Dan has decided to cook a roast dinner for the first time and has invited his friends. He has heard that it is difficult to time everything correctly and has decided to use network analysis method to help him plan the meal. He has estimated the times as shown in the following table: Stage preceded by Optimistic estimate (mins) Most Likely (mins) Pessimistic estimate (mins) Expected (mins) Variance (mins) A – cook meat - 80 95 110 95.0 32.14 B – cook & serve vegetables A 13 15 23 16.0 3.00 C – let meat stand A 10 15 20 15.0 3.57 D – slice meat C 4 5 9 5.5 0.75 E – make gravy C 1 2 6 2.5 0.75 F – serve dinner B, D, E 2 3 4 3.0 0.14 G – prepare drinks A 8 10 18 H – eat dinner F, G 21 25 38 I – cook pudding G 25 30 35 J – serve & eat pudding H, I 12 15 24 (a) Based on Dan’s estimates of duration and precedence rules, draw a network diagram for the meal, including the missing expected values in the table (to one decimal place). (7 marks) Calculate early start, late start, early finish, late finish, total float, free float and interfering float for each activity (to one decimal place). (9 marks) (b) List the activities on the critical path. (2 marks) (c) Calculate the mean and standard deviation of the length of the critical path. If Dan starts cooking at 11:30, what time should he expect the mean to be finished? (3 marks) (d) Using the PERT method, estimate the probability (to four decimal places) that the meal will be finished by 14:00 if he starts cooking at 11:30. (2 marks) (e) Comment on the accuracy of the PERT estimate and the assumptions made.
