(a) A project schedule has the following characteristics.

| Activity | 1-2 | 1-3 | 2-4 | 3-4 | 3-5 | 4-9 | 5-6 | 5-7 | 6-8 | 7-8 | 8-10 | 9-10 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Time | 4 | 1 | 1 | 1 | 6 | 5 | 4 | 8 | 1 | 2 | 5 | 7

Question

(a) A project schedule has the following characteristics.

| Activity | 1-2 | 1-3 | 2-4 | 3-4 | 3-5 | 4-9 | 5-6 | 5-7 | 6-8 | 7-8 | 8-10 | 9-10 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Time | 4 | 1 | 1 | 1 | 6 | 5 | 4 | 8 | 1 | 2 | 5 | 7 |

Construct the network and calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity and determine the Critical path of the project and duration to complete the project.

OR

(b) Compute Quartile deviation from the following data.

| CI | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| --- | --- | --- | --- | --- | --- | --- | --- |
| $f$ | 12 | 19 | 5 | 10 | 9 | 6 | 6 |

Accepted Answer

>

> [!TLDR]
> (a) The project takes 22 time-units along critical path 1–3–5–7–8–10. (b) The quartile deviation is about 16.11.
>
> ## (a) CPM
> **Forward pass (E):** $E_1=0,E_2=4,E_3=1,E_4=\max(5,2)=5,E_5=7,E_6=11,E_7=15,E_8=\max(12,17)=17,E_9=10,E_{10}=\max(22,17)=22.$ **Duration $=22$.**
>
> **Backward pass (L):** $L_{10}=22,L_9=15,L_8=17,L_7=15,L_6=16,L_5=\min(12,7)=7,L_4=10,L_3=\min(9,1)=1,L_2=9,L_1=\min(5,0)=0.$
>
> **Activity table** ($	ext{EST}=E_i,	ext{EFT}=E_i+t,	ext{LFT}=L_j,	ext{LST}=L_j-t$):
>
> | Activity | $t$ | EST | EFT | LST | LFT | Float |
> | --- | --- | --- | --- | --- | --- | --- |
> | 1-2 | 4 | 0 | 4 | 5 | 9 | 5 |
> | 1-3 | 1 | 0 | 1 | 0 | 1 | 0* |
> | 2-4 | 1 | 4 | 5 | 9 | 10 | 5 |
> | 3-4 | 1 | 1 | 2 | 9 | 10 | 8 |
> | 3-5 | 6 | 1 | 7 | 1 | 7 | 0* |
> | 4-9 | 5 | 5 | 10 | 10 | 15 | 5 |
> | 5-6 | 4 | 7 | 11 | 12 | 16 | 5 |
> | 5-7 | 8 | 7 | 15 | 7 | 15 | 0* |
> | 6-8 | 1 | 11 | 12 | 16 | 17 | 5 |
> | 7-8 | 2 | 15 | 17 | 15 | 17 | 0* |
> | 8-10 | 5 | 17 | 22 | 17 | 22 | 0* |
> | 9-10 | 7 | 10 | 17 | 15 | 22 | 5 |
>
> **Critical path** (zero float): $1	o3	o5	o7	o8	o10$, duration $1+6+8+2+5=22.$
>
> ## (b) Quartile deviation …

Activity	$t$	EST	EFT	LST	LFT	Float
1-2	4	0	4	5	9	5
1-3	1	0	1	0	1	0*
2-4	1	4	5	9	10	5
3-4	1	1	2	9	10	8
3-5	6	1	7	1	7	0*
4-9	5	5	10	10	15	5
5-6	4	7	11	12	16	5
5-7	8	7	15	7	15	0*
6-8	1	11	12	16	17	5
7-8	2	15	17	15	17	0*
8-10	5	17	22	17	22	0*
9-10	7	10	17	15	22	5

(a) CPM

(b) Quartile deviation …

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