1. The R&D department is planning to bid on a large project for the development of a new communication system for commercial planes.
The accompanying table shows the activities, times, and sequences required: |Activity |Immediate Predecessor |Time (weeks) | |A |- |3 | |B |A |2 | |C |A |4 | |D |A |4 | |E |B |6 | |F |C, D |6 | |G |D, F |2 | |H |D |3 | |I |E, G, H |3 | a. Construct the appropriate network diagram. (10 points) [pic] [pic] b. What is the project completion time? A-C-F-G-I OR A-D-F-G-I =3+4+6+2+3=18 WEEKS . Suppose you want to shorten the completion time as much as possible, and you have the following options each at an additional cost of $1500: 1) Reduce activity C by one week; 2) Reduce activity D by one week; 3) Reduce activity G by one week; If you will save $2000 for each week that the earliest completion time is reduced, which option, if any, would you choose? (10 points) C, D, G are good options to choose, and the cost are less than $2000. 2. The following table represents a plan for a project: | |Time Estimates (days) | |Job No. Predecessor Job(s) |Optimistic |Most likely |Pessimistic | |1 |- |2 |3 |4 | |2 |1 |1 |2 |3 | |3 |1 |4 |5 |12 | |4 |1 |3 |4 |11 | |5 |2 |1 |3 |5 | |6 |3 |1 |2 |3 | |7 |4 |1 |8 |9 | |8 |5, 6 |2 |4 |6 | |9 |8 |2 |4 |12 | |10 |7 |3 |4 |5 | |11 |9, 10 |5 |7 |8 | a. Construct the appropriate network diagram. (10 points) [pic][pic] b. Which jobs can be delayed without delaying the entire project? (10 points) The critical path is 1-4-7-10-11, thus, the job could be delayed are 2, 3, 5, 6, 8, 9 c. What is the expected completion time for the project? (20 points) |Job No. |a |m |b |ET |AV | 1 |2 |3 |4 |3 |0. 33 | |2 |1 |2 |3 |2 |0. 33 | |3 |4 |5 |12 |6 |1. 33 | |4 |3 |4 |11 |5 |1. 33 | |5 |1 |3 |5 |3 |0. 67 | |6 |1 |2 |3 |2 |0. 33 | |7 |1 |8 |9 |7 |1. 33 | |8 |2 |4 |6 |4 |0. 67 | |9 |2 |4 |12 |5 |1. 67 | |10 |3 |4 |5 |4 |0. 33 | |11 |5 |7 |8 |6. 83 |0. 50 | | | | | | | | | | | | | | | | | | | | | | | | d. Is the probability that the project will take less than 27 days to complete larger than 50% or smaller than 50%? (10 points)
