OPERATIONS AND SUPPLY CHAIN MANAGEMENT Assignment 1
jams_r1
lec_02_online.pptxOperations and Supply Chain Management
MGMT 3306
Lecture 02
Instructor: Dr. Yan Qin
Outline
Project Management
What is Project Management?
Three types of projects
Work Breakdown Structure (WBS)
Project Management Techniques: PERT and CPM
Cost-Time Trade-Offs and Project Crashing
A Critique of PERT and CPM
2
Project Management
A project is a series of related jobs usually directed toward some major output and requiring a significant period of time to perform.
Project Management is the planning, scheduling, and controlling of resources to meet the technical, cost, and time constraints of the project.
3
Examples of Projects
Building Construction
Research Project
Three Phases of Project Management
The management of projects involves three phases:
Planning - goal setting, defining the project, team organization
Scheduling - relates people, money, and supplies to specific activities and activities to each other
Controlling - monitors resources, costs, quality, and budgets; revises plans and shifts resources to meet time and cost demands
Project Planning
Figure 3.1
Before Start of project During
project Timeline project
Project Scheduling
Figure 3.1
Before Start of project During
project Timeline project
Project Controlling
Figure 3.1
Before Start of project During
project Timeline project
Project Planning, Scheduling, and Controlling
Figure 3.1
Before Start of project During
project Timeline project
Project Organizations
There are three types of project based on the organizational structures used to tie the project to the parent firm:
Pure project: A self-contained team works full time on a project;
Functional project: A project housed within a functional division.
Matrix project: A project that uses people from different functional areas.
The project manager decides what tasks to complete and when;
The functional managers control which people and technologies to be used in the project.
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Example of Matrix Project
Marketing Operations Engineering Finance
Project 1
Project 2
Project 3
Project 4
Work Breakdown Structure (WBS)
Work Breakdown Structure (WBS): defines the hierarchy of project tasks, subtasks, and work packages
Program
Project 1
Project 2
Task 1.1
Subtask 1.1.1
Work Package 1.1.1.1
Level
1
2
3
4
Task 1.2
Subtask 1.1.2
Work Package 1.1.1.2
Task is a further subdivision of a project, usually shorter than several months.
Work package is a group of activities combined to be assignable to a single organizational unit, usually an individual.
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Example: WBS – Large Optical Scanner Design
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Purposes of Project Scheduling
Shows the relationship of each activity to others and to the whole project
Identifies the precedence relationships among activities
Encourages the setting of realistic time and cost estimates for each activity
Helps make better use of people, money, and material resources by identifying critical bottlenecks in the project
Project Management Techniques
Gantt chart
Critical Path Method (CPM)
Program Evaluation and Review Technique (PERT)
Gantt Chart
Charts are useful because their visual presentation is easily understood.
Gantt chart: a bar chart showing both the amount of time involved and the sequence in which activities can be performed
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PERT and CPM
Both PERT and CPM are network techniques developed in 1950’s, which consider the inter-dependency among project activities.
CPM by DuPont for chemical plants (1957): A project management technique that uses only one time factor per activity. (Activity times are assumed to be certain.)
PERT by Booz, Allen & Hamilton with the U.S. Navy, for Polaris missile (1958): A technique that uses three time estimates for each activity. (Activities times are assumed to be uncertain.)
Questions PERT and CPM can answer
When will the entire project be completed?
What are the critical activities or tasks in the project?
Which are the noncritical activities?
What is the probability the project will be completed by a specific date?
Is the project on schedule, behind schedule, or ahead of schedule?
Is the money spent equal to, less than, or greater than the budget?
If the project must be finished in a shorter time, what is the way to accomplish this at least cost?
PERT and CPM: 6 Steps
Both PERT and CPM follow six basic steps:
Define the project and prepare the work breakdown structure
Develop relationships among the activities - decide which activities must precede and which must follow others
Draw the network connecting all of the activities
Assign time and/or cost estimates to each activity
Compute the longest time path through the network – this is called the critical path
Use the network to help plan, schedule, monitor, and control the project
Step 3: Draw a project network
A project network is a diagram of all the activities and the precedence relationships between the activities in a project.
