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The observed demand from the four quarters of Year 1 can also be used to develop initial deseasonalized forecast estimates that are required to start making forecasts with the exponential smoothing models. The first real forecast will be for Q1 of Year 2, and the use of simple exponential smoothing requires an estimated deseasonalized forecast from Q4 of Year 1 to use as a starting point. The estimated deseasonalized “forecast” for Q4 of Year 1 should be obtained as the average deseasonalized quarterly demand from Year 1. The estimate can also be used as the starting base forecast component for Q4 of Year 1 for trend-adjusted exponential smoothing. The initial deseasonalized trend component estimate for Q4 of Year 1 should be assumed to be zero.

The observed demand from the four quarters of Year 1 can also be used to develop initial deseasonalized forecast estimates that are required to start making forecasts with the exponential smoothing models. The first real forecast will be for Q1 of Year 2, and the use of simple exponential smoothing requires an estimated deseasonalized forecast from Q4 of Year 1 to use as a starting point. The estimated deseasonalized “forecast” for Q4 of Year 1 should be obtained as the average deseasonalized quarterly demand from Year 1. The estimate can also be used as the starting base forecast component for Q4 of Year 1 for trend-adjusted exponential smoothing. The initial deseasonalized trend component estimate for Q4 of Year 1 should be assumed to be zero.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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The observed demand from the four quarters of Year 1 can also be used to develop
initial deseasonalized forecast estimates that are required to start making forecasts with
the exponential smoothing models. The first real forecast will be for Q1 of Year 2, and
the use of simple exponential smoothing requires an estimated deseasonalized forecast
from Q4 of Year 1 to use as a starting point. The estimated deseasonalized “forecast” for
Q4 of Year 1 should be obtained as the average deseasonalized quarterly demand from
Year 1. The estimate can also be used as the starting base forecast component for Q4 of
Year 1 for trend-adjusted exponential smoothing. The initial deseasonalized trend
component estimate for Q4 of Year 1 should be assumed to be zero.

Sanderson Produce Co. Sanderson Produce Co. (SPC) is a large firm that is a wholesale supplier for fruits and vegetables in North Dakota. The firm obtains products from numerous international sources, and it can therefore easily supply most produce on nearly a year-round basis. SPC obtains advance contracts from suppliers to deliver this produce, and the firm has experienced an increase in its market share over the past several years. This increase has been primarily due to SPC's ability to deliver good quality products to customers in a timely fashion. The firm is committed to continuing this effort, and SPC would find it very useful to have reasonably accurate forecasts of quarterly demand for its products in order to give some advance notice of anticipated demand and of the resulting contracts that must be filled. This advance notice is very useful during preliminary contract negotiations with potential suppliers. SPC management is only interested in short-term forecasts for this application, and they also realize that it is not reasonable to expect to obtain extremely precise forecasts for products of this type. The problem of obtaining forecasts of demand for produce is made more difficult as a result of seasonality that exists in the demand patterns for some items. As an example of these seasonal effects, the quarterly demand for oranges for the past five years is given in Exhibit 4.1, where demand values are given in terms of standard shipping units that are common for the produce industry. This data represents 20 consecutive quarters of observations, starting in Q1 for Year 1 and ending with Q4 of Year 5. The seasonal effect in demand for oranges is primarily due to the tastes of consumers, with demand being highest in winter months and lowest in summer months. Since oranges could be obtained from international sources on nearly a year-round basis, this seasonality is not driven from the supply side. EXHIBIT 4.1. Quarterly demand for oranges at SPC Quarter Year 1 Year 2 Year 3 1 173,200 166,000 181,400 2 145,400 147,000 151,800 3 82,000 86,000 95,000 4 128,200 138,000 141,800 Year 4 193,600 165,800 106,200 155,000 Year 5 211,800 175,200 109,800 165,800 SPC wishes to develop short-term demand forecasts for each of its many different products with a simple forecasting procedure. As a result, only simple exponential smoothing and trend-adjusted exponential soothing are being considered for use. The question that naturally arises is "Which of these exponential smoothing models should be used, and what smoothing parameters should be used with these models to obtain the best expected overall accuracy from forecasts?" Some insight to the answer to this question can be attained by using the data set from Exhibit 4.1 as a test case to determine how well the different