Stock prices over a period of fifty (50) years would most likely exhibit no cyclical component….


QM 670 Final Exam

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  1. Stock prices over a period of fifty (50) years would most likely exhibit no cyclical component.
  1. True
  2. False
  1. On the plot labeled “a”, which of the following is correct?
  1. There is a trend present.
  2. There is a linear relationship.
  3. There is an obvious outlier.
  4. There is a negative relationship.
  1. On the plot labeled “b”, there is an outlier present.
  1. True
  2. False
  1. On the plot labeled “c”, which of the following models is most appropriate?
  1. single-parameter exponential smoothing
  2. regression
  3. regression with seasonality (classical time-series)
  4. none of the above are appropriate
  1. In a simple linear regression, we are using monthly advertising expenditures (in $000) to predict monthly profits (in $000). If the least squares equation is y = 21.5 – .1x and the coefficient of determination is .49, the correlation coefficient = ______.
  1. 0.70
  2. -0.70
  3. unable to be determined from the data.
  1. In a simple linear regression, we are using monthly advertising expenditures (in $000) to predict monthly profits (in $000). If the least squares equation is y = 21.5 – .1x and the coefficient of determination is .49. The predicted profit = __________ when advertising expenses are $0.
  1. 21.5
  2. -0.1
  3. $21,500
  4. none of the above.
  1. If the correlation coefficient is zero, there is no relationship between x and y.
  1. True
  2. False
  1. Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of $30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable:
Order Quantity Price/pair
0-99 $36
100-199 32
200-299 30
300+ 28

For a price of $36, the optimal order quantity is

  1. 129
  2. infeasible for this cost structure.
  3. neither of the above.
  4. both a and b.
  1. Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of $30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable:
Order Quantity Price/pair
0-99 $36
100-199 32
200-299 30
300+ 28

The optimal order quantity is

  1. 129
  2. 141
  3. 146
  4. 300

  1. Foster Inc. carries special holiday items, including Happy Angels (HAs). During the season, the demand for HAs is approximately normally distributed, with a mean of 320 and a standard deviation of 30. It costs Foster $5.00 for each HA unless he orders at least 400, at which the price drops to $4.50/HA. The HAs’ retail price is $10. Unsold items will be given to a local hospital, with a disposal cost of $0.05/HA. Mr. Foster estimates that the goodwill cost of each item short is close to $0.25.
  1. This is a single-period inventory problem.
  2. This is an EOQ problem.
  3. This is a periodic-review problem.
  4. None of the above
  1. Foster Inc. carries special holiday items, including Happy Angels (HAs). During the season, the demand for HAs is approximately normally distributed, with a mean of 320 and a standard deviation of 30. It costs Foster $5.00 for each HA unless he orders at least 400, at which the price drops to $4.50/HA. The HAs’ retail price is $10. Unsold items will be given to a local hospital, with a disposal cost of $0.05/HA. Mr. Foster estimates that the goodwill cost of each item short is close to $0.25. A Christmas-tree model is appropriate.
  1. True
  2. False
  1. A regular EOQ model is appropriate when demand is seasonal.
  1. True
  2. False
  1. See the attached “Regression Data I”. We are using the number of radios, TVs, and DVD players stocked to predict the profit, revenue, and cost for future periods. First, run a model to predict the profit. Select all which apply.
  1. Radios is a significant predictor.
  2. TVs is a significant predictor.
  3. DVDs is a significant predictor.
  4. The overall model is significant.
  5. The intercept is positive.
  6. Severe multicollinearity is present.
  1. See the attached “Regression Data I”. We are using the number of radios, TVs, and DVD players stocked to predict the profit, revenue, and cost for future periods. Next, run a model to predict the cost. Select all which apply.
  1. Radios is a significant predictor.
  2. TVs is a significant predictor.
  3. DVDs is a significant predictor.
  4. The overall model is significant.
  5. The intercept is positive.
  6. Severe multicollinearity is present.
  1. See the attached “Regression Data I”. We are using the number of radios, TVs, and DVD players stocked to predict the profit, revenue, and cost for future periods. Based on the output, which of the following recommendations would be most appropriate?
  1. We should stock more radios.
  2. We should stock fewer TVs.
  3. We should increase floor space, since it is probably constraining our sales ability.
  4. We should consider the time period.

