PSBA-MANILA
ACCOUNTING 14
TOPIC: Quantitative Techniques in Business
Prof. C. Gonzaga
NETWORK PLANNING TECHNIQUES: PERT-CPM (PROJECT EVALUATION AND REVIEW TECHNIQUECRITICAL PATH METHOD)
Network planning techniques involves graphical representation of projects as a sequence of
tasks, forming a picture similar to that of a highway (or electrical) network
 PERT (developed in the late 1950s by the US Defense Department for the purpose of planning
the development of the Polaris missile)
 CPM (developed in the late 1959s) at Remington-Rand and Du Pont for applications in the
chemical industry.)
Sample Application of Network Planning Techniques
 Auditing
 R&D
 Monthly financial closing
 Plant construction
 New product planning
 Shop loading and sequencing
 Personnel planning
 Piping installation
 Refining systems
 Market research
 Computer programming
 Budget preparation

CPM Analysis (Activity-On-Node or AON Diagram)
Nodes – represent the activities
Arrors (Arcs) – represent the predecences between activities
Path- is a sequence of activities connecting the start and finish of the project.
Critical Path – the longest path (in terms of total number of days of completion) which connects
activities with zero slack time from start to finish. Each activity in the critical path is a critical
activity in that it must start and finish on time, otherwise, the completion time of the project will
be delayed.
Non-critical path activity – an activity which has a slack time, therefore, can be delayed.
Slack time – allowable time for delay
Formula: SLACK = Late Start (LS) - Early Start (ES)
Or
Late Finish (LF) – Early Finish (EF)
Two (2) Methods in creating a CPM Network
(1) Enumeration Method
(2) Two-pass method : Forward Pass (ES and EF) ; Backward Pass (LF-LS)
PERT Analysis (AOA Network or activity-on-arc diagram)
Dummy activity - an activity which requires no time to complete and is inserted simply to maintain
the appropriate precedence relationships.
Event – the start or finish of an activity
Formula:
Expected Activity Time
Expected Activity Time = optimistic time + (4 * most likely time) + pessimistic time
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Cost Analysis
 Cost Control The original goal of network planning is to provide decision-makers with the ability
to plan and control the completion of projects by providing them with an understanding of the
task times, with the end purpose of controlling costs.
 Crashing Activities. It is possible that the project completion time as determined by the network
planning may be unsatisfactory in that it is too long. In such cases, it may be possible to
expedite some or all of the activities. Crashing is reducing the completion time for an activity. Of
course crashing usually can be accomplished at some costs – e,g, through the use of overtime,
which is more expensive but faster.
 Crash time – the minimum possible time required to perform the activity
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

