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Answer Questions 1 and 2 based on the information given below: Consider the following activities (times in weeks). Activity IP Mean CT C/W A - 2 2 N/A B A 4 3 Rs. 800 C A 3 2 Rs. 700 D B, C 5 3 Rs. 750 E A 2 1 Rs. 400 F E 3 3 N/A G D, F 5 4 Rs. 1000 IP = Immediate predecessor. CT = Min. completion time with max crash. C/W = Cost/week to reduce completion time.
- The latest start time for activity D is: A) 8 B) 3 C) 6 D) 4 (Ans.: C)
- If the manager does not want to start activity A immediately, how long could he wait before starting this activity and still meet a deadline of 20 weeks? A) 1 week B) 2 weeks C) 4 weeks D) 3 weeks (Ans.: C)
- Assume that activity G has the following times: Early start time = 7 days, Early finish time = 13 days, Late start time = 15 days, Late finish time = 21 days. Which of the following statements is true about activity G? A) Activity G takes 9 days to complete B) Activity G has a slack time of 8 days. C) Activity G is on the critical path. D) Activity G takes 8 days to complete (Ans.: B)
Answer Questions 5 to 16 based on the information given below:
For the project shown below, the indirect costs are Rs.8000 per week. Also, there is a penalty
cost of Rs.20,000 per week after week 65. Before we start the analysis, there is one additional
assumption to be made. This artificiality is seldom true in the real world. In the example data
above, we have assumed that improvement gains in time are related to costs by a linear
function. For example, we can expect to complete the activity F in 10 weeks at a cost of
Rs.10000, in 9 weeks if we spend Rs.11500, 8 weeks if we spend Rs.13000, etc. We have
assumed that we can decrease the activity time one week for each Rs.1500 spent up to 4
weeks.
Activity Immediate Predecessor(s)
Normal Time (wks)
Normal Cost (Rs.)
Crash Time (wks)
Crash Cost (Rs.)
Max Crash Time
Crash Cost (Rs.) per wks A - 12 12000 11 13000 1 1000 B - 9 50000 7 64000 2 7000 C A 10 4000 5 7000 5 600 D B 10 16000 8 20000 2 2000 E B 24 120000 14 200000 10 8000 F A 10 10000 6 16000 4 1500 G C 35 500000 25 530000 10 3000 H D 40 1200000 35 1260000 5 12000 I A 15 40000 10 52500 5 2500 J E,G,H 4 10000 1 13000 3 1000 K F,I,J 6 30000 5 34000 1 4000
5. What is the Critical Path of the project?
A) A-C-G-J-K
B) B-D-H-J-K
C) B-E-J-K
D) A-I-K
(Ans.: B)
Explanation: Construct the AON network so you can visually identify all possible paths through the
proj ect and compute their lengths.
A-I-K: 33 weeks A-C-G-J-K: 67 weeks B-D-H-J-K: 69 weeks B-E-J-K: 43 weeks
6. What is the Project’s normal, without crashing, total cost associated?
A) Rs.
B) Rs.
C) Rs.
D) Rs. 2624000
(Ans.: D)
Explanation: You should identify the critical path as B-D-H-J-K and a project length of 69 weeks. If the project takes 69 weeks in normal time the direct costs are $1,992,000, indirect costs of $552, (69 x $8000) and $80,000 (4 weeks x $20,000) in penalty costs.
7. When we crash the project, which activity we crash FIRST and for how many weeks
we can crash it at most?
A) A for 1 Week
B) C for 4 Weeks
C) J for 3 Weeks
D) J for 2 Weeks
(Ans.: C)
Explanation: If all activities on the critical path were crashed, that path duration would be 56 weeks. If all activities on A-C-G-J-K were crashed, this path length would be 47 weeks. Since the other three paths are already less than these are, you may disregard them in the analysis. The basic approach is to crash the lowest cost activity (or combination of activities) on the critical path(s) keeping in mind that as activities are crashed other paths may become critical and the cost of crashing must continue to provide a cost improvement. The cheapest activity to crash on the critical path is activity J at $ per week and J can be crashed a maximum of 3 weeks. You may not always be able to crash an activity the maximum number of weeks because other paths may become critical. A good approach is to look at crashing activities one week at a time and see what the effects on the project are. The new path lengths are: A-C-G-J-K: 64 weeks B-D-H-J-K: 66 weeks
8. How much we have saved by crashing this activity in the first iteration?
A) Rs.
B) Rs.
C) Rs.
D) Rs. 84000
(Ans.: C)
12. Which activity/activities can be crashed in the THIRD iteration and how much can be
saved?
A) A and B; Rs.
B) C and B; Rs.
C) K; Rs.