16. What is the best answer given this information? (3)

Model 1 Model 2 Model 3
X-variables 6 4 3
R2 .9344 .8857 .8761
Adjusted R2 .9058 .8372 .8497
MSE 5667.53 6044.05 5844.78

  1. Model 1 performs the best in all areas.
  2. Model 2 performs better than Model 3.
  3. We would most likely prefer Model 1.
  4. We would most likely prefer Model 2.
  5. We would most likely prefer Model 3.

17. The table below features three forecasting models used on the same set of data. Select all that apply.

Model 1 Model 2 Model 3
Type Single-parameter Exponential smoothing 2-parameter Exponential smoothing 3-parameter Exponential smoothing
MSE 8755.3 4876.2 5945.8
  1. There is likely a strong seasonal component present.
  2. There is likely a trend present.
  3. There is no random component present.
  4. There is a cyclical component present.
  5. A different smoothing constant could affect the MSE for Model 1.

  1. If we increase the order (setup) cost, the order quantity will _____________ if we hold all other costs constant.
  1. increase
  2. decrease
  3. remain the same as long as there is no shortage cost
  4. become unstable
  1. If demand is normally distributed,
  1. a basic EOQ is appropriate.
  2. a single-period model could not be appropriate.
  3. we should produce to fill demand, rather than filling it through orders.
  4. none of the above would be true.
  1. Which of the following methods may be used to determine future order quantities?
  1. forecasting
  2. regression
  3. inventory models
  4. all of the above
  1. Refer to the inventory output for Betsy’s Blue Bonnet Bakery. Here, Betsy is trying to determine the optimal order policy for birthday kits. What is the safety stock?

____________________

  1. Refer to #21. What is Betsy’s service level if she uses this policy?

____________________

  1. Refer to #21. If Betsy changes to a lost sales model, the order quantity would be expected to increase.
  1. True
  2. False
  3. It depends on the cost associated with a lost sale.
  1. Refer to the forecasting output for Betsy’s. This model is appropriate for the type of data.
  1. True
  2. False
  1. Refer to #24. Look at the forecast errors. Which of the following best describes the situation?
  1. The errors are indicative of what we like to see.
  2. The errors are randomly distributed.
  3. The errors are indicative of a problem with the model.
  4. The errors are indicative of a poor choice of a.
  1. Refer to #24. What recommendation would you make?
  1. We should use the model as is.
  2. We should alter model parameters to improve the fit?
  3. We should use the model, but use extreme caution in doing so.
  4. We should eliminate some time periods for forecasting.

Regression Data I

Profit Revenue Radios TVs DVDs Quarter Errors
6318.96 8395.91 36 65 48
4721.57 6300.28 26 48 39
5049.16 6747.55 33 51 40 2000 – 3 32
5249.44 7028.56 29 53 45 4 46
5290.08 7116.41 32 52 49 2001 – 1 19
5924.41 7951.00 41 58 52 2 23
5251.97 7031.09 36 52 44 3 34
4805.72 6462.88 31 47 44 4 49
5278.60 7162.42 46 49 51 2002 – 1 22
5301.77 7136.35 43 51 46 2 20
6121.98 8249.84 45 59 56 3 31
5416.63 7244.79 29 55 46 4 51
6552.89 8718.21 43 67 48 2003 – 1 16
6352.93 8494.02 46 63 51 2 26
6693.01 8881.75 55 68 43 3 37
5761.97 7669.10 48 58 39 4 48
5419.50 7265.38 33 54 47 2004 -1 22
5474.64 7302.97 35 55 44 2 24
4650.87 6335.89 41 42 49
4781.91 6438.23 48 45 39
MULTI-PERIOD EOQ MODEL (Backordering) – NORMAL LEAD-TIME DEMAND
PROBLEM: Betsy’s Blue Bonnet Bakery
Parameter Values:
Mean of Demand Distribution: mu = 1,000
Stand. Deviation of Demand Distribution: sigma = 100
Fixed Cost per Order: k = 5,000
Annual Demand Rate: A = 52,000
Unit Cost of Procuring an Item: c = 42.00
Annual Holding Cost per Dollar Value: h = 0.20
Shortage Cost per Unit: pS = 10.00
Optimal Values:
Optimal Order Quantity: Q* = 7,919
Optimal Reorder Point: r* = 1,114
Expected Demand: mu = 1,000
Total Expected Cost: TEC(Q*) = $ 67,471.24
Expected Shortages: B(r*) = 6.47
Probability of Shortage: P[D>r*] = 0.13

