THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
Subject:
Quantitative Techniques in Construction Planning
Subject Code:
CSE509
Session:
2019/20
Date:
19 December 2019
Time:
19:00 – 22:00
Time allowed:
3 hours
This question paper has 4 pages.
Instructions to Candidates:
1. This is an open-book examination. You are allowed to use your notes, readings, reference
materials or textbooks.
2. You MUST attempt the questions yourself without any help from any other persons.
3. There is an honor pledge before Question 1. Type or write the honor pledge on the first
page of your submission, your answer will NOT be marked if you failed to do so.
4. There are 4 questions and the full marks is 100. Answer ALL questions.
5. Upload your work using the specified Turnitin assignment link on or before the exam end
time. 15-minute buffer will be given to cater for the possible slow uploading process.
6. Keep the file that you have submitted until the subject grade has been finalized.
7. List clearly all your steps and state your assumptions when necessary.
HONOR PLEDGE
I affirm that I will not give or receive any unauthorized help on this exam and that all
work will be my own. I understand that violation of these principles is an act of
academic dishonesty and will lead to disciplinary actions.
Type or write the above honor pledge on the first page of your answer (your answers
will NOT be marked if you fail to do so).
Question 1. Cost estimation (25%)
(a) Sherry bought an apartment, with 480,000$ down-payment and 1,120,000$ loan. She
needs to pay the loan in 15 years with equal repayment each month. The interest is 6%
annually (for easy calculation, the interest is 0.5% monthly).
i. How much should she pay every month? (6 marks)
ii. For the first three months, list the principal and interest she needs to pay. (list for each
month in the first three months) (9 marks)
(b) Company A bought a piece of advanced equipment at the price of 410,000$. It can be
used for five years with a salvage value of 20000$. (10 marks)
i. Using the Declining Balance Method of depreciation accounting, what are the annual
depreciation amount and the book value of the equipment of each year. (Assume X=2)
ii. Using the Sum of Years Digits (SOYD) Method of depreciation accounting, what are the
annual depreciation amount and the book value of the equipment of each year.
Question 2. Scheduling (25%)
Assume you are responsible for a project designed to refurbish a hospital operating theatre
including the following tasks. All the estimated times and precedence relationships are given
in the following table (all duration is in days; all cost is in 1,000 dollars). Partial crashing is
allowed for all tasks.
i.
ii.
iii.
iv.
What is the expected time and variance for each task? (6 marks)
What is the probability of completing the critical path within 70 days? (6 marks)
Based on the normal duration, what is the slack and slope for each task? (6 marks)
Based on the normal duration, please calculate the minimum total time with the lowest
extra cost. (7 marks)
Task Predecessor Optimistic
Duration
A
4
B
7
C
B
6
D
C
11
E
A
13
F
D, E
13
G
C
8
H
D, G
4
I
D
4
J
H
5
K
F, I
6
L
K, J, N
6
M
G
9
N
M
10
Pessimistic
Duration
8
13
16
17
15
18
12
9
7
11
14
10
15
14
Normal
Duration
6
10
9
13
14
15
10
6
5
7
9
8
11
12
Normal
Cost
5
10
14
24
30
27
15
9
8
12
15
18
22
30
Crash
Duration
4
7
6
11
13
13
8
4
4
5
6
6
9
10
Crash
Cost
9
19
20
30
36
31
21
13
16
18
24
26
27
36
Question 3. EVM and ES (25%)
(a) Let’s assume a 50-week railway project that is planned to spend $400,000 in total. After 10
weeks of work, 15 % of work has been completed and the actual cost is $100,000. However,
the planned value for the 10 weeks of work is $119,175.
Duration
Budget
Actual Cost
% Complete
(weeks)
($)
($)
2
5,000
7,000
100%
A
20
75,000
13,000
8%
A
5
20,000
40,000
100%
A
4
10,000
8,000
100%
A
25
90,000
12,000
10%
C
16
50,000
5,000
4%
D
10
40,000
15,000
20%
G
15
40,000
0
0%
B, E, F, H
19
70,000
0
0%
i. Please calculate the Cost Variance (CV), Schedule Variance (SV), Schedule
Performance Index (SPI), Cost Performance Index (CPI), Critical Ratio (CR) for the
whole project. (15 marks)
ii. Please calculate the Estimate to Complete (ETC) and Estimate at Completion (EAC)
for each activity, if the cost performance of each activity to date will continue? (10
marks)
Activity
A
B
C
D
E
F
G
H
I
Predecessor
Question 4. Decision Tree (25%)
Your company is considering whether it should tender for two contracts (C1 and C2) on offer from
a government department for the supply of certain components. If tenders are submitted, the company
will have to provide extra facilities, the cost of which will have to be entirely recouped from the contract
revenue. The risk, of course, is that if the tenders are unsuccessful then the company will have to write
off the cost of these facilities.
The extra facilities necessary to meet the requirements of contract C1 would cost $100,000. These
facilities would, however, provide sufficient capacity for the requirements of contract C2 to be met also.
In addition, production costs would be $36,000. The corresponding production costs for contract C2
would be $20,000.
If a tender is made for contract C2 only, then the necessary extra facilities can be provided at a cost
of only $48,000. The production costs, in this case, would be $24,000.
It is estimated that the tender preparation costs would be $4,000 if tenders are made for contracts
C1 or C2 only and $6,000 if a tender is made for both contracts C1 and C2.
For each contract, possible tender prices have been determined. In addition, subjective assessments
have been made of the probability of getting the contract with a particular tender price as shown below.
Note here that the company can only submit one tender and cannot, for example, submit two tenders (at
different prices) for the same contract.
Tendering for C1 only
Tendering for C2 only
Tendering for both C1 and C2
Possible tender prices ($)
240,000
220,000
140,000
130,000
120,000
380,000
350,000
320,000
Probability of getting contract
0.3
0.85
0.1
0.65
0.9
0.05
0.6
0.75
In the event that the company tenders for both C1 and C2 will either win both contracts (at the price
shown above) or no contract at all. What do you suggest the company do? Illustrate with the decision
tree and identify the final option. (25 marks)