Question

A7-3 (Static) The expected times and variances... The expected times and variances for the project activities are given below. Complete the table showing which activities are critical ID Description Predecessor te Variance Critical? None None 1 2 3 4 Pilot production Select channels of distrib. Develop mktg, program Test market None 5 Patent 6 Full production 7 8 Ad promotion Release 25.6.7

Answer 1

Based on given data, we prepare a project network diagram as shown below:

Legend EST ID EFT SLK LST DUR LFT 4 10 6 26 6 O 6 10 O 10 016 4 10 16 26 | 6 6 6 5 16 10 16 10 26 26 8 28 027 19 19 7 26 26 2 28 O 34 19 194 | 23 477 19 23 3 26

The above network diagram in the form of formulas is shown below for better understanding and reference:

C D E F G H I J K L M N O 1 A B Legend ID EFT 2 3 4 EST SLK LST DUR LFT 4 =E5+F7 6 =15+J7 "EZ.Es la luz =C7 =E7-E5 =G7-F7 =G5 =17-15 =K7-J7 =A7+B9 4 =17 375 | 16 -M24 16 =M14 =MIN(E7,E11) =C7 5 =E9+F11 =E11-E9 =G11-F11 10 =M14 =A12+B14 701 8 =A9-A7 9 =C9-B96 10 11 12 O 2 13 =A14-A12 14 =C14-B147 15 16 O 3 17 =A18-A16 18 =C18-B18 4 =MAX(K5,69,C12,K16) 8 =M12+N14 M14-M12 014-N14 2 =012 =M14 =A16+B18 =116+J18 =C16 7 =118-116 =K18-J18 3 =118 =M14

The above project diagram is prepared as per the legend shown in the top-left corner.

EST = Early start time

LST = Late start time

EFT = Early finish time

LFT = Late finish time

SLK = Slack = LST - EST or Slack = LFT - EFT

The EST of an activity = EFT of previous activity

EFT of an activity = EST + Duration

Similarly LFT & LST are calculated during backward pass.

There are multiple paths in the diagram:

1-4-6-8

1-5-8

2-8

3-7-8

Out of the above paths, path 1-4-6-8 is the longest path and has 0 slack. Hence, this is the critical path.

As seen from above, the expected duration is 28 periods.

We complete the table in Excel as shown below:

ID te Variance Critical? 6 | Yes 27 4 No | 3 | 4 2 No 4 4 2 Yes 15 10 No 16 16 10 Yes | 7 3 2 No | 8 2 1 Yes

We have to find the probability of completion in 25 weeks

We find Z as:

Z = $\frac{Required.Duration - Expected.Duration}{\sqrt{Variance.over.Critical.path}}$

Variance over critical path = Variance for Activity 1 + Variance for Activity 4 + Variance for Activity 6 + Variance for Activity 8 = 3 + 2 + 10 + 1 = 16

Hence, Z = $\frac{25 - 28}{\sqrt{4}}$ = -1.50

We find Probability in Excel as:

The probability of completing the project in 25 periods 0.067

The above answer in terms of formula is shown below:

The probability of completing the project in 25 periods =NORM.S.DIST(-1.5,TRUE)

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