Betsy’s Blue Bonnet Bakery
a = 0.3 g = 0.5 b = 0.8
Actual Trend Slope Seasonal Forecast Error
Quarter t Sales, Yt Tt bt St Ft
2003 W 1 36,500
1988 S 2 43,750 36,500.00 7,250.00 1.20
1988 S 3 59,920 48,601.00 9,675.50 1.23
1988 F 4 87,440 67,025.55 14,050.03 1.30
2004 W 5 102,240 87,424.90 17,224.69 1.17
1988 S 6 123,420 104,144.98 16,972.38 1.19 125,436.15 (2,016.15)
1988 S 7 139,610 118,753.37 15,790.39 1.19 149,325.16 (9,715.16)
1988 F 8 135,380 125,312.56 11,174.79 1.13 175,522.72 (40,142.72)
2005 W 9 129,470 128,753.89 7,308.06 1.04 159,616.61 (30,146.61)
1988 S 10 137,570 129,989.43 4,271.80 1.08 161,612.88 (24,042.88)
1988 S 11 156,630 133,566.44 3,924.41 1.18 159,379.23 (2,749.23)
1988 F 12 150,980 136,498.26 3,428.11 1.11 154,702.82 (3,722.82)
2006 W 13 143,340 139,362.57 3,146.21 1.03 145,291.38 (1,951.38)
1988 S 14 153,360 142,190.68 2,987.16 1.08 154,509.63 (1,149.63)
1988 S 15 169,730 144,939.30 2,867.89 1.17 170,664.76 (934.76)
1988 F 16 161,990 147,249.54 2,589.07 1.10 164,053.12 (2,063.12)
2007 W 17 154,760 149,940.86 2,640.19 1.03 154,408.75 351.25
1988 S 18 164,780 152,592.38 2,645.85 1.08 164,739.26 40.74
1988 S 19 186,730 156,466.79 3,260.13 1.19 181,930.65 4,799.35
1988 F 20 177,880 160,230.59 3,511.97 1.11 176,029.75 1,850.25
2008 W 21 170,360 164,152.06 3,716.72 1.04 168,951.59 1,408.41
1988 S 22 178,830 167,190.82 3,377.74 1.07 181,270.26 (2,440.26)
1988 S 23 195,550 168,732.72 2,459.82 1.16 202,826.81 (7,276.81)
1988 F 24 187,220 170,501.72 2,114.41 1.10 189,772.64 (2,552.64)
2009 W 25 163,230 168,070.53 (158.39) 0.98 178,936.82 (15,706.82)
1988 S 26 162,890 163,137.87 (2,545.53) 1.01 179,944.64 (17,054.64)
1988 S 27 174,540 157,361.67 (4,160.86) 1.12 187,085.45 (12,545.45)
1988 F 28 163,130 151,724.53 (4,899.00) 1.08 168,543.79 (5,413.79)
2010 W 29 144,517.86
1988 S 30 143,788.09
1988 S 31 153,515.48
1988 F 32 142,720.95
MSE = 175,943,211

