Question

A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Assume that the information desk employee in Problem 1 earns $10 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $12 per hour of time spent waiting in line. Find the total expected costs over an 8-hour day

Answer 1

tsc = 8*1*10 = $80

twc = 8*20*0.0667*12 = $128.06

tc = 80 + 128.06 = $208.06

Explanation:

To find the total expected costs for an 8 hour period, first you must find the total service costs (tsc) and the total waiting costs (twc) as the two costs are what make up the total cost (tc).

Total service cost = (the number of channels)(cost per channel)

tsc = m*Cs

There is only 1 employee so the number of channels is 1.

The cost for this channel is $10 per hour, so 10 * 8 hours in the day.

Total waiting cost = (total time spent waiting by all arrivals)(cost of waiting)

twc = (number of arrivals)(average wait per arrival) Cw

The number arrivals is at the rate of 20 per hour.

The average wait per arrival was found as Wq previously.

Wq = 20/(30*(30-20)) = 0.0667 hours

The cost of waiting (Cw) is the $12 per hour multiplied by the 8 hour day.

Total Expected Cost for an 8 hour day is the sum of the total service cost plus the total waiting cost.