1. What is Forecasting?
A forecast is an estimate of what is likely to happen in the future.
Forecasts are concerned with determining what the future will look like; planning is concerned with what it should look like.
Forecasting provides a basis for coordinating activities in various parts of the company.
Forecasts are an important input to both long-term, strategic decision-making, as well as for short-term planning for day-to-day operations.
What Is Forecasting?
A forecast is a prediction of future events for planning purposes. It is both the art and science of predicting future events. It may involve taking historical data and projecting this data into the future using some type of mathematical model. It may be a judgmental prediction, based on subjective considerations or intuition. Or, it may involve a combination of quantitative analysis adjusted by a manager’s judgment.
Rarely is there a single best technique for forecasting. What works best for one firm at one time may not work for another firm at another time. In addition, you should understand that there are limits to what can be expected from forecasts. They are seldom, if ever, perfect. They are also costly and time consuming to prepare and monitor.
Nevertheless, businesses cannot afford to ignore the process of forecasting by just waiting to see what happens and then taking their chances. Quite the contrary. In recent years, no business function has grown as rapidly as the forecasting function. More and more businesses now recognize that forecasts are the key to good decision making.

2. Importance of Forecasting
Forecasting is important for all of the functional areas of business:
Finance uses long-term forecasts for capital planning and short-term forecasts for budgeting.
Marketing produces sales forecasts for market planning and market strategy.
Operations develops and uses forecasts for scheduling, inventory management, and long-term capacity planning.
Human Resource Management uses forecasts to estimate the need for employees.
Importance of Business Forecasting
Good forecasts are important in all aspects of a business:
Finance uses long-term forecasts to estimate needs for capital and to evaluate capital projects. Short-term forecasts are used in finance to prepare certain budgets such as cash budgets.
Marketing produces sales forecasts for use in the development of marketing plans and for the implementation of marketing strategy.
Human Resources use forecasts to estimate the need for employees. Hiring, training, and the layoff of workers all depend on anticipated demand. If a firm hires additional workers on extremely short notice, the amount of training declines and quality suffers.
Operations develop and use forecasts for decisions regarding scheduling, inventory replenishment, and long-term capacity planning. Forecasting is particularly important for capacity planning, because when capacity is inadequate, resulting shortages result in unreliable delivery schedules. Loss of customers, and loss of market share, on the other hand, when excess capacity is built, costs can skyrocket.

3. Types of Forecasts
There are three major types of forecasts:
Demand Forecasts these are estimates of demand for a company’s goods or services.
Technological Forecasts These are forecasts concerned with the rate of change in technology and the impact on a company’s revenues and/or costs.
Economic Forecasts predict inflation rates, employment rates, money supply, housing starts, and other measures of the performance of an economy.
Types of Forecasts
There are three major types of forecasts: demand forecasts, technological forecasts, and economic forecasts.
Demand Forecasts. These are projections (estimates) of demand for a company’s products or services. These forecasts, often called sales forecasts, drive a company’s marketing, financial, operations, and personnel planning.
Just a brief note here. There is a tendency to assume that demand and sales are the same. If a firm has stockouts at some point of time, then demand will be greater than sales. Our interest is in forecasting demand, not sales.
Technological Forecasts. These are concerned with rates of change in technology, which can result in the development of new products or services, requiring new plants and equipment.
Economic Forecasts. These speak to economic cycles by predicting inflation rates, employment rates, money supply, housing starts, and other economic indicators.
There are two uses for forecasts. One is to help businesses plan their system and the other is to help them plan the use of the system. Planning the system involves long-term planning about products and services to offer, facilities and equipment to have, where to locate and so on. Planning the use of the system is linked to short-and intermediate-term planning, which includes planning about inventory, work-force levels, scheduling, purchasing, and budgeting.
Business forecasting is about more than predicting demand. Forecasts are used to predict financial outcomes such as revenues, costs, and profit prices, productivity changes, interest rates, availability of inputs, changes in key economic indicators, and prices of stocks. Keep in mind, however, that the concepts and techniques apply equally well to other variables.

