Practice Problems: Chapter 4, Forecasting



Practice Problems: Chapter 4, Forecasting

Problem 1:

Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week moving average.

|Week |Auto Sales |

|1 |8 |

|2 |10 |

|3 |9 |

|4 |11 |

|5 |10 |

|6 |13 |

|7 |- |

Problem 2:

Carmen’s decides to forecast auto sales by weighting the three weeks as follows:

|Weights Applied |Period |

|3 |Last week |

|2 |Twoweeks ago |

|1 |Three weeks ago |

|6 |Total |

Problem 3:

A firm uses simple exponential smoothing with [pic] to forecast demand. The forecast for the week of January 1 was 500 units whereas the actual demand turned out to be 450 units. Calculate the demand forecast for the week of January 8.

Problem 4:

Exponential smoothing is used to forecast automobile battery sales. Two value of [pic] are examined, [pic] and [pic] Evaluate the accuracy of each smoothing constant. Which is preferable? (Assume the forecast for January was 22 batteries.) Actual sales are given below:

|Month |Actual |Forecast |

| |Battery Sales| |

|January |20 |22 |

|February |21 |  |

|March |15 |  |

|April |14 |  |

|May |13 |  |

|June |16 |  |

Problem 5:

Use the sales data given below to determine: (a) the least squares trend line, and (b) the predicted value for 2008 sales.

|Year |Sales (Units)|

|2001 |100 |

|2002 |110 |

|2003 |122 |

|2004 |130 |

|2005 |139 |

|2006 |152 |

|2007 |164 |

To minimize computations, transform the value of x (time) to simpler numbers. In this case, designate year 2001 as year 1, 2002 as year 2, etc.

Problem 6:

Given the forecast demand and actual demand for 10-foot fishing boats, compute the tracking signal and MAD.

|Year |Forecast Demand|Actual Demand |

|1 |78 |71 |

|2 |75 |80 |

|3 |83 |101 |

|4 |84 |84 |

|5 |88 |60 |

|6 |85 |73 |

Problem: 7

Over the past year Meredith and Smunt Manufacturing had annual sales of 10,000 portable water pumps. The average quarterly sales for the past 5 years have averaged: spring 4,000, summer 3,000, fall 2,000 and winter 1,000. Compute the quarterly index.

Problem: 8

Using the data in Problem 7, Meredith and Smunt Manufacturing expects sales of pumps to grow by 10% next year. Compute next year’s sales and the sales for each quarter.

ANSWERS:

Problem 1:

[pic]

|Week |Auto Sales |Three-Week Moving Average |

|1 |8 |  |

|2 |10 |  |

|3 |9 |  |

|4 |11 |(8 + 9 + 10) / 3 = 9 |

|5 |10 |(10 + 9 + 11) / 3 = 10 |

|6 |13 |(9 + 11 + 10) / 3 = 10 |

|7 |- |(11 + 10 + 13) / 3 = 11 1/3 |

Problem 2:

[pic]

|Week |Auto Sales |Three-Week Moving Average |

|1 |8 |  |

|2 |10 |  |

|3 |9 |  |

|4 |11 |[(3*9) + (2*10) + (1*8)] / 6 = 9 1/6 |

|5 |10 |[(3*11) + (2*9) + (1*10)] / 6 = 10 1/6 |

|6 |13 |[(3*10) + (2*11) + (1*9)] / 6 = 10 1/6 |

|7 |- |[(3*13) + (2*10) + (1*11)] / 6 = 11 2/3 |

Problem 3:

[pic]

Problem 4:

|Month |Actual Battery Sales |Rounded Forecast with|Absolute Deviation |Rounded Forecast |Absolute Deviation |

| | |a =0.8 |with a =0.8 |with a =0.5 |with a =0.5 |

|January |20 |22 |2 |22 |2 |

|February |21 |20 |1 |21 |0 |

|March |15 |21 |6 |21 |6 |

|April |14 |16 |2 |18 |4 |

|May |13 |14 |1 |16 |3 |

|June |16 |13 |3 |15 |1 |

|  |  |  |  |  |  |

|  |  | Sum = |15 |  |16 |

| |2.5 |  |2.75 |

|[pic] | | | |

|SE |3.7 |  |4.1 |

On the basis of this analysis, a smoothing constant of a = 0.8 is preferred to that of a  = 0.5 because it has a smaller MAD.

Problem 5:

|Year |Time Period |Sales |X2 |XY |

| |(X) |(Units) (Y) | | |

|2001 |1 |100 |1 |100 |

|2002 |2 |110 |4 |220 |

|2003 |3 |122 |9 |366 |

|2004 |4 |130 |16 |520 |

|2005 |5 |139 |25 |695 |

|2006 |6 |152 |36 |912 |

|2007 |7 |164 |49 |1148 |

|  |S X = 28 |S Y =917 |S X2=140 |S XY = 3961|

[pic]

[pic]

[pic]

[pic]

Therefore, the least squares trend equation is:

[pic]

To project demand in 2008, we denote the year 2008 as [pic] and:

Sales in 2008 = 89.16 + 10.46 * 8 = 172.84

Problem 6:

|Year |Forecast Demand|Actual Demand |Error |RSFE |

|1 |78 |71 |-7 |-7 |

|2 |75 |80 |5 |-2 |

|3 |83 |101 |18 |16 |

|4 |84 |84 |0 |16 |

|5 |88 |60 |-28 |-12 |

|6 |85 |73 |-12 |-24 |

[pic]

|Year |Forecast Demand|Actual Demand ||Forecast Error||Cumulative Error |MAD |Tracking Signal |

|1 |78 |71 |7 |7 |7.0 |-1.0 |

|2 |75 |80 |5 |12 |6.0 |-0.3 |

|3 |83 |101 |18 |30 |10.0 |+1.6 |

|4 |84 |84 |0 |30 |7.5 |+2.1 |

|5 |88 |60 |28 |58 |11.6 |-1.0 |

|6 |85 |73 |12 |70 |11.7 |-2.1 |

[pic]

Problem 7:

Sales of 10,000 units annually divided equally over the 4 seasons is [pic] and the seasonal index for each quarter is: spring [pic] summer [pic] fall [pic] winter [pic]

Problem 8:

Next years sales should be 11,000 pumps [pic] Sales for each quarter should be 1/4 of the annual sales [pic] the quarterly index.

[pic]

[pic]

[pic]

[pic]

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