forecasting techniques would have performed if they had been in use over the given five year interval. As mentioned above, there is an obvious seasonality that must be accounted for in this case, and neither of these exponential smoothing models should be used directly with data sets that contain seasonal effects. This leads to a need for seasonal indexes. SPC management wants to have a forecasting model that updates seasonal indexes at the end of each given year to account for demand values that were observed during the given year. This will be helpful in dealing with any possible small shifts in the seasonal indexes that may be occurring over time. In order to reflect this idea, our analysis will treat the problem as if data is being rolled out in a sequential fashion over time. That is, we can only use data that would have been observed up to any given quarter in the sequence, with no knowledge of what demand values might have been in any future quarters. In order to keep the forecasting procedure as simple as possible, computation of seasonal indexes should be based on simple proportions of observed quarterly demand values. As a result of the policy of analyzing data as it is rolled out over time, we can do no real forecasting during Year 1, since the observed changes in quarterly values could have been due to seasonality, trend effects, or random fluctuation. There is no way for us to determine what is causing these observed changes as they occur. However, once the entire first year's demand has been observed, seasonal indexes can be directly computed for use during the second year, which will inherently assume that all observed changes in quarterly demand during Year 1 were due to seasonal effects. At the end of the second calendar year, seasonal indexes can be updated to accumulate observations from the first two years, these updated indexes can be used in the third year. You should update indexes at the end of each calendar year, and then use the accumulated results that would have been observed up to that point for forecasts during the following year. The observed demand from the four quarters of Year 1 can also be used to develop initial deseasonalized forecast estimates that are required to start making forecasts with the exponential smoothing models. The first real forecast will be for Q1 of Year 2, and the use of simple exponential smoothing requires an estimated deseasonalized forecast from Q4 of Year 1 to use as a starting point. The estimated deseasonalized "forecast" for Q4 of Year 1 should be obtained as the average deseasonalized quarterly demand from Year 1. The estimate can also be used as the starting base forecast component for Q4 of Year 1 for trend-adjusted exponential smoothing. The initial deseasonalized trend component estimate for Q4 of Year 1 should be assumed to be zero. The overall accuracy of the forecasting models that are being considered should be based on mean absolute deviation (MAD), using the differences between seasonalized quarterly forecasts and their associated actual observed demands. The MAD values should only be calculated for the relevant quarters when real forecasts were being generated, starting with Q1 of Year 2. We want to develop a forecast for Q1 of Year 6 with simple exponential smoothing, using the a value that most accurately fits the trial
Transcribed Image Text:Sanderson Produce Co. Sanderson Produce Co. (SPC) is a large firm that is a wholesale supplier for fruits and vegetables in North Dakota. The firm obtains products from numerous international sources, and it can therefore easily supply most produce on nearly a year-round basis. SPC obtains advance contracts from suppliers to deliver this produce, and the firm has experienced an increase in its market share over the past several years. This increase has been primarily due to SPC's ability to deliver good quality products to customers in a timely fashion. The firm is committed to continuing this effort, and SPC would find it very useful to have reasonably accurate forecasts of quarterly demand for its products in order to give some advance notice of anticipated demand and of the resulting contracts that must be filled. This advance notice is very useful during preliminary contract negotiations with potential suppliers. SPC management is only interested in short-term forecasts for this application, and they also realize that it is not reasonable to expect to obtain extremely precise forecasts for products of this type. The problem of obtaining forecasts of demand for produce is made more difficult as a result of seasonality that exists in the demand patterns for some items. As an example of these seasonal effects, the quarterly demand for oranges for the past five years is given in Exhibit 4.1, where demand values are given in terms of standard shipping units that are common for the produce industry. This data represents 20 consecutive quarters of observations, starting in Q1 for Year 1 and ending with Q4 of Year 5. The seasonal effect in demand for oranges is primarily due to the tastes of consumers, with demand being highest in winter months and lowest in summer months. Since oranges could be obtained from international sources