4. Features of Forecasts
All forecasting techniques have the same features:
Forecasting techniques assume that the same basic or original system that existed in the past will exist in the future.
Forecasts are rarely perfect.
Forecast accuracy decreases as the time horizon increases.
Forecasts for groups of items are more accurate than forecasts for individual items.
Forecast Features
There are literally dozens of forecasting techniques available, ranging from the judgmental and intuitive on the one hand to the highly quantitative and analytical on the other, Nonetheless, certain features are common to all, and it is important to recognize them.
Forecasting techniques assume that the same underlying system that existed in the past will continue to exist in the future. This “stable” system is assumed to exist for all forecasting techniques, and it is important to recognize that any unplanned events can wreak havoc with the system and the forecasts that come from it.
Forecasts are rarely, if ever, perfect, actual results differ from predicted values. No one is ever able to predict precisely how a large number of factors will impact on the variable we wish to forecast. There is no more humbling experience available to the forecaster than the development of forecasts based on the assumption of perfect knowledge – only to have these forecasts blow up in the face of the forecaster.
Forecast accuracy decreases as the forecast horizon increases. As the time period covered by a forecast increase, there are more opportunities for unplanned events to impact on the forecast. Short-term forecasts simply don’t allow enough time for things to go wrong; consequently, they tend to be more accurate than long-term forecasts.
Forecasts for groups of items are more accurate that forecasts for individual items because forecasting errors among items in a group tend to cancel each other out. Forecasts of total demand developed by financial planners will have smaller errors than the sum of errors created by forecasting item-by-item demand, where errors are in full view and cannot cancel out each other.

5. Elements of a Good Forecast
A properly prepared forecast should meet the following requirements:
The forecast should be accurate.
The forecast should be timely.
The forecast should be reliable.
The forecasting technique should be simple to understand and use.
The forecast should be expressed in meaningful units.
The forecast should be in writing.
Elements of a Good Forecast
If a forecast is prepared properly, it should have the following elements:
Accuracy. Forecasts should be accurate within certain ranges, and these ranges should be known and stated. Knowing the range or level of accuracy will help forecast users plan for errors and provide a basis for comparing forecasts against actual results.
Timeliness. Forecasts have to be prepared well enough in advance of actual so that the information contained in the forecast can be used in an effective manner. For example, a marketing program cannot be implemented overnight. So, a forecast must be developed early enough to be used in both the design and the implementation of the marketing program.
Reliability. As a characteristic of forecasts, reliability is more about consistency than accuracy. If a forecast technique sometimes produces a good forecast and sometimes a poor one, the technique is likely to leave users with the distinct impression that they could get burned anytime they try the technique.
The forecasting technique must be simple to understand and use. It is axiomatic that no one will use a forecasting technique that they do not understand. Users lack confidence in forecasts based on sophisticated techniques; they do no understand if the technique is appropriate or what its limitations might be.
Forecasts must be in useful units. Financial managers need forecasts in dollars. Production planners need demand forecasts in units, particularly when I t comes time to scheduling equipment and personnel. Each department in a business will need to have its forecasts expressed in the units most useful for their planning requirements.
Forecasts must be in writing. There are two reasons for this: (1) a written forecast provides a “hard-copy” basis for evaluating the effectiveness of the forecast once actual results are in and (2) a written forecast increases the likelihood that everyone is using the same information – singing from the same song sheet, so to speak.