QM 670 Final Exam

  1. Stock prices over a period of fifty (50) years would most likely exhibit no cyclical component.
  1. True
  2. False
  1. On the plot labeled “a”, which of the following is correct?
  1. There is a trend present.
  2. There is a linear relationship.
  3. There is an obvious outlier.
  4. There is a negative relationship.
  1. On the plot labeled “b”, there is an outlier present.
  1. True
  2. False
  1. On the plot labeled “c”, which of the following models is most appropriate?
  1. single-parameter exponential smoothing
  2. regression
  3. regression with seasonality (classical time-series)
  4. none of the above are appropriate
  1. In a simple linear regression, we are using monthly advertising expenditures (in $000) to predict monthly profits (in $000). If the least squares equation is y = 21.5 – .1x and the coefficient of determination is .49, the correlation coefficient = ______.
  1. 0.70
  2. -0.70
  3. unable to be determined from the data.
  1. In a simple linear regression, we are using monthly advertising expenditures (in $000) to predict monthly profits (in $000). If the least squares equation is y = 21.5 – .1x and the coefficient of determination is .49. The predicted profit = __________ when advertising expenses are $0.
  1. 21.5
  2. -0.1
  3. $21,500
  4. none of the above.
  1. If the correlation coefficient is zero, there is no relationship between x and y.
  1. True
  2. False
  1. Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of $30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable:
Order Quantity Price/pair
0-99 $36
100-199 32
200-299 30
300+ 28

For a price of $36, the optimal order quantity is

  1. 129
  2. infeasible for this cost structure.
  3. neither of the above.
  4. both a and b.
  1. Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of $30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable:
Order Quantity Price/pair
0-99 $36
100-199 32
200-299 30
300+ 28

The optimal order quantity is

  1. 129
  2. 141
  3. 146
  4. 300

  1. Foster Inc. carries special holiday items, including Happy Angels (HAs). During the season, the demand for HAs is approximately normally distributed, with a mean of 320 and a standard deviation of 30. It costs Foster $5.00 for each HA unless he orders at least 400, at which the price drops to $4.50/HA. The HAs’ retail price is $10. Unsold items will be given to a local hospital, with a disposal cost of $0.05/HA. Mr. Foster estimates that the goodwill cost of each item short is close to $0.25.
  1. This is a single-period inventory problem.
  2. This is an EOQ problem.
  3. This is a periodic-review problem.
  4. None of the above
  1. Foster Inc. carries special holiday items, including Happy Angels (HAs). During the season, the demand for HAs is approximately normally distributed, with a mean of 320 and a standard deviation of 30. It costs Foster $5.00 for each HA unless he orders at least 400, at which the price drops to $4.50/HA. The HAs’ retail price is $10. Unsold items will be given to a local hospital, with a disposal cost of $0.05/HA. Mr. Foster estimates that the goodwill cost of each item short is close to $0.25. A Christmas-tree model is appropriate.
  1. True
  2. False
  1. A regular EOQ model is appropriate when demand is seasonal.
  1. True
  2. False
  1. See the attached “Regression Data I”. We are using the number of radios, TVs, and DVD players stocked to predict the profit, revenue, and cost for future periods. First, run a model to predict the profit. Select all which apply.
  1. Radios is a significant predictor.
  2. TVs is a significant predictor.
  3. DVDs is a significant predictor.
  4. The overall model is significant.
  5. The intercept is positive.
  6. Severe multicollinearity is present.
  1. See the attached “Regression Data I”. We are using the number of radios, TVs, and DVD players stocked to predict the profit, revenue, and cost for future periods. Next, run a model to predict the cost. Select all which apply.
  1. Radios is a significant predictor.
  2. TVs is a significant predictor.
  3. DVDs is a significant predictor.
  4. The overall model is significant.
  5. The intercept is positive.
  6. Severe multicollinearity is present.
  1. See the attached “Regression Data I”. We are using the number of radios, TVs, and DVD players stocked to predict the profit, revenue, and cost for future periods. Based on the output, which of the following recommendations would be most appropriate?
  1. We should stock more radios.
  2. We should stock fewer TVs.
  3. We should increase floor space, since it is probably constraining our sales ability.
  4. We should consider the time period.

