The Catalog Company is a mail and phone order company that sells generic brands of houseware items and clothing. Approximately 95% of customer orders are received by phone; the remaining 5% is received in the mail. Phone orders are accepted at Catalog Companys toll-free number, 800-SAVE-NOW. The toll-free number is available 9 hours per day ( 8 A.M. to 5 P.M.), five days a week.

Sarah Walter 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 companys bottom line. After spending a week learning about Catalogs operations, Sarah feels that a closer evaluation can make a substantial impact on 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 Sarahs 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, Catalogs 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 nailing lists are essential, she thinks that a study of the mailing lists will take far more time than a quick evaluation of the phone order system.

Foregoing ahead, Sarah discovered the following information about the phone order system. The phone operator, Betty Wrangle, is paid $9 per hour in wages and benefits. The average costs 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 the cost of $40 per month per line. Catalogs 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 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 taking 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 other images 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 at 0.036 hours into the day. It takes Betty 0.054 hours 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.

Plot a frequency histogram of interarrival times. Does the distribution of interarrival times appear to be exponential?

1. Average Inter-arrival time :

2. Lambda= /Hour

c) It appears to be

4) Plot a frequency histogram of service times. Does the distribution of service times appear to be exponential?

1. Average service time :
2. Mu= /hour
3. It appears to be

5)

Would you recommend that Catalog acquire additional phone lines and operators? If so, how many? If not, why not?

S (Numer of service Person)	1	2	3
Ps
Revenue/Hour
Profit/Hour
Wages/Hour
Phone line / Hour
Phone calls / Hour
Net Profit / Hour

1. Suppose S =1, What is the net profit per hour?
2. Suppose S =2, What is the net profit per hour?
3. Suppose S =3, What is the net profit per hour
4. What is your recommendation?

I c G Catalog data Call Busy? (1=busy signal) number Bin Bin Call length (hours) 0.0544 0.0503 0.0191 0.0109 Revenue (dollars) 65.21 62.47 62.46 38.11 0 O Ovo AW COVOAWNO OVO AWNO 0.0877 54.02 0.0219 16.82 11 0 0.0544 0.0175 0.0583 26.38 27.88 47.30 Arrival time (hours) 0.0359 0.1564 0.3066 0.3609 0.3610 0.3689 0.4094 0.4652 0.8518 0.8597 0.9653 1.0852 1.5867 1.6252 1.6475 1.6953 1.7270 1.7457 1.7791 1.7876 1.9197 2.1416 2.2508 2.3207 2.4315 2.6049 2.8200 2.9286 2.9494 12 0 1 13 0.0939 56.18 16 15 15 17 0.1049 41.68 0 0.0869 0.0438 0.0818 46.05 25.03 28.75 0 0.0859 0.1466 0.1417 78.54 27.09 33.79 0 4 D F G H 0.0244 0.1513 0.0985 0.0869 46.12 45.88 10.00 27.63 0.0180 0.0309 0.0470 0.0801 25.63 35.40 10.00 68.24 0.0231 0.0141 0.0680 10.00 29.43 58.03 2.9286 2.9494 3.2749 3.5034 3.6799 3.8093 3.8299 4.0392 4.0918 4.1434 4.4357 4.4385 4.7999 4.9794 4.9964 5.0116 5.0591 5.3208 5.3846 5.3927 5.4588 5.5933 5.6614 5.7382 5.8696 6.0807 6.1491 6.1709 6.2136 6.4046 6.4233 6.4693 6.5602 0.1233 68.93 0.0189 0.1212 10.00 12.80 0.1049 0.1155 0.1176 47.04 53.03 25.39 0 0 0.0591 0.2174 56.95 25.35 60 C D E F G H I J K 61 63 0.0384 0.0895 0.0806 27.72 24.74 69.30 64 0.2175 47.75 68 0.1058 10.00 70 B 6.5861 6.6703 6.7295 6.8607 6.9368 6.9474 7.1178 7.1967 7.2355 7.5454 7.6737 7.7762 8.0674 8.1217 8.1224 8.1944 8.3930 8.3989 8.4033 8.4890 0.0253 0.0359 0.0963 0.0743 34.68 33.51 47.12 22.15 72 75 0 79 0.0802 0.0728 28.67 39.02 78 79 80 0.0310 10.00 I c G Catalog data Call Busy? (1=busy signal) number Bin Bin Call length (hours) 0.0544 0.0503 0.0191 0.0109 Revenue (dollars) 65.21 62.47 62.46 38.11 0 O Ovo AW COVOAWNO OVO AWNO 0.0877 54.02 0.0219 16.82 11 0 0.0544 0.0175 0.0583 26.38 27.88 47.30 Arrival time (hours) 0.0359 0.1564 0.3066 0.3609 0.3610 0.3689 0.4094 0.4652 0.8518 0.8597 0.9653 1.0852 1.5867 1.6252 1.6475 1.6953 1.7270 1.7457 1.7791 1.7876 1.9197 2.1416 2.2508 2.3207 2.4315 2.6049 2.8200 2.9286 2.9494 12 0 1 13 0.0939 56.18 16 15 15 17 0.1049 41.68 0 0.0869 0.0438 0.0818 46.05 25.03 28.75 0 0.0859 0.1466 0.1417 78.54 27.09 33.79 0 4 D F G H 0.0244 0.1513 0.0985 0.0869 46.12 45.88 10.00 27.63 0.0180 0.0309 0.0470 0.0801 25.63 35.40 10.00 68.24 0.0231 0.0141 0.0680 10.00 29.43 58.03 2.9286 2.9494 3.2749 3.5034 3.6799 3.8093 3.8299 4.0392 4.0918 4.1434 4.4357 4.4385 4.7999 4.9794 4.9964 5.0116 5.0591 5.3208 5.3846 5.3927 5.4588 5.5933 5.6614 5.7382 5.8696 6.0807 6.1491 6.1709 6.2136 6.4046 6.4233 6.4693 6.5602 0.1233 68.93 0.0189 0.1212 10.00 12.80 0.1049 0.1155 0.1176 47.04 53.03 25.39 0 0 0.0591 0.2174 56.95 25.35 60 C D E F G H I J K 61 63 0.0384 0.0895 0.0806 27.72 24.74 69.30 64 0.2175 47.75 68 0.1058 10.00 70 B 6.5861 6.6703 6.7295 6.8607 6.9368 6.9474 7.1178 7.1967 7.2355 7.5454 7.6737 7.7762 8.0674 8.1217 8.1224 8.1944 8.3930 8.3989 8.4033 8.4890 0.0253 0.0359 0.0963 0.0743 34.68 33.51 47.12 22.15 72 75 0 79 0.0802 0.0728 28.67 39.02 78 79 80 0.0310 10.00