Business Forecasting Study Set 1

Business

Quiz 9 :
Judgmental Forecasting and Forecast Adjustments

Quiz 9 :
Judgmental Forecasting and Forecast Adjustments

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Identify two business situations where the Delphi method might be used to generate forecasts. Can you think of any difficulties and pitfalls associated with using the Delphi method?
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Answer will vary. One of the possible answers is given below:
Delphi method is applied in the forecasting situation for which the pure statistical methods are not possible due to lack of appropriate historical data. Some of the examples are given below:
• Sales of a newly manufactured product for the first year
• Employment for a new project
Potential difficulties and pitfalls that are associated with the Delphi method are given below:
• Gathering of exact group of experts related to the project
• Overwhelm the biases by a particular expert
• Unable to organize for appropriate feedback

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Consider the actual sales shown in Table P-2 along with one-step-ahead forecasts produced by Winters' method and by a regression model. a. Construct the combined forecasts of sales produced by taking a simple average of the forecasts produced by Winters' method and the regression model. b. Construct the combined forecasts of sales produced by taking a weighted average of the Winters' forecasts and the regression forecasts with weights w 1 =.8 and w 2 = 1 - w 1 =.2. c. Using the actual sales, determine the MAPEs for the Winters' forecasts and the regression forecasts. d. Repeat part c using the combined forecasts from parts a and b. Based on the MAPE measure, which set of forecasts do you prefer? img
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a.
Compute the combined forecasts of sales produced by taking a simple average of the forecasts produced by Winter's method and the regression model.
The general formula for combined forecasts using simple average method is given below:
img img Obtain the one-step-ahead combined forecasts using simple average method for the first month.
img Thus, the one-step-ahead combined forecasts using simple average method for the first month is
img .
Obtain the one-step-ahead combined forecasts using simple average method for the second month.
img Thus, the one-step-ahead combined forecasts using simple average method for the second month is
img .
Obtain the one-step-ahead combined forecasts using simple average method for the third month.
img Thus, the one-step-ahead combined forecasts using simple average method for the third month is
img .
Similarly, the combined forecasts of sales produced by Winter's method and the regression method can be calculated. The results of the combined forecasts for all months are tabulated below:
img b.
Compute the combined forecasts of sales produced by taking a weighted average of the forecasts produced by Winters' method and the regression model.
The general formula for combined forecasts using weighted average is obtained below:
img img Obtain the one-step-ahead combined forecasts using weighted average method for the first month.
img Thus, the one-step-ahead combined forecasts using weighted average method for the first month is
img .
Obtain the one-step-ahead combined forecasts using weighted average method for the second month.
img Thus, the one-step-ahead combined forecasts using weighted average method for the second month is
img .
Obtain the one-step-ahead combined forecasts using weighted average method for the third month.
img Thus, the one-step-ahead combined forecasts using weighted average method for the third month is
img .
Similarly, the combined forecasts of sales produced by Winters' method and the regression method can be obtained. The results of the combined forecasts for all months are tabulated below:
img c.
Compute the Mean Absolute Percentage Error ( MAPE ) for the Winters' forecasting method.
img The value of the Mean Absolute Percentage Error ( MAPE ) is,
img Thus, the Mean Absolute Percentage Error ( MAPE ) for the Winter's forecasting method is
img .
Compute the Mean Absolute Percentage Error ( MAPE ) for the regression forecasting method.
img The value of the Mean Absolute Percentage Error ( MAPE ) is,
img Thus, the Mean Absolute Percentage Error ( MAPE ) for the regression forecasting method is
img .
d.
Compute the Mean Absolute Percentage Error ( MAPE ) for the average forecasting method.
img The value of the Mean Absolute Percentage Error ( MAPE ) is,
img Thus, the Mean Absolute Percentage Error ( MAPE ) for the average forecasting method is
img .
Compute the Mean Absolute Percentage Error ( MAPE ) for the weighted average forecasting method.
img The value of the Mean Absolute Percentage Error ( MAPE ) is,
img Thus, the Mean Absolute Percentage Error ( MAPE ) for the weighted average forecasting method is
img .
Identify the preferable forecasts method based on the Mean Absolute Percentage Error ( MAPE ) measure.
From part (b) and (c), it is clear that the simple average and regression forecasts methods are preferable, because the error measures by simple average forecasts and regression forecasts is
img and
img is comparatively lesser than the other forecasts methods.

