Question

1. The activities required to service a car at Zippy-Lube can be viewed as a mini-project as summarized in the following table.

		Time Required			Expected
Activity	Description	Predecessor	Min	Avg	Max	Time	Variance
A	Drain Oil	--	2	3.5	5
B	Replace Filter	A	1	2	3
C	Refill Oil	B, E	1	2.5	4
D	Check Tires	--	2	3	4
E	Wash Windows	D	2	3	5
F	Fill Fluids	E	2	3	4
G	Final Test	C, F	0.5	1	1.5

1. Draw the activity network for this problem.
2. Use PERT to identify the expected time and variance for each activity.
3. What is the expected time and variance of the critical path?

Answer 1

21 The network for the above activities is shown below: B (3.6) A (3.6) C (2.5) D (3) E (3.2) F (3) 4

The procedure to find the expected time and variance is shown below in the excel screenshot: 2 Time RequiredExpected 2 3.55 123 2.00 0.11 Activity Description Predecessor A Drain Oil 3.50 0.25 B Replace Filter Es B, E C Refill Oil 254 2.50 0.25 D Check Tires E Wash Windows F Fill Fluids Final Test 2 34 3.00 0.11 2 353.170.25 2 33.000.11 3.5 10 G C, F 1.5 1.00 0.03 Drag the same formula from H6 to H11 to get the expected time for each activity. 15 f(G5-ES) 2/36 Time RequiredExpected Activity Description Predecessor A Drain Oil B Replace Filter c Refill Oil D Check Tires E Wash Window 0.25 0.11 250 0.25 0.11 3,17 0.25 0.11 0.03 3.5 3.50 1232.00 2 3 4 3.00 3.00 巨 2.5 , 13 10 G Final Test C, F 0.5 1.5 1.00 Drag the same formula from 16 to 111 to get the variance time for each activity.

Hence, the expected time and variance is given below in the table Activity Description Predecessor Time Required Expected A Drain Oil B Replace Filter C Refill Oil D Check Tires E Wash Window MiAvg Max Time 3.50 2.00 2.50 3.00 3.17 3.00 1.00 3.5 5 0.25 0.11 0.25 0.11 0.25 0.11 0.03 B, E 2.5 4 F Fill Fluids Final Test 4 C, F 0.5

Critic al path is defined as the shortest path from the starting node to the ending node, or in other words, the critical path is that path for that node in the network for which forward pass and backward pass are equal or total float is equal to zero. To calculate the expected time and variance of the critical path, firstly compute forward and Backward pass. By using the network: Forward pass Backward pass Set, E 0 Set, L,-E,-10.2 E,-E,+112 =10.2-1.0 -9.2 0+3.5 56 -9.2-2.5 = 6.7 -0+3 L.=min(L -45.4-4) -min 16.7-0,9.2-3 min (6.7,6.2) 3+3.2 -6.2 14:4-4 max {6.2 +0.3.5 +2} max 6.2,5.5 6.2-3.2 3.0 E-max(E, +4-E, +4) max6.2+2.5,6.2+3 max $8.7,9.2 6.7-2.0 -4.7 -9.2 min-13 min $3-3,4.7-3.5) max 0,1.2 67 -10.2 Note: 3.17 3.2

The calculations for expected time and expected variance are as shown below: Expected Time 3.00+3.17+3.00+.00-10.17 10.17 Expected Variance 0.11+0.25+0.+0.03- 0.50 -0.50