6. Steps in the Forecasting Process
There are seven basic steps in the forecasting process:
Determine the purpose of the forecast.
Select the items to be forecast.
Establish a time horizon.
Select the forecasting technique.
Gather and analyze relevant data.
Prepare the forecast.
Monitor the results.
Steps in the Forecasting Process
There are seven basic steps in the process of forecasting:
Determine the purpose of the forecast. How are you going to use the forecast and when will you need it? Identifying the purpose and timing of the forecast will provide you with some guidance as to the level of detail required in the forecast, the amount of resources (time, dollars, and personnel) that should be invested in the forecast, and the level of accuracy required.
Select the items to be forecast. Are you forecasting total demand, demand by product/service group, or individual items?
Determine the time horizon for the forecast. Is it a short-, medium-, or long-term forecast? The forecast must have a time limit, keeping in mind that forecast accuracy decreases as the time period covered by the forecast increases.
Select the forecasting technique. This step is necessary in order to identify the data that will be needed in order to build the forecast. A word of caution, however. Your choice of technique carries with it certain assumptions about the data that will be used in the modest selection of certain time series averaging techniques assumes that there is only random variation in the data, not trend and/of seasonal variation. Remember, “fall in love with your data, not your model!”
Gather the date needed to make the forecast. Before a forecast can be prepared, data must be gathered and analyzed. Is the data consistent with the assumptions in the forecast model? Is there enough data to support the technique? Are we missing data? These, and other questions, need to be answered before we begin to forecast.
Make the Forecast. Forecasts should be monitored to see if they are performing in a satisfactory manner. Monitoring forecasts means making sure that the model, the assumptions, and the data are valid.

7. Forecasting Approaches
There are two major approaches to forecasting: qualitative (judgmental) and quantitative methods.
Further, quantitative methods can be divided into ones that use historical data (time series models) or ones that develop relationships between variables (associative models).
Forecasts Based on Judgment Judgmental forecasts rely on analysis of subjective inputs from a variety of sources including customer surveys, sales staff, managers, and panels of experts.
Forecasts Based on Time Series Data Some forecasting techniques use historical, or time series data, with the assumption that the future will be like the past.
Approaches to Forecasting
There are two general approaches to forecasting: qualitative and quantitative. Qualitative methods incorporate such factors as the decision maker’s intuition, personal opinions, personal experiences, and value system in reaching a forecast. Qualitative methods use a variety of mathematical models that rely on historical data and/or causal variables to forecast demand.
Forecasts Based on Judgment and Opinion. Judgmental forecasts rely on subjective inputs such as consumer surveys, sales staff, managers, and panels of experts. Frequently, these sources provide insights that cannot be obtained by any other means.
Forecasts Based on Time Series Data. A time series is a sequence of evenly spaced date points. Examples might include weekly sales of a running shoe, quarterly earnings of a stock, daily shipments of a beer, and annual consumer price indices. Forecasting time-series data means that future values are predicted only from past values and that other variables, no matter how valuable, may be ignored.
Associative Forecasts. Associative models use equations that consist of one or more explanatory variables that can be used to predict future demand. For example, demand for personal computers might be related to such variables as price, competitor’s price, the amount spent on advertising, and general economic conditions.
Despite the apparent sophistication of quantitative methods, it is useful to remember that forecasting is an art or special skill rather than an exact science. The key inputs in a science are the constant laws of nature, whereas the key inputs of forecasting are information, analysis, experience and informed judgment. There are not natural laws that make the relationships between demand and other variables continue to behave as they have done in the past. Economic conditions, competitor’s actions, consumer’s preferences, and other social phenomena are often whimsical. Judgment must be exercised to see that appropriate methods are developed and properly applied.

