The following CPM network has estimates of the normal time in weeks listed for t
ID: 2747367 • Letter: T
Question
The following CPM network has estimates of the normal time in weeks listed for the activities: Identify the critical path. A-B-D-F-G A-B-D-E-G A-C-D-E-G A-C-D-F-G What is the length of time to complete the project? Which activities have slack, and how much? C, 2 weeks; E, 3 weeks. B, 4 weeks; E, 3 weeks. C, 2 weeks; F, 5 weeks. B, 1 weeks; F, 1 weeks. Here is a table of normal and cash times and costs. Which activities would you shorten to cut two weeks from the schedule in a rational fashion? F,D G,A B,C C,E What would be the total incremental cost? Is the critical path changed? Yes NoExplanation / Answer
Activity Predecessor Activity Time ES EF LS LF Slack A None 7 0 7 0 7 0 Critical Path Activity B A 5 7 12 8 13 1 C A 6 7 13 7 13 0 Critical Path Activity D B,C 4 13 17 13 17 0 Critical Path Activity E D 6 17 23 17 23 0 Critical Path Activity F D 5 17 22 18 23 1 G E,F 3 23 26 23 26 0 Critical Path Activity ES = E of Tail Event EF = ES + Activity Duration LF = L of Head Event LS = LF - Activity Duration Slack - LS - ES E = Earliest occurrence time for the event L = Latest allowable time for the occurrence of event Paths Weeks Duration A-B-D-F-G 7+5+4+5+3 24 A-B-D-E-G 7+5+4+6+3 25 A-C-D-F-G 7+6+4+5+3 25 A-C-D-E-G 7+6+4+6+3 26 Critical Path The Critical path is A-C-D-E-G with estimated duration of 26 weeks Activity B and F have slack of 1 week each Activity Normal Time Crash Time Normal Cost Crash Cost Reduction in days Slope (Crash Cost/day) a b c d e = a-b (d-c)/e A 7 6 $7,600.00 $9,200.00 1 $1,600.00 B 5 4 $5,700.00 $8,300.00 1 $2,600.00 C 6 5 $8,550.00 $10,200.00 1 $1,650.00 D 4 3 $2,600.00 $4,500.00 1 $1,900.00 E 6 5 $3,850.00 $6,000.00 1 $2,150.00 F 5 3 $6,000.00 $8,600.00 2 $1,300.00 G 3 2 $4,400.00 $5,800.00 1 $1,400.00 The objective to shorten the project time frame is to complete the work earlier than its orginal time. Since, Activity B and F have slack, it doesn't make sense to complete those activities earlier. It is ideally the activities on critical path which needs to be reduced. So, the best way to select an activity is with least slope which are activities G and A, from lowest Increase in Cost = $1400 + $1600 = $3000 Since A and G activities are performed on each of the path as described above, the reduction is time for both these acitivities reduces the total time for each path and as such critical path remains same. The duration of all the paths gets reduced by two weeks.