The "Patelco (B)" case offers an example of the economics of call center design. The call volume

data can be downloaded from the file PatelcoB.xls posted on the course web site.

For these questions you may assume that the arrival process is Poisson, and that service times

are exponentially distributed. You should also assume that blocking and abandonment are not an

issue. Ignore Saturdays, focusing instead only on week days, with 20 working days per month.

Clearly state any other assumptions that you make.

1. Develop minimum cost staffing plans for each of the four call centers. Your plan for each

site should:

a. make sure that there are enough people on hand during each half-hour to meet

the company's 60-second average speed of answer (ASA) requirement (i.e., the

average waiting time before a call is answered);

b. have all employees work 8-hour shifts; and,

c. allow each shift to start only on the hour.

2. As an alternative, suppose Patelco considered 4-hour shifts that start on the hour?

Consider only the General Call Center. What is the effect of this plan on staffing levels

and costs? Would you recommend this option?

For the following questions, assume 8-hour shifts that start on the hour.

3. Consider the General Call Center. In order to make the call center more responsive,

suppose the ASA requirement is reduced to 10 seconds. What is the effect of this change

on staffing requirements and costs?

4. Let's go back to the 60-second ASA requirement. Assume that if the cross-selling

proposal is implemented at the General Call Center the average call length will increase

to 5 minutes. What is the effect of this proposal on staffing levels and costs? What crosssell

capture ratio will make this a cost effective proposition?

5. Would CTI be profitable if implemented at the General Call Center? Assume that the

average call length will be 5 minutes whenever cross-selling is attempted, and that the

cross-sell capture ratio is 1% for these calls. Also assume that the average call duration

is 10 seconds lower for the rest of the calls. (Note: You may assume that the resulting

average call duration is a weighted average of the call durations for cases when crossselling

is attempted and when it is not.)

6. Now consider consolidating the four call centers into a single one, with no cross-selling or

CTI. Assuming a 60 second ASA requirement as before, what is the effect of this option

on staffing levels and costs? What explains the resulting differences? Would you

recommend this solution?

Expected Number of Calls per Half-Hour Interval Time General Card Services Mortgage Collections Total 7:00-7:29 0 0 0 0 7:30-7:59 51 12 O 63 8:00-8:29 77 12 3 4 8:30-8:59 96 96 16 7 11 130 9:00-9:29 144 21 12 14 9:30-9:59 191 152 24 13 18 207 10:00-10:29 169 25 19 23 236 10:30-10:59 174 26 19 29 248 11:00-11:29 167 25 19 31 242 11:30-11:59 163 23 21 31 238 12:00-12:29 159 22 14 21 12:30-12:59 217 160 23 18 30 230 1:00-1:29 147 22 15 23 207 1:30-1:59 159 22 16 25 2:00-2:29 221 138 22 21 22 202 2:30-2:59 144 21 21 24 210 3:00-3:29 148 24 19 31 222 3:30-3:59 143 23 17 25 207 4:00-4:29 146 19 17 24 206 4:30-4:59 122 18 17 27 184 5:00-5:29 65 12 3 14 93 5:30-5:59 48 7 14 70 6:00-6:29 21 0 4 25 6:30-6:59 14 3 16 7:00-7:29 0 0 7:30-8:00 0 0 0