Waiting Line Models

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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, The number is available 9 hours per day ( 8 A.M. to 5 P.M.), 5 days a week. Currently, Catalog employs a single full-time operator to take orders over the phone. Sarah, who is company director, wonders whether additional operators should be hired to take phone orders. Ben, who is CEO, 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 $20 per hour in wages and benefits. The average cost to Catalog for a completed 800 number call is $ 1.00. With 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 $50 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 including the cost of the operator or phone call) is 30% of the amount of the order. For example, an order of $100 brings a profit of $30 to Catalog. Sarah

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