8. Forecasts Based on Judgment
Executive Opinion A forecasting method in which the opinions and experience of one or more managers are used to produce a forecast.
Sales Force Opinion Forecasts compiled from estimates of demand made by members of a company’s sales force.
Customer Surveys A forecasting method that seeks input from customers regarding future purchasing plans for existing products or services.
Market Research This method tests hypothesis about new products or services or new markets for existing products or services.
Delphi Method A forecasting technique using a group process that allows experts to make forecasts.
Forecasts Based on Judgment
Qualitative forecasting methods are usually based on judgment about the factors that underlie the sales of particular products or services and on opinions about the relative likelihood of theses factors being present in the future. These methods may involve different levels of sophistication, ranging from scientifically conducted consumer surveys to intuitive hunches about future events.
Executive Opinions. Knowledgeable executives from various departments in an organization form a committee charged with the responsibility of developing a sales forecast. The committee may use many inputs from all parts of the organization. Such forecasts tend to be compromise forecasts, not reflecting the extremes that could be present had they been prepared by individuals.
Sales Force Opinions. Estimates of future regional sales are obtained from individual members of the sales force. These estimates are combined to form an estimate of sales for all regions. Management then transforms this estimate into s sales forecast, using judgment to ensure realistic estimates. This is a popular forecasting method is a company has a good communication system in place and has salespeople who sell directly to customers.
Consumer Surveys. Estimates of future sales are obtained directly from customers. Individual customers are surveyed to determine what quantities of the firm’s products they intend to purchase in each future time period. A sale forecast is determined by combining individual customer’s responses. Companies that have relatively few customers may prefer this method.
Market Research. In market surveys, mail questionnaires, telephone interviews, or field interviews from the basis for testing hypotheses about real markets. In market tests, product marketed on target regions or outlets are statistically extrapolated to total markets. These methods are preferred for new products or for existing products to be introduced into new markets.
Delphi Method. This method is used to achieve consensus within a committee. Under this method, management anonymously answers a series of questions in successive rounds. Each response is fed back to all participants on each round, and the process is then repeated. As many a six rounds may be required before consensus is reached on the forecast. This method can result in forecasts that most participants ultimately agree to in spite of any initial disagreement.

9. Forecasts Based on Time Series Data
A time series is a sequential series of observations taken at regular intervals over a period of time.
The data may be demand (units or dollars), output (units), profits (dollars), or CPI (indices), among others.
Analysis of time series data seeks to identify the underlying behavior of the series. The underlying behavior is made up of patterns such as:
Trend
Cycles
Seasonality
Random variation
Forecasts Based on Time Series
Time series models attempt to predict the future by using historical data. These models make the assumption that what happens in the future is a function of what has happened in the past. In other words, time series models look back at what has happened over a period of time and use a series of past data to make a forecast. Or, to phrase it more succinctly: “Time series forecasting is like driving forward while looking in the rear-view mirror”.
This type of forecasting implies that future values are predicted only from past values and that other variables that might influence demand are ignored.
 Analysis of time series data requires a forecaster to identify the underlying behavior of the series. Graphing the data and visually examining the graph can often accomplish this. One of more patterns might appear: trend, cycles, seasonal variation, and random variations. Once these patterns have been identified, selection of the appropriate forecasting technique will follow.

10. Classification of Forecasting Methods

11. Overview of Time Series Forecasting
A time series consists of a sequential set of data of a variable, such as demand.
There are four possible components of demand:
Trend . A gradual upward or downward movement of the data over time.
Cycles. Wavelike variations in the data that occur every several years.
Seasonality. Short-term, fairly regular variations that are generally related to weather factors or to human-made factors such as holidays.
Random Variations. “Blips “ in the data caused by chance and unusual situations. They follow no discernable pattern, so they cannot be predicted.
Overview of Time Series Forecasting
A time series is based on a sequence of evenly spaced data points. The spacing between the points could be daily, weekly, monthly, quarterly, and so on. Using this data to forecast implies that future values are predicted (developed) only form past values. Other variables that might explain demand are ignored. This does not endear time series modeling to marketers and economists.
Analyzing a time series means breaking down data into components and then project the components into the future. Typically, there are four components: trend, cycles, seasonality, and random variation.
Trend is the gradual upward or downward movement of data over time. A movement in trend may be attributable to changes in demographics such as income, population, age distribution, or cultural aspects.
Cycles are patterns in time series data that occur every several years. They are linked to business cycles, which can have a length from as little as 2 years to as long as 10 years. The problem with cycles is that their length is unpredictable and estimating the business cycle is difficult because they are affected by political events.
Seasonality refers to short-term, regular variations in data. Seasonal variation involves patterns of change within a year, and tends to be repeated from year to year. The patterns of change must exhibit two characteristics:
1. The “peaks” and “valleys” of seasonal variation must be large enough to see. They should not be so small so as to be mistaken for random fluctuations.
2. The “peaks” and “valleys” should occur at approximately the same time each year.
Random variations are “hiccups” in the data caused by chance and unusual situations. They have no pattern, so they cannot be predicted. They also serve to remind us that the future is not perfectly predictable. A lesson in humility, perhaps!

