PERT and CPM - 23 PERT-Scheduling Part 1 of 6 Expected Time and Variances of Activities HD

#OperationsResearch #Math #Statistics #PERT #CPM #Network #Scheduling #Probability #FreeLecture #FreeStudy #Solution #VideoLecture Project Evaluation and Review Technique (PERT) Draw Network Diagram and trace the Critical Path. Also Also find Total, Interfering, Free and Independent floats/slacks : Activity Name: A B C D E F G Activity Node: 1-2 1-3 1-4 2-5 3-5 4-6 5-6 estimated Duration (weeks) Optimistic 1 1 2 1 2 2 3 Most Likely 1 4 2 1 5 5 6 Pessimistic 7 7 8 1 14 8 15 (a) Draw a network diagram of the activities in the project. (b) Find the expected duration and variance for each activity. What is the expected project length? (c) Calculate the variance and standard deviation of the project length. What is the probability that the project will be completed – (i) At least 4 weeks earlier than the expected time? (ii) No more than 4 weks later than the expected time? (d) The project due date is 19 weeks, what is the probability of not meeting the date? The main objective in the analysis through PERT is to find out the completion for a particular event within specified date. The PERT approach takes into account the uncertainties. PERT was developed in the context where many activities associated with the project had never been attempted previously (Research and Development projects). PERT was developed to handle projects where the time duration for each activity is no longer just a single time estimate, but is a random variable that is characterized by some probability distribution – usually Beta Distribution. To estimate the parameters (mean and variance) of the Beta Distribution, the PERT requires 3 time estimates for each activity. From these time estimates a single time is estimated – Expected time. The three time values are associated with each activity 1. Optimistic time – It is the shortest possible time in which the activity can be finished. It assumes that everything goes very well. This is denoted by t0. 2. Most likely time – It is the estimate of the normal time the activity would take. This assumes normal delays. If a graph is plotted in the time of completion and the frequency of completion in that time period, then most likely time will represent the highest frequency of occurrence. This is denoted by tm. 3. Pessimistic time – It represents the longest time the activity could take if everything goes wrong. As in optimistic estimate, this value may be such that only one in hundred or one in twenty will take time longer than this value. This is denoted by tp. In PERT calculation, all values are used to obtain the percent expected value. Expected time – It is the average time an activity will take if it were to be repeated on large number of times and is based on the assumption that the activity time follows Beta distribution, this is given by