16. What is the best answer given this information? (3)

Model 1 Model 2 Model 3
X-variables 6 4 3
R2 .9344 .8857 .8761
Adjusted R2 .9058 .8372 .8497
MSE 5667.53 6044.05 5844.78

  1. Model 1 performs the best in all areas.
  2. Model 2 performs better than Model 3.
  3. We would most likely prefer Model 1.
  4. We would most likely prefer Model 2.
  5. We would most likely prefer Model 3.

17. The table below features three forecasting models used on the same set of data. Select all that apply.

Model 1 Model 2 Model 3
Type Single-parameter Exponential smoothing 2-parameter Exponential smoothing 3-parameter Exponential smoothing
MSE 8755.3 4876.2 5945.8
  1. There is likely a strong seasonal component present.
  2. There is likely a trend present.
  3. There is no random component present.
  4. There is a cyclical component present.
  5. A different smoothing constant could affect the MSE for Model 1.

  1. If we increase the order (setup) cost, the order quantity will _____________ if we hold all other costs constant.
  1. increase
  2. decrease
  3. remain the same as long as there is no shortage cost
  4. become unstable
  1. If demand is normally distributed,
  1. a basic EOQ is appropriate.
  2. a single-period model could not be appropriate.
  3. we should produce to fill demand, rather than filling it through orders.
  4. none of the above would be true.
  1. Which of the following methods may be used to determine future order quantities?
  1. forecasting
  2. regression
  3. inventory models
  4. all of the above
  1. Refer to the inventory output for Betsy’s Blue Bonnet Bakery. Here, Betsy is trying to determine the optimal order policy for birthday kits. What is the safety stock?

____________________

  1. Refer to #21. What is Betsy’s service level if she uses this policy?

____________________

  1. Refer to #21. If Betsy changes to a lost sales model, the order quantity would be expected to increase.
  1. True
  2. False
  3. It depends on the cost associated with a lost sale.
  1. Refer to the forecasting output for Betsy’s. This model is appropriate for the type of data.
  1. True
  2. False
  1. Refer to #24. Look at the forecast errors. Which of the following best describes the situation?
  1. The errors are indicative of what we like to see.
  2. The errors are randomly distributed.
  3. The errors are indicative of a problem with the model.
  4. The errors are indicative of a poor choice of a.
  1. Refer to #24. What recommendation would you make?
  1. We should use the model as is.
  2. We should alter model parameters to improve the fit?
  3. We should use the model, but use extreme caution in doing so.
  4. We should eliminate some time periods for forecasting.

Regression Data I

Profit Revenue Radios TVs DVDs Quarter Errors
6318.96 8395.91 36 65 48
4721.57 6300.28 26 48 39
5049.16 6747.55 33 51 40 2000 – 3 32
5249.44 7028.56 29 53 45 4 46
5290.08 7116.41 32 52 49 2001 – 1 19
5924.41 7951.00 41 58 52 2 23
5251.97 7031.09 36 52 44 3 34
4805.72 6462.88 31 47 44 4 49
5278.60 7162.42 46 49 51 2002 – 1 22
5301.77 7136.35 43 51 46 2 20
6121.98 8249.84 45 59 56 3 31
5416.63 7244.79 29 55 46 4 51
6552.89 8718.21 43 67 48 2003 – 1 16
6352.93 8494.02 46 63 51 2 26
6693.01 8881.75 55 68 43 3 37
5761.97 7669.10 48 58 39 4 48
5419.50 7265.38 33 54 47 2004 -1 22
5474.64 7302.97 35 55 44 2 24
4650.87 6335.89 41 42 49
4781.91 6438.23 48 45 39
MULTI-PERIOD EOQ MODEL (Backordering) – NORMAL LEAD-TIME DEMAND
PROBLEM: Betsy’s Blue Bonnet Bakery
Parameter Values:
Mean of Demand Distribution: mu = 1,000
Stand. Deviation of Demand Distribution: sigma = 100
Fixed Cost per Order: k = 5,000
Annual Demand Rate: A = 52,000
Unit Cost of Procuring an Item: c = 42.00
Annual Holding Cost per Dollar Value: h = 0.20
Shortage Cost per Unit: pS = 10.00
Optimal Values:
Optimal Order Quantity: Q* = 7,919
Optimal Reorder Point: r* = 1,114
Expected Demand: mu = 1,000
Total Expected Cost: TEC(Q*) = $ 67,471.24
Expected Shortages: B(r*) = 6.47
Probability of Shortage: P[D>r*] = 0.13