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GOLDEN GARDENS RESTAURANT Sue and Bill Golden have decided to open a restaurant in a city in the Midwest. They have spent over a year researching the area and visiting medium- to high-price restaurants. They definitely believe that there is room for another restaurant and have found a good site that is available at a good price. In addition, they have contacts with a number of first-class chefs and believe that they can attract one of them to their new restaurant. Their inquiries with local bankers have convinced them that financing will be readily available, given their own financial resources and their expertise in the restaurant business. The only thing still troubling the Goldens is the atmosphere or motif for their restaurant. They have already conducted a series of three focus groups with area residents who eat out regularly, and no consensus on this matter emerged. They have talked about the matter considerably between themselves but now believe some other opinions would be valuable. After reading about some of the techniques used in judgmental forecasting, they believe some of them might help them decide on the atmosphere for their new restaurant. They have identified a number of their friends and associates in other cities who would be willing to help them but are not certain how to utilize their talents. What method would you suggest to the Goldens in utilizing the expertise of their friends to decide on the atmosphere and motif for their new restaurant?
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Identify a method that can be suggested to the Goldens in utilizing the expertise of their friends.
From the given case, it is clear that Sue and Bill Golden had conducted a series of three groups and analyzed about atmosphere and motif of the restaurant. However, they could not get any consensus on the same. Moreover, they had considerable discussions and have some opinions on their own. In addition, they have a number of expert friends and associates and have to find some way to use their expertise.
By applying the Delphi method , they can use their friends and associates knowledge. Sue and Bill Golden can first provide with a short description about the project, the idea about the atmosphere and motif can be raised to their friends and request them to design the restaurant. After receiving the design, Sue and Bill can analyze the design of the restaurant and mail back their descriptions to each of the friends. In addition, they can request their friends to re-design based on the comments given. This process can be continued until there are no changes in the design.

