The Concept of PERT Network - Math Problem Example

Assignment 3 Value: 10% Due 24 June 2005 Word Length: Not applicable(exercise) Format: Essay (APA Referencing) Copy and Turnitin Copy Attempt both questions below:1 Consider the PERT network: ActivityOptimisticEstimateMost LikelyEstimatePessimisticEstimate1-22451-33451-46792-33562-55783-52454-5567Designate the start of the project as time 0, and the scheduled time to complete the project (by contract) is 14 days. Using the 3-time estimate shown above, calculate the expected value and the standard deviation for the expected value of the time required for each activity.

B Using the time given by your expected value calculations determines the critical path for the project. C computes the probability associated with the project being completed by the time specified in the contract. The expected time between events can be found from the expression:te= (o+4m+p)/6Where:o=Optimistic Timem=Most Likely Timep=Pessimistic TimeIn order to calculate the probability of completing the project on time, the standard deviations of each activity must be known. This can be found from the expression: the = (p-o)/6 where he is the standard deviation of expected time, te.

ActivityOptimisticEstimateMost LikelyEstimatePessimisticEstimateExpected Value Standard Deviation, 21-22453,80,50,251-33454,00,30,111-46797,20,50,252-33564,80,50,252-55786,80,50,253-52453,80,50,254-55676,00,30,11BThe PERT network by expected value calculations: 4 7 5 4 4 7 6So there are 2 Critical Paths: 1-2-3-5 and 1-4-5. Each of them takes 13 days the critical path standard deviation is calculated by the square root of the sum of the squares of activity standard deviations using the following expression:c = 21-2-3-5: = (0,25 + 0,25 0+ 0,25 + 0,25 + 0,11) = 1,05We know C=13 (the expected completion time for the critical path) so probability z = (T-C)/ z = (14-13) / 1,05 = 0,95 or 95%2 Below are shown the activities for a project and how they are related(i) RelationshipsActivity C depends on AActivities D, F, K depends on BActivity G depends on FActivity E depends on C, D, and GActivity H depends on E, and K(ii) Activity duration and resourcesActivityDuration (Days)ManningA102B43C21D43E22F21G11H22K42A using the information given above, draw the network and calculate the forward and backward paths.

B Determine the Critical Path. C Construct the Grantt and the manning requirements.D Assume that 5 people have been assigned to the project and that all five can do the activities. Redesign the Gantt chart so that manning requirements do not exceed the resources. The network with the forward (upper) and backward (lower) paths. The Critical Path is A-C-E-H, and its length is 16 days the Gantt chart and the manning requirements:(Number of resources are from the left of the bars)DRedesign of the Gantt chart :(Number of resources are from the left of the bars)