An insurance company receives 220 calls per day from customers who lodge insurance claims. The call center is open from 8 a.m. to 5 p.m. 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 8 a.m. to 11 a.m., the period 11 a.m. to 2 p.m. and the period 2 p.m. to 5 p.m. During the first period, around 60 calls are received. During the 11 a.m. to 2 p.m. period, 120 calls are received, and during the 2 p.m. to 5 p.m. period, 40 calls are received. A customer survey has shown that customers tend to call between 11 a.m. and 2 p.m. because during this time they have a break at work. Statistical analysis shows that the durations of calls follow an exponential distribution. According to the company’s customer service charter, customers should not wait more than 1 min on average for their call to be answered. • Assume that the call center can handle 70 calls per hour using 7 call center agents. Is this enough to meet the 1-min 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 80calls per hour (using 8 call center agents)?"
An insurance company receives 220 calls per day from customers who lodge insurance claims. The call center is open from 8 a.m. to 5 p.m. 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 8 a.m. to 11 a.m., the period 11 a.m. to 2 p.m. and the period 2 p.m. to 5 p.m. During the first period, around 60 calls are received. During the 11 a.m. to 2 p.m. period, 120 calls are received, and during the 2 p.m. to 5 p.m. period, 40 calls are received. A customer survey has shown that customers tend to call between 11 a.m. and 2 p.m. because during this time they have a break at work. Statistical analysis shows that the durations of calls follow an exponential distribution. According to the company’s customer service charter, customers should not wait more than 1 min on average for their call to be answered.
• Assume that the call center can handle 70 calls per hour using 7 call center agents. Is this enough to meet the 1-min 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 80calls per hour (using 8 call center agents)?"
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