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GOLDEN GARDENS RESTAURANT Sue and Bill Golden have decided to open a restaurant in a city in the Midwest. They have spent over a year researching the area and visiting medium- to high-price restaurants. They definitely believe that there is room for another restaurant and have found a good site that is available at a good price. In addition, they have contacts with a number of first-class chefs and believe that they can attract one of them to their new restaurant. Their inquiries with local bankers have convinced them that financing will be readily available, given their own financial resources and their expertise in the restaurant business. The only thing still troubling the Goldens is the atmosphere or motif for their restaurant. They have already conducted a series of three focus groups with area residents who eat out regularly, and no consensus on this matter emerged. They have talked about the matter considerably between themselves but now believe some other opinions would be valuable. After reading about some of the techniques used in judgmental forecasting, they believe some of them might help them decide on the atmosphere for their new restaurant. They have identified a number of their friends and associates in other cities who would be willing to help them but are not certain how to utilize their talents. Are there any other methods they have overlooked in trying to research this matter?
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ALOMEGA FOOD STORES Example 1.1 described how Julie Ruth, the president of Alomega Food Stores, collected monthly sales data for her company along with several other variables she thought might be related to sales. The Alomega cases-Cases 2-3. 3-4, 5-6, and 8-7 - described her attempts to use various forecasting procedures available in Minitab in an effort to produce meaningful forecasts of monthly sales. In Case 8-7, Julie developed a multiple regression model that explained almost 91% of the monthly sales variable variance. She felt good about this model but was especially sensitive to the negative comments made by Jackson Tilson, her production manager, during a recent meeting (see Example 1.1). Tilson said, "I've been trying to keep my mouth shut during this meeting, but this is really too much. I think we're wasting a lot of people's time with all this data collection and fooling around with computers. All you have to do is talk with our people on the floor and with the grocery store managers to understand what's going on. I've seen this happen around here before, and here we go again. Some of you people need to turn off your computers, get out of your fancy offices, and talk with a few real people." Julie decided that office politics dictated that she heed Jackson's advice. She consulted with several people, including Tilson, to determine their opinions of how to forecast sales for January 2007. A large majority felt that using the sales figure for the previous January would provide the best prediction. Likewise, the forecast for February 2007 should be based on the sales figure for February 2006. img Based on this input, Julie developed a naive forecasting model: img that used last year's monthly value to predict this year's monthly value. How accurate is Julie's naive forecasting model?
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ALOMEGA FOOD STORES Example 1.1 described how Julie Ruth, the president of Alomega Food Stores, collected monthly sales data for her company along with several other variables she thought might be related to sales. The Alomega cases-Cases 2-3. 3-4, 5-6, and 8-7 - described her attempts to use various forecasting procedures available in Minitab in an effort to produce meaningful forecasts of monthly sales. In Case 8-7, Julie developed a multiple regression model that explained almost 91% of the monthly sales variable variance. She felt good about this model but was especially sensitive to the negative comments made by Jackson Tilson, her production manager, during a recent meeting (see Example 1.1). Tilson said, "I've been trying to keep my mouth shut during this meeting, but this is really too much. I think we're wasting a lot of people's time with all this data collection and fooling around with computers. All you have to do is talk with our people on the floor and with the grocery store managers to understand what's going on. I've seen this happen around here before, and here we go again. Some of you people need to turn off your computers, get out of your fancy offices, and talk with a few real people." Julie decided that office politics dictated that she heed Jackson's advice. She consulted with several people, including Tilson, to determine their opinions of how to forecast sales for January 2007. A large majority felt that using the sales figure for the previous January would provide the best prediction. Likewise, the forecast for February 2007 should be based on the sales figure for February 2006. img Based on this input, Julie developed a naive forecasting model: img that used last year's monthly value to predict this year's monthly value. How does the naive model compare to the multiple regression model developed in Case 8-7?
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ALOMEGA FOOD STORES Example 1.1 described how Julie Ruth, the president of Alomega Food Stores, collected monthly sales data for her company along with several other variables she thought might be related to sales. The Alomega cases-Cases 2-3. 3-4, 5-6, and 8-7 - described her attempts to use various forecasting procedures available in Minitab in an effort to produce meaningful forecasts of monthly sales. In Case 8-7, Julie developed a multiple regression model that explained almost 91% of the monthly sales variable variance. She felt good about this model but was especially sensitive to the negative comments made by Jackson Tilson, her production manager, during a recent meeting (see Example 1.1). Tilson said, "I've been trying to keep my mouth shut during this meeting, but this is really too much. I think we're wasting a lot of people's time with all this data collection and fooling around with computers. All you have to do is talk with our people on the floor and with the grocery store managers to understand what's going on. I've seen this happen around here before, and here we go again. Some of you people need to turn off your computers, get out of your fancy offices, and talk with a few real people." Julie decided that office politics dictated that she heed Jackson's advice. She consulted with several people, including Tilson, to determine their opinions of how to forecast sales for January 2007. A large majority felt that using the sales figure for the previous January would provide the best prediction. Likewise, the forecast for February 2007 should be based on the sales figure for February 2006. img Based on this input, Julie developed a naive forecasting model: img that used last year's monthly value to predict this year's monthly value. Until Julie can experience each of these two methods in action, she is considering combining forecasts. She feels that this approach would counter office politics and still allow her to use a more scientific approach. Would this be a good idea?