on nearly a year-round basis, this seasonality is not driven from the supply side. EXHIBIT 4.1. Quarterly demand for oranges at SPC Quarter Year 1 Year 2 Year 3 1 173,200 166,000 181,400 2 145,400 147,000 151,800 3 82,000 86,000 95,000 4 128,200 138,000 141,800 Year 4 193,600 165,800 106,200 155,000 Year 5 211,800 175,200 109,800 165,800 SPC wishes to develop short-term demand forecasts for each of its many different products with a simple forecasting procedure. As a result, only simple exponential smoothing and trend-adjusted exponential soothing are being considered for use. The question that naturally arises is "Which of these exponential smoothing models should be used, and what smoothing parameters should be used with these models to obtain the best expected overall accuracy from forecasts?" Some insight to the answer to this question can be attained by using the data set from Exhibit 4.1 as a test case to determine how well the different forecasting techniques would have performed if they had been in use over the given five year interval. As mentioned above, there is an obvious seasonality that must be accounted for in this case, and neither of these exponential smoothing models should be used directly with data sets that contain seasonal effects. This leads to a need for seasonal indexes. SPC management wants to have a forecasting model that updates seasonal indexes at the end of each given year to account for demand values that were observed during the given year. This will be helpful in dealing with any possible small shifts in the seasonal indexes that may be occurring over time. In order to reflect this idea, our analysis will treat the problem as if data is being rolled out in a sequential fashion over time. That is, we can only use data that would have been observed up to any given quarter in the sequence, with no knowledge of what demand values might have been in any future quarters. In order to keep the forecasting procedure as simple as possible, computation of seasonal indexes should be based on simple proportions of observed quarterly demand values. As a result of the policy of analyzing data as it is rolled out over time, we can do no real forecasting during Year 1, since the observed changes in quarterly values could have been due to seasonality, trend effects, or random fluctuation. There is no way for us to determine what is causing these observed changes as they occur. However, once the entire first year's demand has been observed, seasonal indexes can be directly computed for use during the second year, which will inherently assume that all observed changes in quarterly demand during Year 1 were due to seasonal effects. At the end of the second calendar year, seasonal indexes can be updated to accumulate observations from the first two years, these updated indexes can be used in the third year. You should update indexes at the end of each calendar year, and then use the accumulated results that would have been observed up to that point for forecasts during the following year. The observed demand from the four quarters of Year 1 can also be used to develop initial deseasonalized forecast estimates that are required to start making forecasts with the exponential smoothing models. The first real forecast will be for Q1 of Year 2, and the use of simple exponential smoothing requires an estimated deseasonalized forecast from Q4 of Year 1 to use as a starting point. The estimated deseasonalized "forecast" for Q4 of Year 1 should be obtained as the average deseasonalized quarterly demand from Year 1. The estimate can also be used as the starting base forecast component for Q4 of Year 1 for trend-adjusted exponential smoothing. The initial deseasonalized trend component estimate for Q4 of Year 1 should be assumed to be zero. The overall accuracy of the forecasting models that are being considered should be based on mean absolute deviation (MAD), using the differences between seasonalized quarterly forecasts and their associated actual observed demands. The MAD values should only be calculated for the relevant quarters when real forecasts were being generated, starting with Q1 of Year 2. We want to develop a forecast for Q1 of Year 6 with simple exponential smoothing, using the a value that most accurately fits the trial
data set. The tracking signal values that would have been obtained for each quarter should also be computed, with MAD values and tracking signals being calculated as the quarterly demand values are sequentially rolled out. We also want to develop a forecast for Q1 of Year 6 with trend-adjusted exponential smoothing, using the values of a and 8 that most accurately fit the trial data set with trend-adjusted exponential smoothing. Tracking-signal values should also be calculated for each quarter, as they were for the simple exponential smoothing forecasts. Any observations regarding the efficacy of using forecasting techniques on the demand data from this particular example, based on observations from the computed tracking signals, will be of interest to the management of SPC. The management of SPC has also raised some additional issues regarding the forecasting techniques that might be used. In reality, very