Crash cost – the cost of performing the activity in its crash time.
Formula:
Daily crash cost = Cost increase due to crashing
Time decrease due to crashing
= Crash cost – Normal cost
Normal time – Crash time
GATT CHARTS (developed by Henry Gantt) – a representation of the timing of activities on a bar chart.
CLASS PROBLEM 1
Charice Construction Company has the following table that describes the steps necessary for designing
and building a township playground. Each activity that is part of the project is listed along with its
expected length of time to completion and its prerequisite activities.
Code
Activity Name
A
Planning
B
Purchasing
C
D
Excavation
Sawing
E
Placement
F
Assembly
G
Infill
H
Outfill
I
Decoration
Description
Time (In days)
Find
location,
determine
resource
requirements
Requisition lumber
and sand
Dig and grade
Saw lumber into
appropriate sizes
Position lumber in
correct locations
Nail
lumber
together
Put sand in and
under equipment
Put dirt around
equipment
Landscape, paint
20
Immediate
Predecessors
None
60
Planning
100
30
Planning
Purchasing
20
10
Sawing,
excavation
Placement
20
Assembly
10
Assembly
30
Infill, outfill
REQUIRED: 1. Develop a Gantt Chart. What is the completion time (in number of days)? _______
A
B
C
D
E
F
G
H
I
0
50
days
100
days
150
days
200 days
1. Develop a CPM diagram. What is the project’s completion time (in number of days)? Identify the
critical path. Enumerate the critical activities. Determine the slack time of each non-critical
activity.
Activity Code
A
B
C
D
E
F
G
H
I
Early Start
Late Start
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Slack = LS – ES
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2. Give the following table for the normal and crash times and costs for playground activities,
determine the crash cost per day in pesos:
Activity
Normal
Time Normal cost (in Crash time (in Crash Cost (in Crash cost per
(in days)
thousand
days)
thousand
day
(in
pesos)
pesos)
thousand
pesos)
A
20
300
15
450
B
60
2,100
50
2,140
C
100
4,000
75
4,500
D
30
2,850
20
3,000
E
20
500
F
10
200
G
20
400
H
10
600
I
30
1,350
12,300
CLASS PROBLEM 2
Given the following table of a project:
Activity Code
Immediate predecessor
A
None
B
A
C
A
D
B, C
E
B, D
F
E
G
F
H
G
Time (in number of months)
1
6
1
2
2
2
12
4
REQUIRED:
1. Draw a CPM diagram.
2. Determine the project’s completion time.
3. Determine the critical path.
4. Determine the slack time per activity using the two-pass method.
CLASS PROBLEM 3
Given a PERT diagram below, answer the following questions:
•
•
•
•
•
1: Which tasks are on the critical path?
2: What is the slack time for tasks C, D and G?
3: Task C is delayed by one day. What impact would this have on the completion date of the
project? Why?
4: Task A will be delayed by 2 days because some equipment has arrived late. If the project
manager wants to finish the project on time he will need to shorten the duration of one or more
of the tasks. How can he achieve this?
5: The project manager reduces the durations of tasks D and F by one day each. How will this
affect the finishing date of the project?
CLASS PROBLEM 4
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California Building Corporation uses the critical path method to monitor construction jobs. The
company is currently 2 weeks behind schedule on Job#181, which is subject to a P10,500 per week
completion penalty. Path A-B-C-F-G-H-I has a normal completion time of 20 weeks, and critical path AD-E-F-G-H-I has a normal completion time of 22 weeks. The following activities can be crashed:
Activities
BC
DE
EF
Cost to Crash 1 week
P8,000
10,000
8,800
Cost to Crash 2 weeks
P15,000
19,600
19,500
California Building desires to reduce the normal completion time of Job#181 and, at the same time,
report the highest possible income for the year. California building should crash: (Multiple choice)
a.
b.
c.
d.
Activity
Activity
Activity
Activity
BC 1 week and activity EF 1 week.
DE 1 week and activity EF 1 week.
BC 2 weeks.
EF 2 weeks.
CLASS PROBLEM 5
The network below describes the interrelationships of several activities necessary to complete a
project. The arrows represent the activities. The numbers between the arrows indicate the number of
months to complete each activity:
REQUIRED:
1. How many paths are there in this PERT diagram?
2. What is the critical path in the PERT diagram?
3. What is the shortest time to complete the entire project?
4. What is the slack time (in number of months) for Path A-B-E?
5. What is the slack time for Path A-B-C-D-E
end
start
Activity
A-B
A-C
B-C
B-E
C-D
D-E
Time (in months)
4
6
8
12
10
14
CLASS PROBLEM 6
The PERT network diagram and corresponding activity cost chart for a manufacturing project at
Networks, Inc. is presented below. The numbers in the diagram are the expected times (in days) to
perform each activity in the project.
Activity
AB
AC
AD
BE
CE
DE
BC
BD
Expected Time
4.5 days
5.0
5.5
7.0
6.5
7.5
1.0
0.50
Normal Cost
P3,000
5,000
4,000
6,000
8,000
6,000
2,500
2,000
Crash Time
3.5 days
4.5
4.0
5.0
5.0
6.5
0.50
0.25
Crash Cost
P4,000
5,250
4,750
7,000
9,200
6,750
3,500
2,500
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REQUIRED:
1. The critical path is:
a. ACE
b. ABE
c. ADE
d. ABCE
e. ABDE
2.
a.
b.
c.
d.
The expected time of the critical path is:
12.0 days
13.0 days
11.5 days
11.0 days
3. In order top keep costs at a minimum and decrease the completion time by 1.5 days, Networks, Inc.
should crash activity(ies):
a. AD and AB.
b. DE.
c. AD.
d. AB and CE.
MULTIPLE CHOICE
4. PERT and the critical path method (CPM) are used for:
a. Determining the optimal product mix.
b. Determining project costs.
c. Project planning and control.
d. Determining the number of servers needed in a fast-food restaurant.
5.
a.
b.
c.
d.
The critical path through a network is the:
Shortest path.
Longest path.
Path with the most nodes.
Path with the most slack.
6. When making a cost-time trade-off in PERT analysis, the first activity that should be crashed is the
activity:
a. With the largest amount of slack.
b. With the lowest unit crash cost.
c. On the critical path with the maximum possible time reduction.
d. On the critical path with the lowest unit crash cost.
7. In PERT, slack is the:
a. Number of days an activity can be delayed without forcing a delay for the
entire project.
b. Uncertainty associated with time estimates.
c. Path that has the largest amount of time associated with it.
d. Difference between the latest starting time and earliest finishing time.
8.
a.
b.
c.
d.
The primary difference between PERT and CPM is that:
CPM uses probabilities on the activity times and PERT does not.
PERT considers activity costs and CPM does not.
PERT can assign probabilities to activity times and CPM does not.
CPM considers activity costs and PERT does not.
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9.
a.
b.
c.
d.
A Gantt chart:
Does not necessarily show the critical path through a network.
Shows the critical path for a project.
Is used for determining an optimal product mix.
Shows only the activities along the critical path of a network.
10. Manning Corporation is preparing a proposal for the government to produce a steam generator to
be used in nuclear submarines. Manning has three factories that can initiate and complete the
generator; however, completion times vary due to different technologies and older equipment
within each of the three factories. The decision tool that would best assist Manning in its factory
selection is:
a. Queuing theory.
b. Time series analysis.
c. PERT-cost analysis.
d. Linear programming.
11. When using PERT, the expected time for an activity when given optimistic time (A), a pessimistic
time (B), and a most likely time (M) is calculated by which one of the following formulas?
a. (B - A) / 2
b. (A + B) / 2
c. (A + 4M + B) / 6
d. (4ABM) / 6
LEARNING CURVE THEORY

