McM Cog is a supplier of industrial parts. Most orders are received at a call center. The call center currently has 10 phone lines total, i.e., a maximum of 10 callers may be in the call center system at any time. On average, calls arrive at a rate of three per minute. Each customer service representative (CSR) averages 2.5 minutes per customer call. Mc Cog estimates there is a cost of two dollars per customer for each minute spent waiting by a caller. Assume that callers getting a busy signal take their business elsewhere resulting in a loss to McM of $155 per lost call. CSRs are paid $15 per hour, and it costs McM Cog $4 per hour per line.
a. What is the total hourly cost of the call center and associated activities at McM Cog with the minimum number of CSRs?
b. What is the total hourly cost to McM Cog if they decide to hire another CSR? What is the total hourly cost to McM Cog if they decide to add another line? Note: Perform each of these two system adjustments separately based off the answer to part a. Of the three options investigated so far, which is best?
c. Given the freedom (and cost) of adding or removing additional telephone lines and CSRs what the best recommendation for McM Cog management in terms of total hourly cost? Justify your answer.