Assumption.

A call center is open 12 hours a day, 7 days a week for a total of 360 hours in the month of April. We are trying to judge requiired staffing needs for the month of March which is our peak month. Using both information and from the datat given for March where we know that the total number of calls in the month is 125,084. The total call volume in hours is 56,940.44 and the average duration of each call is 0.46hrs. we are expected to calculate an arrival rate in calls per hour. Assume that the coefficient of variation of inter-arrival times is 1.You can get values for the service rate and the coefficient of variation of the service rate directly from the data.

Question

1. If all customer service representatives (CSRs) work in one large pool, handling all calls and customer types, how many CSRs are needed to handle the call volume with an average customer wait time of under three minutes?

2. We are considering creating two different call center pools, with one focusing on only HNW customers ( the total number of calls in the month is 21,996, the total call volume in hours is 7,575.44 and the average duration of each call is 0.34hrs) and another focusing on all other customers (the total number of calls in the month is 103,088, the total call volume in hours is 49,365 and the average duration of each call is 0.30hrs). How many CSRs are needed for each pool to achieve the same target of average wait time under three minutes?