BMS 303 CAT 2023

1 University: St Paul University Campus: Nairobi Campus Module: Evening Department: Course Name: Course Code: BMS 303 Admission Number: BLMNRB 569622

2 BMS 303 CAT 2023 1. Draw the PERT network for the project To draw the PERT network, we will draw a node for each activity in the project: A, B, C, D, E, F, G, H. We will then draw arrows between the nodes to indicate the sequence of activities. The tail of the arrow should point to the preceding activity, and the head of the arrow should point to the activity that follows. If an activity has multiple preceding activities, we will draw arrows from each of them to the activity. We will draw circles for each activity (labeled A through H) and label each circle with the activity name and estimated time. 2. Prepare the activity schedule for the project

4 To calculate the latest start and finish times, we need to consider the latest finish time of the following activity. The latest finish time of an activity is the minimum of the latest start time of all its following activities. Then, the latest start time can be calculated by subtracting the expected duration from the latest finish time, and the latest finish time is the maximum of the latest start time plus the expected duration. Activity Schedule Activity Preceding Activity Most optimistic time (a) Most likely time (m) Most pessimistic time (b) Expected duration Variance Earliest start Earliest finish Latest start Latest finish A - 2 4 12 5 25/9 0 5 0 5 B - 10 12 26 14 64/9 0 14 1 15 C A 8 9 10 9 1 5 14 6 15 D A 10 15 20 15 25/9 5 20 5 20 E A 7 7.5 11 8 4/9 5 13 16 24 F B, C 9 9 9 9 0 14 23 15 24 G D 3 3.5 7 4 4/9 20 24 20 24 H F, G 5 5 5 5 0 24 29 24 29 3. Determine the critical path

5 The critical path is the longest path of activities through the network. It is the sequence of activities that determines the total project duration. In this case, critical path of the project is 1-2- 4-5-6, critical activities being A, D, G and H. From the table we just completed, we can see that the earliest finish time for activity H is 29, which is the longest duration of any path in the network. Expected project length = 5 + 15 + 4 + 5 = 29 weeks. Therefore, the critical path consists of activities A, D, G, and H, with a total duration of 29 weeks. 4. If a 30-week deadline is imposed, what is the probability that the project will be finished within the time limit? To calculate the probability that the project will be finished within the 30-week deadline, we need to use the z-score formula. z = (Due date - expected project completion time) / standard deviation Where deadline is 30 weeks, the expected project completion time is 29 weeks (the duration of the critical path), and the standard deviation is 2.45 weeks. We arrived at the standard deviation by adding the sum of variances for all activities on the critical path A, D, G and H 25/9 + 25/9 + 4/9 + 0 = 6 This is the total variance of the critical path. To get the standard deviation, we need to take the square root of the variance: