Use the complete information in the file c13_01.xlsx to answer the following questions:

1. Approximately what fraction of the time is Betty idle? Is Ben’s estimate correct?

2. Approximately how many calls are lost in an average hour due to a busy signal?

3. Use the data to estimate the average arrival rate of all attempted calls to Catalog. Give an approximate 95% confidence interval for the estimate. Plot a frequency histogram of inter-arrival times. Does the distribution of inter-arrival times appear to be exponential?

4. Use the data to estimate the average service rate of all completed calls. Give an approximate 95% confidence interval for the estimate. Plot a frequency histogram of service times. Does the service time distribution appear to be exponential? Give an approximate 95% confidence interval for the average revenue per call.

5. Would you recommend that Catalog acquire additional phone lines and operators? If so, how many? If not, why not? Justify your answer in enough detail so that Ben Gleason would be convinced of your recommendation.

The Catalog Company is a mail- and phone-order company that sells generic brands of house-ware items and clothing. Approximately 95% of customer orders are received by phone; the remaining 5% are received in the mail. Phone orders are accepted at Catalog Company’s toll-free 800 number, 800-SAVE-NOW. The number is available nine hours per day (8 a.m.to 5 p.m.), five days per week.

Sarah Walters, a recent graduate of Columbia Business School, has just been hired by Catalog to improve its operations. Sarah would like to impress her boss, Ben Gleason, the president of Catalog Company, with some ideas that would quickly improve the company’s bottom line. After spending a week learning about Catalog’s operations, Sarah feels that a substantial impact can be made by a closer evaluation of the phone order system.

Currently, Catalog employs a single full-time operator to take orders over the phone. Sarah wonders whether additional operators should be hired to take phone orders. Ben feels that Sarah’s time might be better spent studying the catalog mailing lists. Ben reasons that the mailing lists are where customers are generated, and improving the list will bring in more revenue. And besides, Ben says, “Catalog’s phone operator, Betty Wrangle, seems to be doing nothing more than half of the time that I walk by. Hiring more operators to do nothing will just waste more money.” Although Sarah knows the mailing lists are important, she thinks that a study of the mailing lists will take far more time than a quick evaluation of the phone order system.

Forging ahead, Sarah discovers the following information about the phone order system. The phone operator, Betty Wrangle, is paid $9 per hour in wages and benefits. The average cost to Catalog for a completed 800 number call is $1.50. With only one phone line, any incoming calls that arrive when Betty is on the phone to another customer get a busy signal. The cost of the phone line is $40 per month. The phone company can immediately add up to four additional phone lines using the same 800 number, each at a cost of $40 per month per line. Catalog’s phone system is such that it cannot be upgraded in the near future to allow incoming calls to be placed on hold. The average profit on an order (not in cluding the cost of the operator or phone call) is 40% of the amount of the order. For example, an order of $100 brings a profit of $40 to Catalog. Sarah decided that additional information needed to be collected about the frequency of incoming calls, the length of the calls, and so on. After talking to the phone company, Sarah learned that she could borrow equipment for one day that could detect when a call was coming in, even when Betty was on the phone. The caller would still get a busy signal and be lost, but Sarah would know that a call had been attempted. Sarah collected almost nine hours of data the next day; these data are presented in the file c13_01.xlsx. Sarah believes that most of the callers who receive a busy signal take their business elsewhere and are totally lost to Catalog. Sarah does not feel that extending the hours of operation of the 800 number would be beneficial because the hours of operation are printed prominently in all of the catalogs. The first call arrives 0.036 hour into the day.

It takes Betty 0.054 hour to process the call and record the order for $65.21 worth of merchandise. Callers 5 and 6 get busy signals when they call, because Betty was still processing caller 4. Because calls 5 and 6 were lost, no call length information was available and no orders were placed. Data collection was stopped at call number 80.