different costs are incurred, depending upon whether you over forecast demand or under forecast demand. If you over forecast actual demand for any quarter, you will be contracting to buy more produce than will be required. Some types of surplus produce will have to be discarded as a complete loss, while other types of produce can be sold at a discount. Some types can only be sold at significant discount, to be used as food for animals. Other types of produce can be sold to canneries for a less significant discount. If you under forecast, you will not be able to meet demand, which will result in lost sales, and you will also have some unhappy customers as a result. Such an outcome would be in sharp contrast with the company's commitment to meeting the needs of customers, as discussed above. However, the high cost of routinely discarding or discounting surplus produce would be prohibitive for SPC to absorb on a long term basis. Given all this information, the use of the standard measures of "accuracy" of overall forecast error might be called into question. The SPC management estimates that the penalty cost for overcasting should be assessed as roughly six times as much per unit of forecast error as the penalty cost for under forecasting. They are interested in having some insight on the significance of the impact that this relative cost consideration might have on standard forecasting techniques, relative to the results that were found above. This impact can be shown by developing a quarterly forecast for Q1 of Year 6, with the same exponential smoothing forecasting model that was considered to be accurate in the first part of this study. However, the parameters for the "most accurate" forecasting model in this situation should be determined on the basis of trying to minimize the total overall cost of forecasting error.* *Technical note: If you use the Solver option in Excel to search for the specific a and 8 that minimize MAD, be careful to use multiple starting points in the a and 8 cells at the start of the search to avoid the possibility of obtaining "local minimum" solutions for MAD.
Transcribed Image Text:data set. The tracking signal values that would have been obtained for each quarter should also be computed, with MAD values and tracking signals being calculated as the quarterly demand values are sequentially rolled out. We also want to develop a forecast for Q1 of Year 6 with trend-adjusted exponential smoothing, using the values of a and 8 that most accurately fit the trial data set with trend-adjusted exponential smoothing. Tracking-signal values should also be calculated for each quarter, as they were for the simple exponential smoothing forecasts. Any observations regarding the efficacy of using forecasting techniques on the demand data from this particular example, based on observations from the computed tracking signals, will be of interest to the management of SPC. The management of SPC has also raised some additional issues regarding the forecasting techniques that might be used. In reality, very different costs are incurred, depending upon whether you over forecast demand or under forecast demand. If you over forecast actual demand for any quarter, you will be contracting to buy more produce than will be required. Some types of surplus produce will have to be discarded as a complete loss, while other types of produce can be sold at a discount. Some types can only be sold at significant discount, to be used as food for animals. Other types of produce can be sold to canneries for a less significant discount. If you under forecast, you will not be able to meet demand, which will result in lost sales, and you will also have some unhappy customers as a result. Such an outcome would be in sharp contrast with the company's commitment to meeting the needs of customers, as discussed above. However, the high cost of routinely discarding or discounting surplus produce would be prohibitive for SPC to absorb on a long term basis. Given all this information, the use of the standard measures of "accuracy" of overall forecast error might be called into question. The SPC management estimates that the penalty cost for overcasting should be assessed as roughly six times as much per unit of forecast error as the penalty cost for under forecasting. They are interested in having some insight on the significance of the impact that this relative cost consideration might have on standard forecasting techniques, relative to the results that were found above. This impact can be shown by developing a quarterly forecast for Q1 of Year 6, with the same exponential smoothing forecasting model that was considered to be accurate in the first part of this study. However, the parameters for the "most accurate" forecasting model in this situation should be determined on the basis of trying to minimize the total overall cost of forecasting error.* *Technical note: If you use the Solver option in Excel to search for the specific a and 8 that minimize MAD, be careful to use multiple starting points in the a and 8 cells at the start of the search to avoid the possibility of obtaining "local minimum" solutions for MAD.
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