Mai Chen, fresh from business school, has been hired by Listen-Up.com, a small, start-up manufacturer of hearing aids, to resolve the difficulties within its customer service group. The company’s products are sold over the Internet or phoned in using the company’s toll-free telephone lines, but telephone orders is the main and growing sales channel. During its three years of existence the company has experienced rapid growth with the number of units produced more than doubling each year, but now faces a problem, scheduling its customer service staff and to optimize its toll free line capacity, in order to satisfy customers. The issue is that during the peak period of 7:30 am to 2:00 pm the average waiting time is over 127 seconds. Approximately 76% of all callers have to wait. Customers now have been telling the Listen-Up.com sales staff that it is next to impossible to get through to ask questions and place orders.
The customer service department has eight customer service representatives (CSR's) and a supervisor. There are 12 incoming phone lines. The phone system automatically assigns an incoming call to an available CSR. If no CSR is available, the caller waits as the call is placed in a queue for the next available CSR on a “first-come, first-serve basis.” Sometimes, when all 12 lines are in use (e.g. 8 having CSR's assisting customers and 4 customers holding in queue) the caller receives a busy signal. Incoming calls can be classified into one of six categories: standard product order, custom order, order status check, new account creation, hearing aid supply order and information request.
1. What is the average arrival rate, λ, for incoming calls during a typical day? Average arrival rate stands for the number of customers calling in a certain time. If we assume the unit time is hour, the calculations are as follows.
* Sum up the Average No. Calls (Figure 1 in Appendix)
Total No. Calls=1348.7
* Average arrival rate: λ=1348.7÷12=112.39 calls/Hour
First, we add all the Average No. Calls together. Second, we use this result to be divided by the working hours.
In conclusion, the average arrival rate is 112.39 calls / hour.
2. What is the average service rate, µ, for the CSR's to handle incoming calls during a typical day? Service rate represents the number of customers CSRs can serve in unit time. If we assume the unit time is hour, the calculations are as follows.
* Average service time: (0.60 x 85 sec) + (0.15 x 120 sec) + (0.15×220 sec) +(0.05×450 sec) +(0.03×125 sec) + (0.02×120 sec)=130.65 sec * Average service rate: µ=(60 min×60 sec)÷130.65=27.55 calls/ Hour
First, we calculate the weighted CSR Time Spent. As there are 6 call types and the frequency of each type happening differs, we will make frequency multiply CSR Time Spent to the result.
Second, after we’ve got the average service time, we use the amount of working hours to be divided by the total service time. Finally, we have the average service rate.
Therefore, the average service rate is 27.55 calls/ Hour.
3. What is the standard deviation of the service rate, µ?
Since the exponential distribution describes the waiting time of a specific event, the service rate is exponential distribution.
According to the formula, standard deviation is the square root of variance, and the variance can be calculated based on 1/µ2.
* Standard deviation=
As a result, the stand deviation is 27.55
4. Which waiting line model is most appropriate for the incoming calls?
Since there are 8 CSR in charging of answering questions, the number of channels is 8.
According to the case, the customer population is infinite, because the number of customers is large enough and there will be no influence on the system if the customers decline.
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