This is an application of the Pareto’s Law, which states that “productivity rate marginally
increases as employees gain experience in his work.” Normally, efficiency increases by an
average of 20% for every doubling of output. Hence, this theory also follows the Pareto’s Law or
the “80-20” rule.

Two (2) Models Used in the Learning Curve Theory
2. Wright Model (Cumulative Average-Time Learning Model)- it states that each time the
cumulative quantity of output doubles, the cumulative (or moving) average time to produce
per unit decreases by a certain percentage. The decrease in percentage to produce an
additional unit is 20%. This rate changes across industries between 60% and 85%.
3. Crawford Model ( Incremental-unit-time learning Model) – it predicts the time required to
produce the last unit and requires getting of each unit’s time to compute cumulative total
time and cumulative average time per unit.

Learning curves describe the fact that the more experience people have with something, the
more efficient tfiey become in doing that task. Higher costs per unit early in production are
part of the start-up costs. It is commonly accepted that new products and production
processes experience a period of low productivity followed by increased productivity.
However, the rate of productivity improvement declines over time until it reaches a level
where it remains, until another change in production occurs.

Learning curve analysis is used in planning, budgeting and forecasting and also to
determine costs when bidding on a contract.
Benefits of Learning Curve Analysis
Decisions such as the following can be aided by learning curve analysis;
t) Make or buy decisions - die analysis of the cost to make will be affected,
2)
Life-Cycle costing -- In calculating the cost of a contract, learning curve analysis can ensure
that the cost estimates are accurate over the life of the contract, leading to better bidding.
3)
Cost-Volume-Profit analysis - in determining a breakeven point. If learning is not considered,
the result may be overstatement of the number of units required to break even.
4)
Development of standard costs - labor costs should be adjusted regularly in recognition of the
fact that learning causes standard costs to change over time.
5)
Capital budgeting - costs can be projected more accurately over the life of the capital
investment
when expected improvements in labor productivity due to learning are included.
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6) Development ol production plans and labor requirements - production and labor budgets should
be adjusted to accommodate learning curves.
7 ) Management control - recognizing that higher costs will occur in theeariy phase of the product life
cycle allows more effective evaluation of managers.
Limitations of Learning Curve Analysis
There are three limitations and problems associated with learning curve analysis;
1)
Learning curve analysis is appropriate only for labor-intensive operations involving
repetitive tasks where repeated trials improve performance. If the production process is
designed to have fast set-Lip times using robotics and computer controls, there is little
repetitive labor and thus little opportunity for learning to take place.
2)
The learning rate is assumed to be constant. Iri real life, the decline in labor time might not
be so constant. It might be that the learning rate would decline at the rate of 70% for the first
75,000 units, followed by 80% for the next 50,000 units and 95% for the next 25,000 units.
CLASS PROBLEMS:
1. The Valentine Manufacturing Company assumes a 20% learning rate of workers. A worker initially
needs 20 hours to produce the first unit. The average direct labor cost is P30 per direct labor hour.
REQUIRED: Analyze the effects of the learning curve theory.
a
Unit
s
b
Moving average labor
hours per unit
c = (a x b)
Estimated total
hrs. to produce
the units
d
Direct labor
cost per hour
e = (c x d)
Total Direct
labor cost
f = (e/a)
Average Direct
labor cost/ unit
01
02
04
08
16
32
Learning Curve Rate (based on average DLH per unit) = ___________
Learning Curve Rate (based on average DL cost per unit) = _______________
2. Given a 90% learning сurve, the following data about productivity may apply:
Number of unit
100
200
400
Cumulative average time per unit, minutes
5
4.5 (5 x 90%)
4.05 (4.5 x 90%)
REQUIRED : What is the average time per unit required for the second 200 units? _____________
End of Part 1
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