Consumer Convenience, Inc Subject: Decision Theory - Case Study Example

Consumer Convenience, Inc Decision Theory (US MBA and Section # of Introduction (Background) Consumer Convenience, Inc. (CCI) is a retail catalog company that offers products by mail-order and by telephone booking. CCI’s corporate target is to achieve $45,000 per day in sales revenues from telemarketing operations. The daily cost of the telemarketing operations is $40,000 per day. Kim LePage promoted to director of telemarketing operation at CCI five month ago. Kim LePage along with her manager has been concerned about the variability in the sales revenues from the telemarketing operations. Therefore, Kim has decided to study the daily sales revenue data from the last five months of operations (see table 1 in appendix) in order to get a better understanding of the sales revenue variability. This paper will present a descriptive analysis and probability estimate of the daily sales revenue data from the last five month of telemarketing operations so that Kim would report to her manager as much information regarding sales revenues as possible. Discussion Questions (a) What is the shape of the distribution daily sales revenue from telemarketing operations? The average daily sales revenue from telemarketing operations is about $49274 with half of the daily sales revenue from telemarketing operations are above $49921 (See table 2 in appendix). For the five-month sales revenue from telemarketing operations, the mean ($49274) and the median ($49921) values of sales revenue are approximately close that suggest normal distribution. Figure 1 (histogram) also suggest that the shape of the distribution of the five-month sales revenue from telemarketing operations is normal. This visual normal distribution is supported numerically by the value of the coefficient of skewness, which is -0.14 that is very close to zero. Figure 1: Histogram of Daily Income of Telemarketing for 150 Days (b) What is an estimate of the expected daily sales revenue from telemarketing operations? How confident should Kim be about this estimate? Is there a need for more data? The average daily sales revenue from telemarketing operations is about $49274 with half of the daily sales revenue from telemarketing operations are above $49921 (See table 2 in appendix). The average daily sales revenue of $49274 is an estimate of the expected daily sales revenue from telemarketing operations. The 95 percent confidence interval for the average daily sales revenue is about $47914 to $50634. There is a probability of 0.95 that an interval constructed this way will contain the average daily sales revenue from telemarketing operations. In other way, Kim should be 95 percent confident about this estimate that the average daily sales revenue is in-between $47914 to $50634. The sample ‘Daily Income of Telemarketing for 150 Days’ is very large, therefore there is no need for more data. (c) What is an estimate of the standard deviation of the daily sales revenue from telemarketing operations? The sample ‘Daily Income of Telemarketing for 150 Days’ standard deviation is about $8427, which is an estimate of the standard deviation of the daily sales revenue from telemarketing operations. (d) On any given day, what is an estimate of the probability that daily sales revenue from telemarketing operations will be at least $45,000? How confident should Kim be about this estimate? Is there a need for more data? The standardized score (Z-score) for any daily sales revenue (X) can be calculated by formula. Therefore, the Z-score for the daily sales revenue of $45,000 is Pr{X ≥ $45,000} = 1 – φ(-0.5072) = 1 – 0.3060 = 0.6940 or 69.40% An estimate of the probability that daily sales revenue from telemarketing operations will be at least $45,000 is 69.40%. Figure 2 (Ogive curve) also suggest that approximately 70% of daily sales revenue from telemarketing operations is at least $45,000. Kim should be very much confident about this estimate as the shape of the distribution of daily sales revenue from telemarketing operations is approximately normal. The sample ‘Daily Income of Telemarketing for 150 Days’ is very large and normally distributed, therefore there is no need for more data. Figure 2: Ogive Curve of Daily Income of Telemarketing for 150 Days (e) On any given day, what is an estimate of the probability that daily sales revenue from telemarketing operations will be less than $40,000? How confident should Kim be about this estimate? Is