MS3053 MANAGEMENT SCIENCE & OPERATIONS TECHNOLOGY 6.1 Practice

The Farmers American Bank of Leesburg is planning to install a new computerized accounts system. Bank management has determined the activities required to complete the project, the precedence relationships of the activities, and activity time estimates, as shown in the following table:

			Time Estimates (weeks)
Activity	Activity Description	Activity Predecessor	a	b	c
A	Position recruiting	---	5	8	17
B	System development	---	3	12	15
C	System training	A	4	7	10
D	Equipment training	A	5	8	23
E	Manual system test	B, C	1	1	1
F	Preliminary system changeover	B, C	1	4	13
G	Computer-personnel interface	D, E	3	6	9
H	Equipment modification	D, E	1	2.5	7
I	Equipment testing	H	1	1	1
J	System debugging and installation	F, G	2	2	2
K	Equipment changeover	G, I	5	8	11

1. Using the PERT approach, use the three estimates of duration to calculate a mean duration and standard deviation for all activities.

2. Construct/draw a network diagram for this problem using the mean durations, calculate LS(Foll.), ES(Prec.), and the total float for each task, and hence identify the critical path. What is the standard deviation of the critical path?

3. What is the 94% confidence interval for the length of the critical path?

4. What is the probability of completing the project within 40 weeks?

5. Answer the project managers question:

   I want to tell the client a project length which I am 89.44% sure that we can meet - what figure should I give them?

6. What is the probability of completing the project between 35 and 39 weeks?