A solar panel manufacturer located in Renton, WA sells its product in two countries: U.S. and Mexico. Currently, two customer service staff are working independently to answer phone calls at the call...

A solar panel manufacturer located in Renton, WA sells its product in two countries: U.S. and Mexico.  Currently, two customer service staff are working independently to answer phone calls at the call center. The first staff “Vanessa” speaks English only, and she is assigned to a line dedicated to domestic calls. The second staff “Gabriela” speaks Spanish only, and she is assigned to a line dedicated to international calls from Mexico. For simplicity, assume that all domestic calls are in English and all international calls are in Spanish, calls are taken first-come first-serve and are placed on hold if the line is busy.

Currently, incoming calls to
each
staff follow a Poisson distribution with a mean of 10/hr (total mean arrival rate to the
customer service center
is 20/hr.) The processing time of each staff is exponential with a mean of 4 minutes.

In any given period, one staff is usually very busy while the other has nothing to do. For example, when there are many calls from Mexico, Gabriela must put calls on hold even when Vanessa is available, and vice versa. So the company is considering training the two staff to be bilingual. This way, only one line is needed. Both staff will still work independently, but as long as there are calls on hold then both will be busy. (Hint:
look at the following figure for the comparison of the current system and proposed system)

Since the scope of work for each staff is slightly expanded in the proposed system, the mean processing time is expected to increase to 4.5 minutes (still exponential). Suppose the two key performance measures are:

• Expected number of calls in the call center (i.e. #being served plus #on hold).


• Expected time for each call (from dialing to call center to finishing the conversation).

1. Calculate the two key performance measures above for both systems, and conclude which system is better based on these measures .

1. b) If each customer is being paid 60 $/hour for being in the system, and each staff is being paid the minimum wage (i.e., 15 $/hour), what is the hourly cost of this system (by “this system” I mean the system you chose in part a) ?