1. MODULE 5: OPERATIONS MANAGEMENT UNIT 5.8 – PROJECT MANAGEMENT
Content
Critical Path Analysis (CPA)
Decision Trees

2. Learning Outcomes
Construct and interpret a network, identify the critical path and calculate the free and total float.
Describe how a Gantt Chart may supplement a CPA.
Construct and interpret decision trees and assess their value.

3. CRITICAL PATH ANALYSIS
Context
One of the largest construction project ever to take place was the channel Tunnel. The actual construction probably took the best part of five years, in addition to the planning process involved before the first excavator begin digging. Such a project required thousands of different tasks to be planned and coordinated, involving labour, materials and various pieces of machinery.
Each task will also have taken a different amount of time, which further complicates the planning process. Some of the tasks took place simultaneously, whilst some had to be scheduled before others, for example, the tunnel had to be dug before the rail lines could be laid.

4. CRITICAL PATH ANALYSIS
Context - Continued
Each activity will have been planned to take place for a certain number of days, weeks, months or even years. It would have been pointless, and very inefficient if the physical resources required for laying the track had been brought together at the beginning of the project when they would not have been needed for about two years. This would have resulted in huge cost for Eurotunnel's shareholders given that they would have been paying for resources simply to wait for their turn.
In order to plan for efficient scheduling of resources, create deadlines which acts as a target for completion and control costs of major projects like the channel tunnel, Eurotunnel will have used Critical Path Analysis. This allows for all activities to be displayed in diagrammatic forms, so as to calculate exactly when the resources are required and for how long. This process can then be used to organise and plan resources so that the business maximises their use and at the same time attempts to minimise costs.

5. The Nature of Projects
CPA may be used where the business faces problems that display the following characteristics.
Dependent Activities
Deadlines
Restricted Resources
ACTIVITY
Think of various ‘projects’ that display the characteristics for Critical Path Analysis. Write down the separate activities involved and try to establish a logical order in which the activities ought to be carried out.

6. Constructing the Critical Path Analysis Network
Arrow: Denotes an activity which has a duration
Node: Denotes the start and finish of each activity B A D C
The above means A begins on its own, then B and C may begin once A has finished. D may start once C has Finished

7. Critical Path Analysis Network DiagramB D
A and B begins together, C follows B, D follows A and E follows C and D.
Activity
Draw a network using the following information:
A,B and C begins together. D follows A, E follows B, F follows C and E.

8. Critical Path Analysis Network Diagram - The Use of Dummy Activity
Question:
If the arrowhead of the dummy activity was pointing the other way, describe the order and dependency of the network. A C
Dummy Activity – Used to ensure logical dependence of each activity is represented A B D
In this example, activity C is dependent upon the completion of both activities A and B while D is dependent on only B. To make the required link between A, B and C needs the use of a dummy activity, otherwise there would be no obvious dependent link between C and B.

9. Critical Path Analysis Network Diagram
Earliest Start Time of following activity (EST)
Latest Finish Time of previous activity (LFT)
Reference Number of Node
Earliest Start Time of each activity: The earliest time an activity can begin. This depends on the duration and order of previous activities.
Latest Finishing Time of each activity: The latest time an activity must finish so that the entire project can finish within minimum duration time.
Minimum Duration of the project: The earliest time a project may finish, given the order and duration of all activities.

10. Question From the following information construct a CPA Network
Activity
Description
Preceded by
Duration A
Order and deliver component A - 8 B
Order and deliver component B 5 C
Record sales/purchase on spreadsheet 1 D
Receive and check all components
A,B 2 E
Manufacture stage 1 6 F
Sub - assembly 1 G
Manufacture stage 2 3 H
Dispatch to customer
F,G

11. ANSWER D Node 1: EST of first three activities is 0.
Node 2: EST of D = 8 days
Node 3: EST of D + duration of D gives the EST of E and F as 10 days
Node 4: EST of E is 10 days, + duration of E means EST of G is 16 days.
Node 5: EST of F is 10 days, + duration of F is 18, but EST of G is 16 days + duration of G (3) which means H cannot take place until 19, that is, until the latest of both G and F.
Node 6: H and C takes 1 day which means that the earliest time the project can finish is 20 days.
ANSWER G 16 E 4 3 16 6 A 19 20 8 D 10 H 8 5 6 3 2 F 19 1 20 2 10 8 8 1 B 5 C 1

