

Max. time reduction

(wks)

Cost of crashing per week

A 12 $12 11 $13 1 $1,000

B 9 50 7 64 2 7,000

C 10 4 5 7 5 600

D 10 16 8 20 2 2,000

E 24 120 14 200 10 8,000

F 10 10 6 16 4 1,500

G 35 500 25 530 10 3,000

H 40 1,200 35 1,260 5 12,000

I 15 40 10 52.5 5 2,500

J 4 10 1 13 3 1,000

K 6 30 5 34 1 4,000

Totals $1,992 $2,209.517

Hospital Project Minimum-Cost Schedule

Critical path

Crash activity

Project duration

Crash costIndirect

cost change

Penalty cost

change

Total cost

change

B-D-H-J-K 69 weeks

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Assume:Indirect cost = $8,000/week, Penalty cost = $20,000 per week after Week 65