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ALOMEGA FOOD STORES Example 1.1 described how Julie Ruth, the president of Alomega Food Stores, collected monthly sales data for her company along with several other variables she thought might be related to sales. The Alomega cases-Cases 2-3. 3-4, 5-6, and 8-7 - described her attempts to use various forecasting procedures available in Minitab in an effort to produce meaningful forecasts of monthly sales. In Case 8-7, Julie developed a multiple regression model that explained almost 91% of the monthly sales variable variance. She felt good about this model but was especially sensitive to the negative comments made by Jackson Tilson, her production manager, during a recent meeting (see Example 1.1). Tilson said, "I've been trying to keep my mouth shut during this meeting, but this is really too much. I think we're wasting a lot of people's time with all this data collection and fooling around with computers. All you have to do is talk with our people on the floor and with the grocery store managers to understand what's going on. I've seen this happen around here before, and here we go again. Some of you people need to turn off your computers, get out of your fancy offices, and talk with a few real people." Julie decided that office politics dictated that she heed Jackson's advice. She consulted with several people, including Tilson, to determine their opinions of how to forecast sales for January 2007. A large majority felt that using the sales figure for the previous January would provide the best prediction. Likewise, the forecast for February 2007 should be based on the sales figure for February 2006. img Based on this input, Julie developed a naive forecasting model: img that used last year's monthly value to predict this year's monthly value. Should Julie use a simple average or weighted average approach to combining the forecasts?
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THE LYDIA E. PINKHAM MEDICINE COMPANY This case demonstrates an actual application of the usage of neural networks to forecast time series data. The authors understand that students have not been provided with the background to completely understand this case. However, it is felt that benefits will be derived from experiencing this actual case. The Lydia E. Pinkham Medicine Company and Lydia Pinkham's Vegetable Compound were introduced in Case 9-4. There have been many attempts to use networks to forecast time series data. Most of the work has been in the field of power utilization, since power companies need accurate forecasts of hourly demand for their product. However, some research has focused on more traditional business time series, such as micro- and macroeconomic series, demographic data, and company-specific data. Virtually all this work has used a feed-forward network trained using backpropagation. This case study will employ this type of network to forecast the Lydia Pinkham sales data. The resulting forecasts will be compared to the forecasts from the AR(2) model presented in Case 9-4. Figure 10-3 depicts a 2-4-1 feed-forward neural network-the network used for this study. The 2 in the 2-4-1 indicates the number of inputs to the network. In this case, the two inputs are Y t-1 and Y t-2. (Using the two previous periods to predict the current period is consistent with the AR(2) model; thus, both the AR(2) model and the neural network model use the same "information" in computing the one-step-ahead predictions.) The 4 indicates the number of nodes, or processing units, in the hidden layer. (It is termed hidden because it is not directly connected to the "outside world," as are the input and output layers.) The number of nodes in the hidden layer is chosen arbitrarily in a sense: Too few hidden nodes restrict the network's ability to "fit" the data, and too many hidden nodes cause the network to memorize the training (or estimation) data. The memorization leads to very poor performance over the testing sample. In this case, the number of nodes in the hidden layer is simply twice the number of inputs. Finally, the 1 indicates that one output node gives the one-step-ahead forecast, or Y t. FIGURE 10-3 A 2-4-1 Feed-Forward Network img img The neural network computes its output in the following manner: Each of the connecting arcs between nodes in two adjacent layers has an associated weight. Each node in the hidden layer computes a weighted sum of its inputs. (The input layer nodes simply pass the inputs on to the hidden layer.) This weighted sum is then "transformed" in some fashion, such as Y = 1/(1 + e -x ) where Y is the "transformed" data and X is the weighted sum. The Y is then passed on to the output layer, where each node again computes a weighted sum. This final weighted sum is the output of the network. The network is trained by adjusting all the connecting weights in an iterative fashion. THE NEURAL NETWORK MODEL The neural network was trained using BrainMaker. 9 For this study, the step size was set to 0.500 and the training tolerance to 0.001. (Other packages might require the user to specify a learning rate and a momentum term.) As in Case 9-4, the first 42 observations are used to train the network; the last 12 are used to assess the performance of the network predicting one step ahead. One problem with using neural networks to forecast time series data lies in determining how long to train the network; an overtrained network tends to memorize the training data and perform poorly on the testing data. Thus, some researchers have suggested simply stopping the training "early"-before the network has memorized the data. To determine the training effect, the network was trained for 10,000, 20,000, 50,000, 75,000, and 100,000 iterations. (One iteration is the presentation of one observation; the iterations listed represent 250, 500, 1,250, 1,875, and 2,500 passes through the complete training set, respectively.) This allows the analyst to assess the possible impact of overtraining. (The work was originally done on an Intel 386SX-20-based PC, and the "time" to train for 100,000 iterations was approximately 20 minutes.) RESULTS The MAD, MAPE, and MSE for the various neural network models are presented in Table 10-5. They do not compare favorably with the AR(2) model. The author of this case is currently experimenting with a different type of neural network-a radial basis function neural network-which produces results comparable to those of the AR(2) model. 10 Why are neural networks viewed as a viable alternative to the other forecasting methods discussed in this text?
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