Question

If both the average flow rate and average flow time of a process are increased by 50%, the percentage change in the average number of units in the process is:


(a) 125%

(b) 50%

(c) Cannot be determined

(d) 225%

Answer 1

Answer:

The percentage change in the average number of units in the process is 125%.

Explanation:

Based on Little's law;

Average inventory = average flow rate * average flow time

Let  inventory  = I,  average flow rate = R and average flow time = T

Thus, I = R*T = RT

Now, Average flow rate and average flow time are increased by 50%

R' = R + 0.5R = 1.5R

T = T + 0.5T = 1.5T

So, inventory, I' = 1.5R*1.5T=2.25RT

Hence, the percentage change in the average number of inventory units in the process.

% change = I' - I = 2.25RT - RT= 1.25RT or 125%

Thus correct answer = 125%

Answer 2

Given the increase in the Average Flow Rate, the percentage change in the average number of units in the process is 125%. (Option A)

What is Average Flow Rate?

The average flow rate is simply the total number of reading for a flow rate, divided by the number of readings.

Following Little's law, we know that

Average inventory = average flow rate * average flow time

Assume that inventory  = I,  average flow rate = R and average flow time = T

Thus, I = R X T = RT

Now, recall that the Average flow rate and average flow time are upped by 50% therefore,

R' = R + 0.5R = 1.5R

T = T + 0.5T = 1.5T

therefore, inventory, I' = 1.5R*1.5T=2.25RT

From the above, we can draw inferences regarding the percentage change.

% change = I' - I = 2.25RT - RT= 1.25RT or 125%

Therefore, the correct answer = 125%

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