Question

Run Scenario 1 using the following inputs: Inter-arrival time = 5 hours, mean length of stay = 16 hours, standard deviation of inter-arrival time = 2 hours, standard deviation of length of stay = 4 hours. Using the equation for theoretical utilization (demand / capacity), what is the theoretical utilization?

Answer 1

The theoretical utilization is 3.2.

Step-by-step explanation:

Theoretical utilization is the ratio of demand to capacity, where demand is the average number of customers arriving per unit of time and capacity is the average service rate.

In this scenario, the inter-arrival time is 5 hours, which means we expect one customer to arrive every 5 hours on average. The mean length of stay is 16 hours, which means each customer stays for an average of 16 hours.

To calculate the demand, we find the reciprocal of the average inter-arrival time: 1 / 5 = 0.2 customers per hour. To calculate the capacity, we find the reciprocal of the average length of stay: 1 / 16 = 0.0625 customers per hour.

Theoretical utilization = demand / capacity = 0.2 / 0.0625 = 3.2.

Answer 2

80%

Step-by-step explanation:

The capacity utilization rate evaluate the proportion of potential economic output that is actually realized.

To solve for theoretical utilization, we use the following formula as given below;

Theoretical Utilization = {p/(ma)}×100

Where we have our variables as,

p=16

m=4

a=5

Imputing variables into the formula we have

Theoretical utilization = {16÷(4×5)}×100

= {16/20}×100

=0.8×100

=80%