Question

Management is worried about the cost of excessive customer waiting time, because each moment that customers wait increases the chance of customer abandonment and balking. After some analysis, the manager estimates that the hourly cost to the coffee shop for a customer’s total time in the store is $10 (that is, the waiting cost rate is $10 per customer per hour, which accounts for time in the queue and time being served). If you estimate that the average total time in the store for each customer is W minutes, what is the total waiting cost per hour?
a. $10 x (W/60) b. $10 x 36 x (W/60) c. $10 x 40 x (W/60) d. $10 x (36/40) x (W/60)

Answer 1

ANSWER: b. $10 x 36 x (W/60)

Total time in the store = W minutes = W/60 hour

Waiting cost, Cw = $ 10 per customer per hour

Total waiting cost per hour = Cw*L , where L is the number of customers in the store (waiting plus being served)

L = $\lambda$*(W/60), where $\lambda$ is the arrival rate of customers per hour

So, total waiting cost per hour = Cw*$\lambda$*(W/60)

If arrival rate, $\lambda$ = 36 customers per hour

Then, total waiting cost per hour = $ 10 x 36 x (W/60)