Betsy’s Blue Bonnet Bakery
a = 0.3 g = 0.5 b = 0.8
Actual Trend Slope Seasonal Forecast Error
Quarter t Sales, Yt Tt bt St Ft
2003 W 1 36,500
1988 S 2 43,750 36,500.00 7,250.00 1.20
1988 S 3 59,920 48,601.00 9,675.50 1.23
1988 F 4 87,440 67,025.55 14,050.03 1.30
2004 W 5 102,240 87,424.90 17,224.69 1.17
1988 S 6 123,420 104,144.98 16,972.38 1.19 125,436.15 (2,016.15)
1988 S 7 139,610 118,753.37 15,790.39 1.19 149,325.16 (9,715.16)
1988 F 8 135,380 125,312.56 11,174.79 1.13 175,522.72 (40,142.72)
2005 W 9 129,470 128,753.89 7,308.06 1.04 159,616.61 (30,146.61)
1988 S 10 137,570 129,989.43 4,271.80 1.08 161,612.88 (24,042.88)
1988 S 11 156,630 133,566.44 3,924.41 1.18 159,379.23 (2,749.23)
1988 F 12 150,980 136,498.26 3,428.11 1.11 154,702.82 (3,722.82)
2006 W 13 143,340 139,362.57 3,146.21 1.03 145,291.38 (1,951.38)
1988 S 14 153,360 142,190.68 2,987.16 1.08 154,509.63 (1,149.63)
1988 S 15 169,730 144,939.30 2,867.89 1.17 170,664.76 (934.76)
1988 F 16 161,990 147,249.54 2,589.07 1.10 164,053.12 (2,063.12)
2007 W 17 154,760 149,940.86 2,640.19 1.03 154,408.75 351.25
1988 S 18 164,780 152,592.38 2,645.85 1.08 164,739.26 40.74
1988 S 19 186,730 156,466.79 3,260.13 1.19 181,930.65 4,799.35
1988 F 20 177,880 160,230.59 3,511.97 1.11 176,029.75 1,850.25
2008 W 21 170,360 164,152.06 3,716.72 1.04 168,951.59 1,408.41
1988 S 22 178,830 167,190.82 3,377.74 1.07 181,270.26 (2,440.26)
1988 S 23 195,550 168,732.72 2,459.82 1.16 202,826.81 (7,276.81)
1988 F 24 187,220 170,501.72 2,114.41 1.10 189,772.64 (2,552.64)
2009 W 25 163,230 168,070.53 (158.39) 0.98 178,936.82 (15,706.82)
1988 S 26 162,890 163,137.87 (2,545.53) 1.01 179,944.64 (17,054.64)
1988 S 27 174,540 157,361.67 (4,160.86) 1.12 187,085.45 (12,545.45)
1988 F 28 163,130 151,724.53 (4,899.00) 1.08 168,543.79 (5,413.79)
2010 W 29 144,517.86
1988 S 30 143,788.09
1988 S 31 153,515.48
1988 F 32 142,720.95
MSE = 175,943,211

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