01_Solutions to Suggested Exercises

01_Solutions to Suggested Exercises - CHAPTER 3 PROJECT...

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CHAPTER 3 PROJECT MANAGEMENT P ROBLEM 1 a. C (7) G (7) F (3) E (4) D (2) B (3) 69 61 3 1 3 1 5 15 19 19 15 18 26 19 26 19 16 19 15 13 13 6 15 12 15 A (6) 06 b. A-C-D-E-G, also shown in the network above as the bold path. c. 26 weeks, 6+7+2+4+7. d. 6 weeks, 15-9. P ROBLEM 3 a. Note that G has both D and F as immediate predecessors. However, D is redundant because F has D as an immediate predecessor. b. A-C-F-G-I, and A-D-F-G-I. c. B is not on a critical path and has slack of 4; therefore, do not shorten as it will not change the project completion time. Shorten C, D, and G one week each. C and D are on parallel critical paths, reducing them will only reduce project completion time by 1 week. d. A-C-F-G-I; and A-D-F-G-I. Project completion time is reduced from 18 to 16 weeks. P ROBLEM 5
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a. A-E-G-C-D. b. 26 weeks. c. No difference in completion date. B already has slack time of 2 and F has slack time of 1. P ROBLEM 7 a. 100 Hours. b. b and d are not on the critical path. Their start can be delayed without delaying the start of any subsequent activities.
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P ROBLEM 9 a. A-C-D-F-G. b. 25 weeks, 7+4+5+4+5. c. B, 2weeks; E, 2 weeks. Activity Normal Time (NT) Crash Time (CT) Normal Cost (NC) Crash Cost (CC) NT-CT Cost/week to expedite A 7 6 $7,000 $8,000 1 1,000 B 2 1 5,000 7,000 1 2,000 C 4 3 9,000 10,200 1 1,200 D 5 4 3,000 4,500 1 1,500 E 2 1 2,000 3,000 1 1,000 F 4 2 4,000 7,000 2 1,500 G 5 4 5,000 8,000 1 3,000 First, shorten activity A by one week at a cost of $1,000. This is the lowest cost/week activity on the critical path. Second, shorten activity C by one week at a cost of $1,200. This is the next lowest cost/week activity on the critical path.
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P ROBLEM 11 11. Activity Normal Time (NT) Weeks Crash Time (CT) Weeks Normal Cost (NC) Crash Cost (CC) NT-CT Cost/week to expedite A 2 1 $50 $70 1 20 B 4 2 80 160 2 40 C 8 4 70 110 4 10 D 6 5 60 80 1 20 E 7 6 100 130 1 30 F 4 3 40 100 1 60 G 5 4 100 150 1 50 a. b. Critical path is A-B-E-G c. Duration Activity to crash Cost to crash Total direct costs 18 None $0 $500 17 A 20 520 16 E 30 550 15 G 50 600 14 B & D 60 660 13 B & F 100 760 d. Duration Total direct costs Total indirect costs Total Costs 18 $500 $400 $900 17 520 350 870 16 550 300 850 15 600 250 850 14 660 200 860 13 760 150 910
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Select either 15 or 16 weeks at a total cost of $850. An alternative solution could be developed for this problem. When crashing an activity, there are two assumptions that can be made with in regards to the crash time. One, which was used above, is that any time between the normal time and the crash time can be used. In this problem, activity B could be reduced to either 3 weeks or to 2 weeks. In many cases, this is a realistic approach. However, in some cases it is an either/or situation. For example, activity B could be either the normal time of 4 weeks, or the crash time of 2 week, but nothing in-between. If we calculate the cost per time period to expedite, we generally assume that a linear approximation for the cost is appropriate, and any time in-between normal time and crash time is acceptable. This is the case in the above solution. If you do not make this assumption, the following solution is what you would develop.
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This note was uploaded on 12/18/2010 for the course ADMS 1000 taught by Professor Sumwaru during the Spring '09 term at York University.

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01_Solutions to Suggested Exercises - CHAPTER 3 PROJECT...

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