there a need for more data? The Z-score for the daily sales revenue of $40,000 is Pr{X < $40,000} = φ(-1.1005) = 0.1356 or 13.56% An estimate of the probability that daily sales revenue from telemarketing operations will be less than $40,000 is 13.56%. Figure 2 (Ogive curve) also suggest that approximately 13% of daily sales revenue from telemarketing operations is less than $40,000. Kim should be very much confident about this estimate as the shape of the distribution of daily sales revenue from telemarketing operations is approximately normal. The sample ‘Daily Income of Telemarketing for 150 Days’ is very large and normally distributed, therefore there is no need for more data. Conclusion The shape of the distribution of the daily sales revenue from telemarketing operations is approximately normal. The average daily sales revenue from telemarketing operations is about $49274 and an estimate of the daily sales revenue standard deviation is about $8427. Therefore, CCI’s corporate target to achieve $45,000 per day in sales revenues from telemarketing operations is achieved. An estimate of the probability that daily sales revenue from telemarketing operations will be at least $45,000 is 69.40%. An estimate of the probability that daily sales revenue from telemarketing operations will be less than $40,000 is 13.56%. References: Freund. R. & Bertsimas. D (2000). Data, Models & Decision: The Fundamentals of Management Science. South Western College Publishing. Appendix Table 1: Daily Income of Telemarketing for 150 Days Date Sales Income (US$) Date Sales Income (US$) Date Sales Income (US$) 1-Feb 49,887.78 23-Mar 45,716.91 12-May 40,185.18 2-Feb 61,440.47 24-Mar 47,283.17 13-May 56,076.65 3-Feb 40,644.97 25-Mar 47,807.66 14-May 58,921.80 4-Feb 42,811.79 26-Mar 39,437.27 15-May 37,948.46 5-Feb 48,145.60 27-Mar 45,959.62 16-May 39,364.31 6-Feb 39,025.98 28-Mar 54,508.11 17-May 35,964.13 7-Feb 56,855.29 29-Mar 50,166.20 18-May 54,230.25 8-Feb 52,069.28 30-Mar 40,722.15 19-May 64,697.71 9-Feb 41,353.28 31-Mar 63,593.24 20-May 49,907.70 10-Feb 61,110.75 1-Apr 39,728.90 21-May 50,072.89 11-Feb 52,067.93 2-Apr 36,947.77 22-May 54,801.06 12-Feb 46,255.42 3-Apr 58,810.62 23-May 58,914.52 13-Feb 47,437.37 4-Apr 41,929.42 24-May 44,374.26 14-Feb 35,913.85 5-Apr 62,517.95 25-May 50,320.26 15-Feb 51,006.90 6-Apr 58,958.33 26-May 34,754.95 16-Feb 51,916.32 7-Apr 44,150.94 27-May 40,410.26 17-Feb 48,316.69 8-Apr 49,477.70 28-May 40,785.87 18-Feb 58,179.03 9-Apr 54,623.36 29-May 47,082.23 19-Feb 45,195.08 10-Apr 53,765.15 30-May 50,655.90 20-Feb 45,274.06 11-Apr 41,398.38 31-May 37,727.27 21-Feb 30,000.00 12-Apr 49,264.65 1-Jun 50,349.69 22-Feb 40,440.08 13-Apr 49,260.73 2-Jun 59,997.03 23-Feb 51,244.84 14-Apr 30,000.00 3-Jun 56,171.33 24-Feb 46,848.92 15-Apr 40,309.05 4-Jun 43,917.70 25-Feb 45,216.40 16-Apr 63,235.51 5-Jun 35,945.86 26-Feb 38,582.15 17-Apr 52,851.02 6-Jun 46,329.04 27-Feb 47,553.81 18-Apr 56,128.86 7-Jun 49,694.23 28-Feb 59,089.63 19-Apr 50,697.70 8-Jun 52,477.06 1-Mar 40,823.95 20-Apr 45,157.53 9-Jun 65,820.83 2-Mar 37,171.39 21-Apr 50,481.36 10-Jun 54,239.87 3-Mar 59,416.87 22-Apr 57,739.92 11-Jun 40,501.48 4-Mar 30,000.00 23-Apr 39,567.94 12-Jun 58,087.21 5-Mar 50,762.22 24-Apr 44,534.88 13-Jun 54,378.58 6-Mar 40,157.58 25-Apr 54,427.55 14-Jun 49,950.13 7-Mar 49,934.94 26-Apr 57,848.26 15-Jun 49,234.40 8-Mar 54,549.14 27-Apr 51,011.35 16-Jun 50,645.49 9-Mar 58,655.00 28-Apr 40,058.62 17-Jun 30,000.00 10-Mar 48,683.40 29-Apr 30,000.00 18-Jun 52,796.12 11-Mar 56,727.74 30-Apr 47,677.31 19-Jun 54,896.83 12-Mar 61,504.60 1-May 56,820.43 20-Jun 60,760.31 13-Mar 71,280.90 2-May 51,865.85 21-Jun 45,644.64 14-Mar 51,839.67 3-May 64,014.88 22-Jun 40,096.17 15-Mar 51,903.67 4-May 51,759.17 23-Jun 54,705.09 16-Mar 58,660.49 5-May 34,818.02 24-Jun 46,739.59 17-Mar 55,272.50 6-May 58,397.65 25-Jun 49,014.71 18-Mar 42,544.51 7-May 58,337.14 26-Jun 44,226.34 19-Mar 45,033.38 8-May 48,187.68 27-Jun 58,289.80 20-Mar 50,753.84 9-May 54,060.26 28-Jun 54,789.39 21-Mar 55,549.87 10-May 41,694.70 29-Jun 64,267.29 22-Mar 45,282.94 11-May 48,808.57 30-Jun 63,038.82 Table 2: Summary Statistics of Daily Income of Telemarketing for 150 Days Sales Revenue (US$) Mean 49274.08 Standard Error 688.08 Median 49921.32 Mode 30000.00 Standard Deviation 8427.28 Sample Variance 71018968.13 Kurtosis -0.35 Skewness -0.14 Range 41280.90 Minimum 30000.00 Maximum 71280.90 Sum 7391112.40 Count 150 Confidence Level (95.0%) 1359.66 Lower Limit 47914.42 Upper Limit 50633.75 Read More