D) K; Rs. 3600
(Ans.: C)
Explanation: Notice now that we have two critical paths so to reduce the project length activities on both paths must be crashes. We may crash one activity common to both paths or an activity unique to each path. Here are the alternatives to be considered: Crash (A and B), (A and H), (C and B), (C and H), (G and B), (G and H), or K (which is common to both paths). The cost to crash all alternatives except (C and B) at $7600 per week and K at $4000 per week cost more than $8000 per week potential saving so we can remove these from considerations. So, crash K the maximum possible amount - 1 week. The paths are now: A-C-G-J-K: 63 weeks and B-D-H-J-K: 63 weeks.
13. What is the total project cost after 3rd^ iteration?
A) Rs.
B) Rs. 2343000
C) Rs.
D) Rs.
(Ans.: A)
Explanation: The project cost is now $2,511,000 - ($8000 - $4000) = $2,507,
14. Which activity/activities can be crashed in the 4th^ iteration, for how many weeks and
what will be the savings involved in crashing?
A) B and C; 1 Week; Rs.
B) B and C; 2 Weeks; Rs. 800
C) K; 1 Week; Rs.
D) None of the above
(Ans.: B)
Explanation: The last step - Crash B and C 2 weeks simultaneously at a cost of $7600 per
week yielding a net saving of $
15. What is the project cost after 4th^ iteration and total time needed for completion?
A) Rs.
B) Rs.
C) Rs.
D) Rs.
(Ans.: A)
Explanation: The minimum cost project schedule is $2,506,200 with a project length of 61
weeks.
16. Which activity/activities can be crashed in the 5th^ iteration?
A) B and C
B) K
C) G and H
D) None of these
(Ans. D)
Explanation: 4th^ iteration is the last.
- A project with Earned Value (EV) = $250, Actual Cost (AC) = $200 and Planned Value (PV) = $350. What is the Schedule Performance Index (SPI)? A. 1. B. 0. C. 0. D. 1. (Ans.: A) Explanation: SV = EV – PV SV = $1000 – $800 = $ Note that the Actual Cost (AC) is not used in the calculation.
- Estimate at Completion (EAC) — the estimated total amount of money needed to be put into the project based on the information available as today. For a project with Estimate at Completion (EAC) = $120,000 and Cost Performance Index (CPI) is 0.90. What is the Budget at Completion (BAC)? A. $108, B. $118, C. $158, D. $208, (Ans.: A) Explanation: As no information is given on the future performance of the project, we could safely assume that the project will spend at the same rate. So we will make use of the formula: EAC = BAC / CPI $120,000 = BAC / 0. BAC = $120,000 * 0.90 = $108,
- Estimate at Completion (EAC) — the estimated total amount of money needed to be put into the project based on the information available as today. For the project with Earned Value (EV) = $350, Actual Cost (AC) = $300 and Planned Value (PV) = $400. The original project budget is $1,000. Assuming the remaining work will be impacted by the current cost performance and current schedule performance, what is the Estimate At Completion (EAC) of the project? A. $ B. $ C. $ D. $1, (Ans.: B) Explanation: As the project will be impacted by the current cost performance and current schedule performance, the formula would be: EAC = AC + [(BAC-EV)/(SPI*CPI)] SPI = EV / PV = $350 / $400 = 0. CPI = EV / AC = $350 / $300 = 1. EAC = BAC/(EV/AC) = $300 + [($1000 – $350) / (0.875 * 1.167)] = $
- Estimate at Completion (EAC) — the estimated total amount of money needed to be put into the project based on the information available as today. For the project with Earned Value (EV) = $300, Actual Cost (AC) = $250 and Planned Value (PV) = $300. The original project budget is $1000. Assuming the project will continue to spend money at the same rate, what is the Estimate At Completion (EAC) of the project? A. $ B. $ C. $1, D. $1, (Ans.: A) Explanation: As the project will continue to spend at the same current rate, the formula to be used would be: EAC = BAC/CPI CPI = EV/AC EAC = BAC/(EV/AC) = $1000 / ($300/$250) = $
- With reference to the diagram below, it can be inferred that the project is currently:
A. Ahead of schedule and under budget B. Ahead of schedule and over budget C. Behind schedule and under budget D. Behind schedule and over budget (Ans.: B)
Explanation: As of today, AC > PV = over budget and EV > PV = ahead of schedule, so the project is “ahead of schedule and over budget”.
- For a project with Earned Value (EV) = $300, Actual Cost (AC) = $350 and Planned Value (PV) = $400. The overall project budget is $1,000. Assume that you will continue to spend at the same rate as you are currently spending. What is the Variance At Completion (VAC)? A. -$ B. $ C. -$ D. $ (Ans.: C) Explanation: As the project will continue to spend at the same current rate, the formula to be used would be: VAC = BAC – EAC EAC = BAC/CPI CPI = EV/AC VAC = BAC – BAC/(EV/AC) =$1000 – $1000/($300/$350) = -$
