# Exponential Smoothing and Week Auto Sales

**Topics:**Exponential smoothing, Moving average, Time series analysis

**Pages:**7 (841 words)

**Published:**October 3, 2011

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 2003 sales.

|Year |Sales (Units)|

|1996 |100 |

|1997 |110 |

|1998 |122 |

|1999 |130 |

|2000 |139 |

|2001 |152 |

|2002 |164 |

To minimize computations, transform the value of x (time) to simpler numbers. In this case, designate year 1996 as year 1, 1997 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, 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 | ...

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