# An insurance company receives 220 calls per day from customers who want to lodge an insurance…

An insurance company receives 220 calls per day from customers who want to lodge an insurance claim. The call center is open from 8am to 5pm. The arrival of calls follows a Poisson process. Looking at the intensity of arrival of calls, we can distinguish three periods during the day: the period 8am to 11am, the period 11am to 2pm and the period 2pm to 5pm. During the first period, around 60 calls are received. During the 11am–2pm period, 120 calls are received, and during the 2pm– 5pm period, 40 calls are received. A customer survey has shown that customers tend to call between 11am and 2pm because during this time they have a break at work and they take advantage of their break to make their personal calls.

Statistical analysis shows that the durations of calls follow an exponential distribution.

According to the company’s customer service charter, customers should wait no more than one minute on average for their call to be answered.

• Assume that the call center can handle 70 calls per hour using seven call center agents. Is this enough to meet the 1-minute constraint set in the customer service charter? Please explain your answer by showing how you calculate the average length of the queue and the average waiting time.

• What happens if the call center’s capacity is increased so that it can handle 80 calls per hour (using eight call center agents)?

• The call center manager has been given a mandate to cut costs by at least 20 %. Give at least two ideas to achieve this cut without reducing the salaries of the call center agents and while keeping an average waiting time below or close to one minute.