12. Figure 1: Product Demand Charted Over 4 Years with a Growth Trend and Seasonality
component
Seasonal peaks
Average demand
over four years
Random variation
Year 1
Year 2
Year 3
Year 4

13. Naive Forecasts
A forecast that assumes that demand in the next period will be equal to demand in the most recent period.
Can handle the following components of demand:
Random variation. The last data point becomes the forecast for the next period.
Seasonal variation. The forecast for “this season” is equal to the value of the series “last season”.
Trend. The forecast is equal to the last value of the data series, plus or minus the difference between the last two values.
Naïve Forecasting
A simple, but widely used approach to forecasting is the naïve approach. A naïve forecast assumes that demand in the next period will be equal to demand in the most recent period. The naïve approach can be used with a stable series (random variation only), with seasonal variation, or with trend.
Stable Series. If the data series has only random variation, the last data point becomes the forecast for the next period. For example, if demand for a product last month was 950 units, the forecast for this month is 950 units.
Seasonal Variation. For seasonal data, the forecast for this “season” is equal to the value of the series last “season”. For example, the forecast of demand for a particular toy this Christmas is equal to the demand for the toy last Christmas.
Trend. For data with trend, the forecast is equal to the last value of the data series plus or minus the difference between the last two values of the series. For example, suppose the last two values of a series were 125 and 140:
Change From
Period Actual Previous Value Forecast
t – t
t = 155
This forecast, then, is , or 155.
At first glance, the naïve approach may appear both simple and simplistic. Nevertheless, it is a legitimate forecasting tool. Consider the benefits:
It has virtually no cost,
It is quick and easy to prepare.
Data requirements are minimal.
It is easily understood.
If the naïve approach generates acceptable forecasts, it is worthwhile considering. Moreover, even if other forecasting techniques offer better accuracy, they will almost certainly involve greater cost. You must answer the question: Is the increased accuracy of another method worth the additional cost required to achieve that accuracy?

14. Techniques for Averaging
These are techniques that are useful for data that has only random variation.
These techniques smooth fluctuations in a time series.
Forecasts that are based on an average are more “stable” than the original data.
There are three popular averaging techniques:
Simple moving average
Weighted moving average
Simple exponential smoothing
Technique For Averaging
Historical data typically contains a certain amount of random variation, or noise that tends to hide systematic movements in the data. This randomness arises from the combined influence of many – perhaps a great many – relatively unimportant factors, and it cannot be predicted with any reliability. Averaging techniques smooth variations in the data and leave only “real” variations, such as changes in the demand. As a practical matter, however, it is usually impossible to distinguish between these two kinds of variations, so the best one can hope for is that the small variations are random and the large variations are “real”.
Averaging techniques smooth fluctuations in a time series because the individual highs and lows of the data offset each other when they are combined into an average. A forecast based on an average thus tends to exhibit less variability than the original data. Minor variations are treated as random variations, whereas larger variations are viewed as more likely to reflect “real” changes, although these, too, are smoothed to a certain degree.
Averaging techniques generate forecasts that reflect recent values of a time series (e.g. the average value over the last several periods). These techniques work best when a data series tends to vary around in average; i.e., when the primary fluctuation in the data is due to random variation. However, these techniques can also handle step changes or gradual changes in the level of the series.
Three techniques for averaging are described here:
1. Simple moving average
2. Weighted moving average
3. Simple exponential smoothing

