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Chapter 3, Project Management Problem 1: For the following project, draw a AON network and find all the paths and duration of the paths. Activity A B C D E F G H Predecessors Start A A B B, C C D, E E,F Paths Critical path: Project completion time: t Successors 3 9 6 3 8 5 6 4 Duration Problem 2: For the project from problem #1, determine the earliest and latest schedules and the slacks of all the activities. B 9 D 3 G 6 END A 3 START E 8 H 4 C 6 F 5 Project start: Activity t A 3 B 9 C 6 D 3 E 8 F 5 G 6 H 4 Earliest Start Project completion time: Earliest Finish Latest Start Latest Finish Slack Critical Problem 3: The following represent activities in a major construction project. Activity A B C D E F G H a 2 4 1 1 2 6 7 2 Activity a m b A 2 5 14 B 4 7 10 C 1 2 9 D 1 2 3 E 2 4 6 F 6 6 6 G 7 9 17 H 2 8 8 m 5 7 2 2 4 6 9 8 b 14 10 9 3 6 6 17 8 Expected time (t) Predecessors Start Start A A B B C, E D, F Variance 2) Draw the network to represent this project. Find the Critical Path, expected project completion and project variance. Problem 4: a. What is the probability of finishing the project in 24 weeks or less? b. What is the probability of finishing the project in 20 weeks or less? c. The due date for the project is set so that there is a 90% chance that the project will be finished by this date. What is the date? Problem 5: Development of a new software product is being considered. The activities are listed in the table below along with their costs and completion times in weeks. Activity A B C D E F G Immediate Predecessor A A B, D C E Normal Time 4 2 3 8 6 3 4 Crash Time 3 1 3 4 3 2 2 Normal Cost 2,000 2,200 500 2,300 900 3,000 1,400 Crash Cost 2,600 2,800 500 2,600 1,200 4,200 2,000 a. What is the project expected completion date? b. What is the total cost required for completing this project on normal time? c. Activity A If you wish to reduce the time required to complete this project by 1 week, which activity should be crashed, and how much will this increase the total cost? MCA Cost difference = (Normal time – Crash time) Crash cost – Normal cost B C D E F G MCA = Maximum crashing allowed Crashing cost/week d. 1 Solver Model C A B Class practice problem #5 2 Activity D E Normal Time (NT) Crash time (CT) Normal Cost (NC) Crash cost (CC) F MCA = NT - CT G H CC - NC Crashing cost/week = (CC-NC)/MCA I Predecessors 3 A 4 3 2000 2600 Start 4 B 2 1 2200 2800 Start 5 C 3 3 500 500 A 6 D 8 4 2300 2600 A 7 E 6 3 900 1200 B, D 8 F 3 2 3000 4200 C 9 G 4 2 1400 2000 E 10 Normal cost = J Successors A 11 12 B C D E F G H Weeks crashed Actual duration ES EF LS LF Slack Project start Activity 13 A 14 B 15 C 16 D 17 E 18 F 19 G 20 Project duration 21 Normal project cost = 22 Cost of crashing = 23 Total cost = Solver Parameters: Step 1: Minimize project completion time Set Target cell □ Maximize □ Minimize (Set objective) Changing cells Constraints Options Step 2: Minimize project cost for the minimum project completion time Set Target cell Changing cells Constraints Options □ Maximize □ Minimize