12. ANSWER FINDING THE LFT D
The LFT on Node 5 = 19 days.
Node 4: 19 – duration of G (3) = 16 days.
Node 3: LFT of F = 16 – 6 = 10 days. 19 – duration of F (8) = 11 days, so the lower of the two numbers is the LFT of D.
Node 2: 10 – 2 = 8.
Node 1: This must be zero, that is the lower of 8-8 = 0
ANSWER
FINDING THE LFT G 16 E 4 3 16 6 A 19 20 8 D 10 H 8 5 6 3 2 F 19 1 20 2 10 8 8 1 B 5 C 1
Note: If the project is to finish within 20 days, activity H must finish within 20 days, so activities F and G must finish by day 19

13. Calculation of Total Float:
Calculating the Float
The float identifies which activity can be delayed and will the delay affect the minimum duration time. This can be done in two ways:
The Total Float: Represents the amount of delay available on any activity which does delay the project duration, that is, how long an activity can be delayed or postponed so that the project is still completed within minimum duration time.
Calculation of Total Float:
Latest Finishing Time (LFT) – Duration - Earliest Starting Time (EST) of an individual activity

14. Calculating the Float Using the Diagrammatic Version1 8 1 2 7 3 10
Total Float = LFT – Duration – EST
10 – 7 – 1 = 2
Interpretation: The amount of delay available on this activity which does not delay the project duration is 2 days

15. From the CPA network below determine the Total Float of Each Activity
Question
From the CPA network below determine the Total Float of Each Activity G 16 E 4 3 16 6 A 19 20 8 D 10 H 8 5 6 3 2 F 19 1 20 2 10 8 8 1 B 5 C 1

16. Answers Activity LFT - Duration - EST = Total Float A 8 B 5 3 C 20 1B 5 3 C 20 1 19 D 10 2 E 16 6 F G H
Note: A,D,E,G,H represents the Critical Path - This means there can be no delays between completing the proceeding tasks and starting the next one on this path without prolonging the total time of the project.

17. The Free Float
This represent the amount of delay available on each activity which does not delay the EST of the next activity.
Calculation of the Free Float
Free Float = EST at the end – Duration – EST at the beginning 10 6 3

18. From the CPA network below determine the Free Float of Each Activity
Question
From the CPA network below determine the Free Float of Each Activity G 16 E 4 3 16 6 A 19 20 8 D 10 H 8 5 6 3 2 F 19 1 20 2 10 8 8 1 B 5 C 1

19. Answers Activity EST (at end) - Duration - EST (at beginning)
= Free Float A 8 B 5 C 20 1 19 D 10 2 E 16 6 F G 3 H
Note: Free float tends to be more appropriate when the delivery of materials must be on time or when labour is involved in other activities and cannot be moved on to another job. For example, F can be delayed by 1 day and H will still be able to commence on time

20. Advantage of Critical Path Analysis
It provides decision makers with a picture of a problem which may be easier to interpret.
It can be used to suit a range of circumstances and help solve a variety of business problems.
It reduces the time lost between tasks, ensuring that projects run smoothly.
It encourages forward planning.
It forces decision makers to consider all aspects of the project.
Improve efficiency in production.
Control cash flow

21. Disadvantages of Critical Path Analysis
Construction of network alone will not guarantee the smooth completion of a project.
Some projects are immense, making network diagrams complex and unmanageable.
Network analysis will only be helpful if the data used to construct diagrams is reliable.

22. Must be preceded by activity (ies)
Questions
Activity
Must be preceded by activity (ies)
EST. Duration (days) A - 4 B 5 C 6 D 7 E 14 F
C, D G 12 H
E,F I 10 J
H,I K

23. Source: IBO, May 1999, Business and Organisation Paper 2
Questions
a). Construct a network (Critical Path) diagram for the construction project. (7 marks).
b). Calculate the Earliest Starting and Latest Finishing Times for each activity and identify the Critical Path (3 marks).
c). Late delivery in materials cause the delays of the following activities:
Activity C – 5 days
Activity E – 3 days
Activity F - 8 days
Show through worked examples whether these delays will lead to an increase in the total duration time of the project. Support your conclusions with suitable explanations. (4 marks)
d). Evaluate the use of network (Critical Path) analysis to improve labour, efficiency, cash flow and stock control.
Source: IBO, May 1999, Business and Organisation Paper 2

24. Decision Trees Context
No technique can eliminate the risk involved in taking decisions, but managers can help themselves greatly if they adopt a logical approach to decision-making. One method of considering all the options available and the chance of them occurring is known as decision trees.
This device is a diagram that is drawn to represent three main features of a decision:
All the options open to a manager.
The different possible outcomes resulting from these options.
The chances of these outcomes occurring.
In brief, a decision tree may be defined as a diagram that sets out the options connected with a decision and the outcomes that my result from ‘chance’, following these options. The manager can minimise the risk involved.

