A project consists of four consecutive tasks that have average duration and worst-case duration estimates (in days)as shown in the table.Use Goldratt's model to determine the aggregated buffer for this project. $$\begin{array} { | l | l | l | }
\hline \text { Activity } & \text { Average } & \text { Worst-Case } \
\hline\mathrm { X } & 12 & 20 \
\hline\mathrm { Y }& 20 & 25 \
\hline \mathrm { Z} & 14 & 24 \
\hline \mathrm { W } & 18 & 26 \
\hline
\end{array}$$
A)8.5 days
B)15.9 days
C)7.9 days
D)15.5 days

Question

A project consists of four consecutive tasks that have average duration and worst-case duration estimates (in days)as shown in the table.Use Goldratt's model to determine the aggregated buffer for this project. $$\begin{array} { | l | l | l | } 
\hline \text { Activity } & \text { Average } & \text { Worst-Case } \
\hline\mathrm { X } & 12 & 20 \
\hline\mathrm {  Y }& 20 & 25 \
\hline \mathrm { Z} & 14 & 24 \
\hline \mathrm { W } & 18 & 26 \
\hline
\end{array}$$
A)8.5 days
B)15.9 days
C)7.9 days
D)15.5 days

Quizplus · Accepted Answer

Goldratt's model calculates the project buffer as half the difference between the worst-case and average durations for all tasks, summed up, plus the square root of the sum of the squares of half these differences. For this project: $$ \text{Buffer} = \frac{1}{2}[(20-12) + (25-20) + (24-14) + (26-18)] + \sqrt{\left(\frac{1}{2}(20-12)\right)^2 + \left(\frac{1}{2}(25-20)\right)^2 + \left(\frac{1}{2}(24-14)\right)^2 + \left(\frac{1}{2}(26-18)\right)^2} $$ $$ \text{Buffer} = \frac{1}{2}[8 + 5 + 10 + 8] + \sqrt{(4)^2 + (2.5)^2 + (5)^2 + (4)^2} $$ $$ \text{Buffer} = \frac{1}{2}[31] + \sqrt{16 + 6.25 + 25 + 16} $$ $$ \text{Buffer} = 15.5 + \sqrt{63.25} $$ $$ \text{Buffer} = 15.5 + 7.95 $$ $$ \text{Buffer} \approx 15.5 \text{ days} $$

A Project Consists of Four Consecutive Tasks That Have Average