15. Moving Average
A technique that uses a number of historical data values to generate a forecast.
Involves finding a series of successive averages by dropping the first data value in the series and adding the last data value.
Useful for data without trend, seasonality, or cycles.
Moving Average
If we eliminate the idea that things will remain as they are, the simplest quantitative forecasting method is the moving average. The moving average method assumes that demand has no trend, cycles, or seasonal patterns. This leaves only a “horizontal” pattern with random variation. The horizontal pattern is, effectively, the average of demand, so we focus on forecasting methods that estimate the average of a time series. Consequently, the forecast of demand for any period in the future is the average of the time series computed in the current period.
Consider the figure in the slide, which shows patient arrivals at a medical clinic. Assume that the demand pattern for patient arrivals has no trend, cyclical, or seasonal patterns. The time series has only a horizontal and random pattern. As no one can predict random error, we focus on estimating the average.

16. Simple Moving Average
A key decision involves selecting the number of periods that will be included in the average.
The larger the number of periods, the greater the smoothing; the smaller the number of periods, the quicker the forecast reacts to changes in the data.
Simple Moving Average
The simple moving average method is used to estimate the average of a demand series and thereby remove the effects of random fluctuation.
Calculation of the simple moving average consists of funding a series of successive averages by dropping the first data value in the series and adding the last data value. For example, to calculate a three-period moving average, total the first three items in the series and divide by 3 for the first moving average. Next, drop the first value and add the fourth on; again, divide by 3 for the second moving average. This process would be followed for all items in the series.
A simple moving average can use any number of periods in the calculation of the average. The number of periods used depends on what you are trying to achieve – either a smoothed average or a forecast that reacts to the most recent changes in the data. If the data values change little between periods, then it makes sense to produce a smoothed average. To do so, use a large number of periods in the average. What is a large number? Probably, 6 or more periods would do.
If the data has wide fluctuations, fewer periods in the average will produce a forecast that reflects more recent data values. If the number of periods is small, the most recent data has more importance.
Comparing the three-period and the five-period moving averages can show this relationship for the ten periods of demand given in the slide. Notice that the three-period average fluctuates more than the five-period average. If the moving average is being used as a forecasting technique, the average for a given period becomes the forecast for the next period. Thus, in this example, the moving average for Period 3 of 66.3 would be the forecast for Period 4.

17. Example 1 – Simple Moving Average Illustration
Market Mixer, Inc. sells can openers. Monthly sales for an eight-month period were as follows:
Month Sales Month Sales
Forecast next month’s sales using a 3-month moving average.
Solution:
Period Sales Moving Average Forecast
1 450
2 425
3 445
( ) / 3 = 440
( ) / 3 = 435
( ) / 3 = 447
( ) / 3 = 450
( ) /3 = 448
9 ( ) / 3 =
Example 1 – Simple Moving Average Illustration
Comments:
1. Any forecasts beyond Period 9 will have the same value as the Period 9 forecast; i.e., 435.
2. As a new actual value becomes available, the forecast will be updated by adding the newest value and dropping the oldest one.
3. SMA gives equal weight to all values in the average. Hence, the oldest value has the same weight, or importance, as the newest.
Simple Moving Average Illustration
The Problem
The company has eight months of sales data for its product, a can opener. Sales appear to fluctuate randomly over the eight-month period and so a simple moving average (SMA) model seems appropriate for forecasting.
The Solution
The forecaster has selected a three-month simple moving average model. A relatively few number of periods in the average makes the method sensitive to real changes in the data.
The first back forecast will start at Period 4 because the first three data values must be used to generate the moving average. For each forecast after the first one, dropping the oldest data point and adding one new data point calculate the moving average.
The first forward forecast is for Period 9. If the forecaster wishes to forecast beyond Period 9, any forward forecast will have the same value as the one for Period 9.
Tips and Hints
1. If you are really only interested in forward forecasts, you don’t need to do the back forecasts that were done in the illustration. The simple moving average model does not use previous forecasts to generate subsequent forecasts, unlike exponential smoothing. However, it is useful to do back forecasts so that you can see the errors that your model creates. For more discussion about the errors associated with this SMA forecast model, see the next slide.
2. The SMA model should only be used for data with random variation. If you sense a trend or seasonal variation, DO NOT USE THIS MODEL.
3. Be careful how far forward you forecast. Even though SMA will allow you to forecast several periods into the future (each subsequent forecast is equal to the previous forecast).
435

