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# Forecast

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Question 1.

Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown in the following table:

Year Demand for Fertilizer (1,000s of bags)
1 4
2 6
3 4
4 5
5 10
6 8
7 7
8 9
9 12
10 14
11 15

a) Develop a three-year moving averages to forecast sale.
b) Then estimate demand again with a weighted moving average in which sales in the most recent year are given a weight of 2 and sales in the other two years are each given a weight of 1.
c) Which method do you think is best?

Question 2.

Use exponential smoothing with a smoothing constant 0.3 to forecast the demand for fertilizer given in problem (question 1). Assume that last period's forecast year 1 is 5,000 bags to begin the procedure. Would you prefer to use the exponential smoothing model or the weighted average model developed in problem (question 1)? Explain your answer.

Question 3.

Emergency calls to Winter Park, Florida's 911 system, for the past 24 weeks are as follows:

Week Calls Week Calls Week Calls
1 50 9 35 17 55
2 35 10 20 18 40
3 25 11 15 29 35
4 40 12 40 20 60
5 45 13 55 21 75
6 35 14 35 22 50
7 20 15 25 23 40
8 30 16 55 24 65

(A) Compute the exponential smoothing forecast of calls for each week. Assume an initial forecast of 50 calls in the first week and use &#945; = 0.1. What is the forecast of the 25th week?
(B) Reforecast each period using &#945; = 0.6.

(C) Actual calls during the 25th week were 85. Which smoothing constant provides a superior forecast?

Question 4.

A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are compiled and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data (in \$millions) for one particular area of southeast Texas follow:

Quarter Year 1 Year 2 Year 3 Year 4
1 218 225 234 250
2 247 254 265 283
3 243 255 264 289
4 292 299 327 356

(A) Compute seasonal indices for each quarter based on a CMA (centered moving average).
(B) Deseasonalize the data and develop a trend on the deseasonlized data.
(C) Use the trend line to forecast the sales for each quarter of year 5.
(D) Use the seasonal indices to adjust the forecasts found in part (C.) to obtain the final forecasts.

Question 5.

In the past, Judy Holmes's tire dealership sold an average of 1,000 radials each year. In the past two years, 200 and 250, respectively, were sold in fall, 350, and 300 in winter, 150 and 165 in spring, and 300 and 285 in summer. With a major expansion planned, Judy projects sales next year to increase to 1,200 radials. What would the demand be each season?

https://brainmass.com/math/optimization/forecast-313187

#### Solution Summary

This solution is comprised of detailed analysis and step-by-step calculations of various Forecast Techniques like Exponentially Smoothed Forecast, Trend Projection, Seasonal Indices etc. in EXCEL. The solution provides students with a clear perspective of the given problems and the related aspects of forecast analysis.

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## Moving Average Forecast, Exponential Smoothing Forecast, Adjusted Exponential Smoothing Forecast, MAD, MAPD, Cumulative Error, Comparison among different Forecast Techniques and Regression Analysis

1. The saki motorcycle dealer in Minneapolis wants to make an accurate forecast of demand for the Saki Super TXII motorcycle during the next month.
Because the manufacturer is in Japan, it is difficult to send motorycles back or reorder if the proper number is not ordered a month ahead.
From sales records, the dealer has accumulated the following data for the past year:

Month Motorcyle Sales
January 9
February 7
March 10
April 8
May 7
June 12
July 10
August 11
September 12
October 10
November 14
December 16

a) Compute a 3-month moving average forecast of demand for April thru January of the next year
b) Compute a 5-month moving average forecast for June thru January
c)Compare the two forecasts computed in (a) and (b) using MAD-which should be used next year January?

2. The chairperson of the department of management at State University wants to forecast the number of students
who will enroll in production and operations mgmt next semester-- in order to determine how many sections to schedule.
The chair has acumulated the following enrollment data for the past 8 semesters:

Semester Students enrolled
1 400
2 450
3 350
4 420
5 500
6 575
7 490
8 650

a) Compute a three semester moving average forecast for semesters 4 thru 9
b)compute the exponentially smoothed forecast for the enrollment data &#945; = 0.20
c) compare the two forecasts using MAD-which is more accurate?

3. Whistle Stop Café is well known for its homemade ice cream, made in a small plant in back of café. People drive
all the way from Atlanta and Macon to buy the ice cream. The two women who own the cafe want to develop a forecasting model
so they can plan their ice cream production operation and determine the number of employees they need to sell ice cream in the café.
They have accumulated the following sales records for their ice cream for the past 12 quarters:

Year Quarter Ice Cream sales(gallons)
2003 1 350
2 510
3 750
4 420
2004 5 370
6 480
7 860
8 500
2005 9 450
10 550
11 820
12 570

Develop an adjusted exponential smoothing model with &#945; = 0.50 and &#946; = 0.50 to forecast demand and assess
its accuracy using cumulative error(e) and average error. Does there appear to be any BIAS in the forecast?

4. Aztec Industries has developed a forecasting model that was used to forecast during a 10-month period.
The forecasts and actual demand were as follows:

Month Actual Demand Forecast Demand
1 160 170
2 150 165
3 175 157
4 200 166
5 190 183
6 220 186
7 205 203
8 210 204
9 200 207
10 220 203

Measure the accuracy of the forecast by using MAD, MAPD, and cumulative error.
Does forecasting method appear to be accurate?

5. The manager of Ramona Hotel believes that how well the local Blue Sox professional baseball team is has an impact on the occupancy rate at the hotel during summer months.
Following are the number of victories for the Blue Sox( in a 162-game schedule) for the past 8 years and the hotel occupancy rates:

Year Blue Sox Wins Occupancy Rate in %
1 75 83
2 70 78
3 85 86
4 91 85
5 87 89
6 90 93
7 87 92
8 67 91

Develop a linear regression model for these data and forecast the occupancy rate for the next year if Blue Sox wins 88 games.

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