There are two approaches for drawing a project network:
Activity-on-Node (AON): A network diagram in which nodes represent activities.
Activity-on-Arrow (AOA): A network diagram in which arrows represent activities.
AON Vs. AOA
Activity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
A comes before B, which comes before C.
(a)
A
B
C
B
A
C
A and B must both be completed before C can start.
(b)
A
C
C
B
A
B
B and C cannot begin until A is completed.
(c)
B
A
C
A
B
C
AON Vs. AOA
Activity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
C and D cannot begin until both A and B are completed.
(d)
A
B
C
D
B
A
C
D
C cannot begin until both A and B are completed; D cannot begin until B is completed. A dummy activity is introduced in AOA.
(e)
C
A
B
D
Dummy activity
A
B
C
D
AON Vs. AOA
Activity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
B and C cannot begin until A is completed. D cannot begin until both B and C are completed. A dummy activity is again introduced in AOA.
(f)
A
C
D
B
A
B
C
D
Dummy activity
AON Vs. AOA
The AOA approach sometimes needs the addition of a dummy activity, represented by a dashed line, to clarify relationships.
A dummy activity consumes no time or resources, but is required in AOA when
A network has two activities with identical starting or ending events; or
Two or more activities follow some, but not all, “preceding” activities.
We will focus on AON in this class.
AON Example: Milwaukee Paper
| Activity | Description | Immediate Predecessors |
| A | Build internal components | — |
| B | Modify roof and floor | — |
| C | Construct collection stack | A |
| D | Pour concrete and install frame | A, B |
| E | Build high-temperature burner | C |
| F | Install pollution control system | C |
| G | Install air pollution device | D, E |
| H | Inspect and test | F, G |
Table 3.1
Given the following activities and precedence relationships in a project, draw an AON network representing the project.
AON Example: Project Network
A
Start
B
Start Activity
Activity A
(Build Internal Components)
Activity B
(Modify Roof and Floor)
We add a dummy activity called “Start” to serve as the unique starting activity of the project since we have more than one original starting activity (A and B) in this example.
AON Example: Project Network
C
D
A
Start
B
Activity A Precedes Activity C
Activities A and B Precede Activity D
We now add activity C and activity D to the network. Node C represents activity C and Node D represents activity D.
Note that arrows indicate precedence relationships between different activities in AON.
AON Example: Project Network
G
E
F
H
C
A
Start
D
B
Arrows Show Precedence Relationships
We will now look at Step 4
Both PERT and CPM follow six basic steps:
Define the project and prepare the work breakdown structure
Develop relationships among the activities - decide which activities must precede and which must follow others
Draw the network connecting all of the activities
Assign time and/or cost estimates to each activity
Compute the longest time path through the network – this is called the critical path
Use the network to help plan, schedule, monitor, and control the project
Step 4: Determine project schedule
To determine project schedule, we calculate two distinct starting and ending times for each activity.
Earliest start (ES): earliest time at which an activity can start, assuming all predecessors have been completed.
Earliest finish (EF): earliest time at which an activity can be finished
Latest start (LS): latest time at which an activity can start so as to not delay the completion time of the entire project
Latest finish (LF): latest time by which an activity has to be finished so as to not delay the completion time of the entire project
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A node symbol with times
A
Activity Name or Symbol
Earliest Start
ES
Earliest Finish
EF
Latest Start
LS
Latest Finish
LF
Activity Duration
2
Forward Pass
ES and EF are determined using Forward Pass.
In the forward pass, we begin with the starting node and work forward.
