# Operations Management: Other Operations Management Problems – #29463

Question: Question 7: The following time estimates (in months) for ten activities required for the planning of a huge hospital complex are shown in the table below:

 Activity a Optimistic m Most Probable b Pessimistic Immediate Predecessors Expected Time Variance A 10 15 20 – B 5 9 12 – C 15 25 30 A D 12 20 25 C E 5 8 12 C 8.17 1.36 F 6 14 20 E 13.67 6.25 G 16 20 25 B, F 20.17 4.69 H 15 25 35 D 25 1.36 I 8 15 20 D 14.67 5.44 J 16 23 30 D 23 2.25 K 4 9 12 J 8.67 11.11 L 3 7 12 H 7.17 4 M 3 5 7 I 5 5.44 N 2 4 8 G, I, K 4.33 1.78 O 4 7 10 L 7 2.25 P 4 5 9 G, I, K 5.5 0.44 Q 15 20 30 M, N, O 20.83 1

a) In the headings of the last two columns show the formulas for tiMeand variance. Show the times and variances for activities A, B, C and D. The times and variances have been shown for all other activities. Obey the rules of rounding (if the last digit is 5 or more, round the previous digit up. If the last digit is 4 or less, keep the previous digit as is. This applies to all your problems). (1 mark)

b) Draw a CPM/Pert diagram of the activities using the following convention. You may use PAINT to copy your network onto your word document or attach a separate sheet to your assignment. Show ‘start’ and ‘finish’ nodes: (3 marks)

c) Calculate the expected project length, variance of the critical path, standard deviation of the critical path and the activities along the critical path. (1 mark)

d) What is the probability the activities will NOT be completed within the due time of nine and a half years? Is 9.5 years an unrealistic estimate? (1 mark)