Question

A project consists of 4 activities with the following data :


$\text{Indirect cost = Rs.100/day.}$
The minimum cost project duration (days) is ____.

• A. $18$
• B. $20$
• C. $19$
• D. $17$

Answer 1

The correct option is B $20$

$\begin{array}{ccc}\text{Activity}& \text{Cost slope}=\frac{C_c-N_c}{N_T-C_T}& \text{Crashing}\\ & & \text{Possibility}\\ A& (220-100)9-7=60& 2\\ B& -& -\\ C& (320-200)/6-4=60& 2\\ D& (450-300)/10-9=150& 1\end{array}$




$\underset{–}{\text{Path}}\underset{–}{\text{Duration}}$
$\text{A - D : 9 + 10 = 19}$
$\text{B - C - D : 6 + 6 + 10 = 22}$

$\text{Crashing Possibility :}$
$\begin{array}{ccc}\text{Critical}& \text{Cost Slope}& \text{Crashing}\\ \text{Activity}& & \text{provision}\\ B& -& \text{Not Possible}\\ C& 60& \text{2 days}\\ D& 150& \text{1 day}\end{array}$

By crashing activity 'C' by 2 days.
'C' can be crashed because the crash cost per day is less than indirect cost/day. Hence the total cost will decrease



$\underset{–}{\text{path}}\underset{–}{\text{Duration}}$
A - D : 9 + 10 = 19
B - C - D : 6 + 4 + 10 = 20

Crashing Possibility at this stage :
$\begin{array}{ccc}\text{Critical}& \text{Cost Slope}& \text{Crashing}\\ \text{Activity}& & \text{problem}\\ B& -& \text{Not Possible}\\ C& 60& \text{Not Possible}\\ & & \text{(fully crashed)}\\ D& 150& \text{Not economical}\end{array}$

Further crashing is possible but not economical because the crash cost per/day is greater than indirect cost per/day and the total cost will start increasing, Hence minimum cost project duration = 20 days.