Earliest Start Time Rule:
If an activity has only a single immediate predecessor, its ES equals the EF of the predecessor
If an activity has multiple immediate predecessors, its ES is the maximum of all the EF values of its predecessors
ES = Max {EF of all immediate predecessors}
Forward Pass
Earliest Finish Time Rule:
The earliest finish time (EF) of an activity is the sum of its earliest start time (ES) and its activity time
Start
0
0
ES
0
EF = ES + Activity time
Take the Start node in the previous Milwaukee problem for example:
Forward Pass
Here are the ES and EF of Node A in the previous Milwaukee example:
Start
0
0
0
A
2
2
EF of A = ES of A + 2
0
ES of A
Forward Pass
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
Here are the ESs and EFs of all the activities in the previous Milwaukee example:
Backward Pass
In backward pass, we begin with the last event and work backwards.
Latest Finish Time Rule:
If an activity is an immediate predecessor for just a single activity, its LF equals the LS of the activity that immediately follows it
If an activity is an immediate predecessor to more than one activity, its LF is the minimum of all LS values of all activities that immediately follow it
LF = Min {LS of all immediate following activities}
Backward Pass
Latest Start Time Rule:
The latest start time (LS) of an activity is the difference of its latest finish time (LF) and its activity time
LS = LF – Activity time
Milwaukee Example: LS/LF
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
LF = EF of Project
15
13
LS = LF – Activity time
We start from the ending node and work backward.
Milwaukee Example: LS/LF
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
13
15
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
LF = Min(LS of following activity)
10
13
LF of Node F = LS of Node H since Node H is the only node following Node F.
Milwaukee Example: LS/LF
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
13
15
10
13
8
13
4
8
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
LF = Min(4, 10)
4
2
There are two nodes, Node E and Node F, following Node C.
Milwaukee Example: LS/LF
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
13
15
10
13
8
13
4
8
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
4
2
8
4
2
0
4
1
0
0
Project network with all the ES/EF and LS/LF.
We will now look at Step 5
Both PERT and CPM follow six basic steps:
Define the project and prepare the work breakdown structure
Develop relationships among the activities - decide which activities must precede and which must follow others
Draw the network connecting all of the activities
Assign time and/or cost estimates to each activity
Compute the longest time path through the network – this is called the critical path
Use the network to help plan, schedule, monitor, and control the project
Step 5: Determine Critical Path
The critical path is the longest path through the network.
The critical path is the shortest time in which the project can be completed.
Any delay in critical path activities delays the project.
Critical path activities have no slack time.
So in order to find the critical path(s), we need to first calculate the slack times of each activity and identify the activities with zero slack time.
Notes – Critical path and ES EL
Any sequence of activities between a project’s start and finish is a path.
The critical path is just the path that takes the longest time to complete.
There can be more than one critical paths.
An activity can be started at ES, LS, or any time between ES and LS.
Notes – Slack times
Activity slack is the maximum length of time an activity can be delayed without delaying the entire project.
Activities on the critical path have zero slack.
Activity slack can be calculated in two ways:
Slack = LS – ES OR
Slack = LF – EF
Example: Milwaukee
We have calculated the ES/EF, LS/LF times for the activities in the Milwaukee example. Now we would like to determine the critical path of the project.
Earliest Earliest Latest Latest On Start Finish Start Finish Slack Critical Activity ES EF LS LF LS – ES Path?
A 0 2 0 2 0 Yes
B 0 3 1 4 1 No
C 2 4 2 4 0 Yes
D 3 7 4 8 1 No
E 4 8 4 8 0 Yes
F 4 7 10 13 6 No
G 8 13 8 13 0 Yes
H 13 15 13 15 0 Yes
Example: Milwaukee
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
13
15
10
13
8
13
4
8
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
4
2
8
4
2
0
4
1
0
0
The path formed by blue arrows is the critical path.
Example: Start from Step 3
Consider the following consulting project:
Identify the critical path in the project and determine the duration of the critical path and slack times for all activities.
Detailed solution is given in the document titled “In-class examples” posted under this week’s learning module.
