Question

.8-6. A project consists of 12 activities, represented by the project network below, where number by each arc represents the duration (in days) of the associated activity 4 12 4 12 10 a) Find the earliest time, latest time, and slack for each event as well as the slack for each activity. Also identify the critical path. (b) The project has been scheduled to be completed in the minimum possible time.If all previous activities have begun as early as possible and if activity (3, 5) has just been completed, how many days can the start of activity (5, 8) be delayed without delaying the completion of the project?

Answer 1

Procedure Total effective time is calculated using the formula: (a+4m+b)/6 Early Start and Early Finish I. The activities having no predecessor start at time 0. For them, ES = 0 2. EF - ES Time 3. If activity A precedes activity B, then ES of B EF of ATime of B 4. If 2 activities precede an activity, then the largest value of EF of the 2 activities is considered For example: If activity A and B precede activity C, EF of A-2 and EF of B-3, then ES of C EF of B+Time of C Late Start (LS) and Late Finish (LF) 1. We backtrace in this case, so we start from the last activity. 2. LS = LF-Time 3. If activity A precedes activity B, then LF of A- LS of B- Time of A 4. If 2 activities follow an activity, then the smallest value of LS of the 2 activities is considered For example: If activity E and F follow activity B, LS of E-11 and LS of F 10, then LF of B- LS of F - Time of B Slack = LF-EF or LS-ES Critical Activities: Activities with Slack 0: Activities which can be crashed

EF ES Time Slack LF-EF LS LF-Time Activity Activity Code Time Predecessor ES LF Calculation Calculation Value Calculation Value 10 1-2 NA 10-6 10-6 4 NA 1-3 2-4 10 13 6 13-3 13-9 4 13 4+9 13-9 13-13 13 4+12 17-12 17-16 3-5 16 17 12 10 4+10 21-10 3-6 14 21 21-14 13 22-9 13 4-7 13+9 22-22 16 21 17 22-21 5-7 16+5 22-5 19 25-19 5-8 16 16+3 25-3 25 14+4 18 21 25-18 6-8 14 25-4 25 G,H 22+12 34-12 34 34-34 7-9 12 34 8-9 19+9 25 19 34-9 34 34-28 28 Critical path: B->D->G->K i.e. (1-3)->(3-4)->(4-7)->(7-9) Project completion time 34 days The activity (5,8) i.e. activity I is a non critical activity. So its delay will have no effect on project completion time