Category Archives: Forecasting

Problem solve

Problem 2

A specific forecasting model was used to forecast demands for a product. The fore a t and the corresponding demands that subsequently occurred are shown below.

Use the MAD and tracking signal technique to evaluate the forecasting model.

Solution

Evaluate the forecasting model using MAD, MAPE, and Jacking signal.

Forecast model is well within the distribution.

1. Demand for stereo headphones and CD players for joggers has caused Nina Industries to experience a growth of almost 50 percent over the past year. The number of jogger is continuing to expand, so ina expects demand for headsets to also expand.
Demands for the stereo units for last year were as follows:

a. Using least squares regression analysis, what would you estimate demand to be for each month nextyear? Follow the general format in Exhibit 9.14.

b. To be reasonably confident of meeting demand, Nina decides to use three standard errors of estimate for safety, How many additional units should be held to meet this level of confidence?

2.Following are the actual tabulated demands for an item for a nine-month period, from

January through September. Your supervisor wants to test two forecasting methods to
see which method was better over this period.

a. Forecast April. through September using a three-month simple moving average.
b. Use simple exponential smoothing to estimate April through September. (Use a = .3 and assume that the forecast for March was 130.)
c. Use MAD to decide which method produced the better forecast over the six-month period.

3.A forecasting method you have been using to predict product demand is shown in the following table along with the actual demand that occurred.

a. Compute the tracking signal using the MAD ana running urn of forecast errors (RSFE).
b. Calculate the MAPE.
c. Comment on whether you feel the forecasting method is giving good predictions.

4.Josh Francis recently has been named Director of Marketing for a consumer products company. The company has divided up the United States into different territories, with a sales manager assigned to each territory. The sales and populations for the current territories in which her firm now does business are as follows:

a. Using an electronic spreadsheet, calculate the least squares regression line that tits the above data.
b. What is the regression equation? What is the coefficient of determination?
c. Josh's company is planning to expand into two additional territories in the coming year. The populations of these two territories are 7.43 million and 3.87 million. What are the estimated sales that Josh. can expect from these two territories?

5.Chez Alex i a haute cuisine restaurant that is only open tor dinner. In order to determine the proper number of wait stuff to schedule for each meal. A-pen Wang. the dining room manager needs to forecast the number of meals that will be served. To do this she has collected the following data:

a. Use exponential smoothing with a = .4 and a = .8 to forecast the number of calls for next Monday.
b. Using Map as a criterion, which of the two values of a do you recommend?

c. Construct a table to calculate the average MAD for values of a = .1, .2, .3, ... , .9. Which value of a do you recommend be used?

Solved Problems

Problem 1

Sunrise Baking Company markets doughnuts through a chain of food stores and has been experiencing over- and underproduction because of forecasting errors. The following data are their daily demands in dozens of doughnuts for the past four weeks. The bakery is closed Saturday so Friday’s production must satisfy demand for both Saturday and Sunday.

Make a forecast for this week on the following basis:
a. Daily, using a simple four-week moving average.
b. Daily, using a weighted average of OAO for last week, 0.30 for two weeks ago, 0.20 for three weeks ago. and O.I0 for four weeks ago.
c. Sunrise is also planning its purchases of ingredients for bread production. If bread demand had been forecast for last week at 22,000 loaves and only 21.000 loaves were actually demanded, what would Sunrise’s forecast be for this week using exponential smoothing with a = 0.1 O?

d. Supposing, with the forecast made in (c). this week’s demand actually turns out to be 22,500.
What would the new forecast be for the next week?

Solution

a. Simple moving average, 4 weeks.

b. Weighted average with weights of AO, .30 .. 20, and .10.

Internet Exercise

The Wharton School at the University of Pennsylvania has a website devoted to forecasting at www.rnarketing.wharton.upenn.edu/forecastlwelcome.html. Visit this website and select a firm that provides business forecasting software. Visit that firm’s website and perform the following:
Describe the company.
Select one of its forecasting software products and describe it in detail including costs.
Identify specific applications for which this program would be most suitable.

Review and Discussion questions 

1. Examine Exhibit 9.3 and suggest which forecasting technique you might use for
(a) bathing suits. (b) demand for new house-. (e) electrical power usage. (d) new plant’
expansion plans.
2. In terms of the errors, why would the operations manager wish to use the least method when doing simple linear regression?
3. All forecasting methods using exponential smoothing. adaptive smoothing. and exponential smoothing including trend require starting values to initialize the equations. How would you select the starting value for say Free?

4. From the choice of simple moving average. weighted moving average. exponential smoothing, and simple regression analysis. which forecasting technique would you consider the most accurate? Why?
5. What is the main disadvantage of daily forecasting using regression analysis?
6. What are the main problems with using adaptive exponential smoothing in forecasting?
7. What is the purpose of a tracking signal?
8. What are the main differences between traditional forecasting techniques and neural networks?
9. Discuss the basic differences between the mean absolute deviation (MAD) and the standard error of the estimate?
10. What implications do the existence of forecast errors have for the search for ultra sophisticated statistical forecasting models such as neural networks?

Key Formulas

Simple Moving Average Forecast

Weighted moving Average Forecast

and

Exponential Smoothing

Exponential Smoothing with Trend Effects

Mean Absolute Deviation (MAD)

Tracking Signal