Activity
Designation
Immed. Pred.
Time (Weeks)
Assess customer's needs
A
None
2
Write and submit proposal
B
A
1
Obtain approval
C
B
1
Develop service vision and goals
D
C
2
Train employees
E
C
5
Quality improvement pilot groups
F
D, E
5
Write assessment report
G
F
1
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Variability in Activity Times
CPM assumes we know a fixed time estimate for each activity and there is no variability in activity times
PERT uses a probability distribution, Beta distribution, for activity times to allow for variability
Statistical analysis requires three reasonable estimates of activity times
Optimistic time (a)
Most likely time (m)
Pessimistic time (b)
Beta Distribution
The mean of the beta distribution can be estimated by
The variance of the beta distribution for each activity is
We use Beta Distribution to calculate the mean and variance of the completion time of each activity.
Example: Mean and Variance
Suppose that the project team has arrived at the following time estimates for activity B (site selection and survey) of the St. John’s Hospital project:
a = 7 weeks, m = 8 weeks, and b = 15 weeks
Calculate the expected time and variance for activity B.
Note that the expected time does not equal the most likely time. These will only be the same only when the most likely time is equidistant from the optimistic and pessimistic times.
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Example: Solution
Expected completion time of the activity
Variance
= 1.78
Determine probabilities of project completion times
According to the Central Limit theorem, the expected completion of the whole project
, which is the mean of the normal distribution.
Assume that the activities times are independent, the variance of the completion time of the whole project
Determine probabilities of project completion times
Let D denote the expected project completion time, 6 weeks for example.
Using z-transformation,
z is the # of standard deviations to the left or right of zero in the standard normal distribution.
Using the z value, we then find the corresponding probability in Appendix I of the textbook. That probability is the probability of the project being completed in D amount of time.
Example: Determine Probability
Questions: What is the probability of completing the project in 35 weeks? Detailed solution is available in the doc “In-class Examples”.
Outline
Project Management
What is Project Management?
Three types of projects
Work Breakdown Structure (WBS)
Project Management Techniques: PERT and CPM
Cost-Time Trade-Offs and Project Crashing
A Critique of PERT and CPM
56
Project Crashing
Basic assumption: There is a relationship between activity completion time and project cost.
Time cost models: Determine the optimum point in time-cost tradeoffs
Activity direct costs: costs associated with expediting activities.
Project indirect costs: costs associated with sustaining the project.
Procedure for Project Crashing
Prepare a network diagram for the project
Determine the cost per unit of time to expedite each activity
Find out the critical path
Repeatedly shorten the critical path by crashing the least expensive activity based on the costs to crash per period.
Stop until it is not profitable to crash.
Finding the minimum cost schedule
Crash only activities that are critical.
Crash from least expensive to most expensive.
Each activity can be crashed until
it reaches it’s maximum time reduction
it causes another path to also become critical
it is more expensive to crash than not to crash
Continue until no more activities should be crashed.
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Example: Cost to crash per period
Please calculate the cost to crash per period for each of the following activities.
Detailed solution available in the document “In-class examples”.
Example: Project crash
This project, under normal conditions takes 20 days. Suppose each day the project runs incurs an indirect project cost of $1400 (overhead). What activities should be crashed if any?
Detailed solution available in the document “In-class examples”.
Advantages of PERM/CRM
Especially useful when scheduling and controlling large projects
Straightforward concept and not mathematically complex
Graphical networks help highlight relationships among project activities
Critical path and slack time analyses help pinpoint activities that need to be closely watched
Project documentation and graphics point out who is responsible for various activities
Applicable to a wide variety of projects
Useful in monitoring not only schedules but costs as well
Disadvantages of PERM/CRM
Project activities have to be clearly defined, independent, and stable in their relationships
Precedence relationships must be specified and networked together
Time estimates tend to be subjective and are subject to fudging by managers
There is an inherent danger of too much emphasis being placed on the longest, or critical, path
