Question

Consider two digital fuel pumps A and B that could be used in a... Consider two digital fuel pumps A and B that could be used in a single gas station. Pump A has a mean effective process time of 4 minutes with squared-coefficient of variation of 0.5. Pump B has a mean effective time of 3 minute with squared-coefficient of variation of 5.

(a) Assume that the arrival rate of cars is 0.2 car per minute with squared-coefficient of variation of 1. Which pump will have a longer average cycle time? (Hint: the number of machines, m, is 1.)

Answer 1

Pump B will likely have a longer average cycle time than Pump A because it has a higher squared-coefficient of variation, indicating more variable and inconsistent service times.

Step-by-step explanation:

To determine which pump will have a longer average cycle time, we can consider the squared-coefficient of variation (SCV) of the service times and the arrival rate. Pump A has an SCV of 0.5, and Pump B an SCV of 5. The higher the SCV, the greater the variability in service times. The arrival rate has an SCV of 1, indicating a Poisson arrival process with exponential inter-arrival times.

Since Pump B has a much higher SCV, the variance in service times is much higher, implying that the service times are highly inconsistent. On the other hand, Pump A has a lower SCV, meaning it provides service times that are more consistent. We know that with only one machine (m=1) and higher variability in service times lead to longer queues, thus longer cycle times.

Therefore, Pump B will likely have a longer average cycle time due to its high variability in service times, compared to Pump A which has lower variability and hence a potentially shorter cycle time.