25. Features of a decision tree
Decision Point: Points where decisions have to be made. They are represented by squares.
Outcomes: Points where there are different possible outcomes in a decision tree are represented by circles called decision nodes.
Probability or Chance: The likelihood of possible outcomes happening is represented by probabilities.
Expected Values: This is the financial outcome of a decision, which is based on the predicted profit and loss of an outcome and the probability of that outcome occurring.

26. Constructing a Decision Tree
It is constructed from left to right.
Each branch of the tree represents and option together with a range of consequences of outcomes and the chances of these occurring.
Decision points are denoted by a square – these are decision nodes.
A circle shows that a range of outcomes may occur – a chance node.
Probabilities are shown alongside each of these possible outcomes. These probabilities measure the chance of an outcome occurring.
They pay-offs are the expected financial gains of losses of a particular outcome.

27. Outcomes/Chance Nodes
A Simple Decision Tree
Expected Values
Outcomes/Chance Nodes
Probability/ Chance
Profit or Loss
Decision Point
Success
$15 Million
0.2
Launch New Campaign B
Failure A
-$2 Million
0.8
Success
$7 Million
0.4 C
Retain old Campaign
Failure
-$1 Million
0.6
A simple decision tree based on a decision whether to retain and existing advertising campaign or begin a new one

28. Calculating the Expected Value
Expected Value = Probability of an event occurring * Expected Results
Calculating the expected Value of the new campaign
Expected Value = 0.2 * $15m * (-$2m)
(Probability) (Expected Profit)+ (Probability) (Expected Profit)
=$3m - $1.6m
=$ 1.4m
Calculating the expected Value of retaining current campaign
Expected Value = 0.4 * $7m + 0.6* (-$1m)
= $2.28m – 0.6m
= $2.2m

29. Question
A friend has given you a sum of money for your 18th birthday. Which you want to invest in shares. A local independent financial advisor suggest that you ought to consider three companies:
Techy-Co- A high tech manufacturer.
Risky – Co- A new manufacturer, selling a brand new product which is predicted to be all ranges over the next two or three years.
Large – Co – A multinational conglomerate which sells to a wide range of industries.

30. Question Cont’d Chance of Success Chance of Failure 0.5 0.3 0.7 0.8
Techy-Company
0.5
Risky - Company
0.3
0.7
Large Company
0.8
0.2
Pay-off if Successful
Pay-off if Failure
$2,000
$800
$3,000
$500
$1,200
$900
Required: Calculate the expected value for each of the three companies and decide on the best investment

31. Mini Case This information is summarised below
A business is deciding whether or not to launch a new product. It could do some market research, costing $12,000 which would mean the chance of a successful launch would be estimated at 70%. Without market research the chance of a successful launch would be only 50%. A successful launch would earn profit of $ 60,000 for the business, but if it failed, only $20,000 would be earned.
This information is summarised below
Forecast pay –off with market research
Without Market Research
Successful Launch
$60, %
50%
Failed Launch
$20, %
From the information, prepare a diagram of expected values and discuss the best course of action for the business.

32. ANSWER Expected Values Node 1:( 60,000*0.7) + (20,000*0.3) =$48,000
$60,000
Success 0.7
Launch
Research($12,000)
Failure 0.3
$20,000
Do not launch $0
Success 0.5
$60,000
Launch without research
Success 0.5
$20,000
Expected Values
Node 1:( 60,000*0.7) + (20,000*0.3) =$48,000
Node 2: (60,000*0.5) + (20,000*0.5) = $40,000
Question? Which option do you recommend? Justify your answer.

33. Problems of using decision trees
It is purely quantitative technique, which is designed to allow for probability and pay-off. There is no allowance for external issues which may be relevant to the decision being made.
The probabilities are extremely difficult to predict accurately, given their nature.
The forecast pay-offs are assumed to be correct, which may not be the case in reality. If both probability and forecast pay-offs are incorrect then the decision becomes as good as the information which is issued.
There are no in-between value for probability, that is, the pay-off can be one of three options – successful, moderate, poor. All the probabilities must add up to one, but in reality there is a wider range of answers, each with an associated probability.

34. Conclusion
Given the problems and assumptions, what is the point of using decision trees in the first place?
They provide a starting point in terms of allocating probabilities and pay-offs to different decisions.
They allow all potential decisions to be viewed simultaneously.
They can therefore act as an aid to decision making and must be used in conjunction with other factors which affect the decision.

35. END OF UNIT