18. Weighted Moving Average
A model that applies different “weights” to each value in the moving average calculation.
Two key decisions:
The number of periods that will be included in the average. The larger the number of periods, the greater the smoothing; the smaller the number of periods, the quicker the forecast reacts to changes in the data.
The weight that will be applied to each period. The higher the weight applied to more recent data, the quicker the model reacts to changes; the lower the weight that is applied to the more recent data, the greater is the smoothing process.
Weighted Moving Average
The simple moving average method weights historical data equally in developing a forecast. A weighted moving average assigns more weight to some values than to others. In certain situations, it may be desirable to apply unequal weights to the historical data. When an apparent trend or pattern is present, weights can be used to place more emphasis on recent values. This practice makes forecasting more responsive to changed because more recent periods are more heavily weighted.
Choice if weights is somewhat arbitrary because there is no set formula to determine them. Therefore, deciding which weights to use requires some experience. For example, if the latest period is weighted too heavily, the forecast might reflect a large unusual change in the demand or sales pattern too quickly.
Both simple and weighted moving averages are effective in smoothing out fluctuations in the demand pattern in order to provide stable estimates. Moving averages do, however, present three problems:
1. Determining the number of periods in the average depends on what you are trying to achieve: a nice smoothed average or a forecast that responds quickly to changes in historical data. It is not possible to achieve both objectives simultaneously, so the challenge for you is to decide which is more important in terms of developing useful forecasts.
2. Increasing the number of periods in the average does smooth out fluctuations, but it makes the method less sensitive to real changes in the data.
3. Moving averages cannot pick up trends very well. Because they are averages, they will still lag behind demand. You cannot average past sales data and get a higher value than any past sales value, which is what you would like to get when trying to forecast the next value in an upward trend.

19. Example 2 – Weighted Moving Average Illustration
(Let us continue with the same problem as we had in Example 1.) Market Mixer, Inc. sells can openers. Monthly sales for an eight-month period were as follows:
Month Sales Month Sales
Forecast next month’s sales using a 3-month weighted moving average, where the weight for the most recent data value is 0.60; the next most recent, 0.30; and the earliest, 0.10.
Solution:
Period Sales Weighted Moving Average Forecast
1 450
2 425
3 445
(450*.10) + (425*.30) + (445*.60) = 440
(425*.10) + (445*.30) + (435*.60) = 437
(445*.10) + (435*.30) + (460*.60) = 451
(435*.10) + (460*.30) + (445*.60) = 455
(460*.10) + (455*.30) + (430*.60) = 441
(445*.10) + (430*.30) + (420*.60) =
Example 2 – Weighted Moving Average Illustration
Comments:
1. Any forecasts beyond Period 9 will have the same value as the Period 9 forecast, i.e., 427.
3. WMA gives greater weight to more recent values in the moving average and is more responsive to recent changes in the data.
Weighted Moving Average Illustration
The Problem
We have kept the problem the same as the simple Moving Average illustration. In this way, we can compare the results of the two forecasting methods.
The company’s sales data does fluctuate randomly, so a Weighted Moving Average model would also be appropriate. The new information: weights for each of the three periods in the moving average.
The Solution
The forecaster is using a three-period weighted moving average model. By putting a weight of 60 percent on the most recent data, it seems that we are interested in developing forecasts that respond very quickly to changes in recent sales data. The first forecast starts at Period 4. For each forecast after the first one, dropping the oldest data point and adding one new data point calculate weighted moving average.
The first forward forecast is for Period 9. Forecasts beyond this point are simply equal to the Period 9 Forecast.
Tips ‘n Hints
1. Back forecasts are unnecessary if your only interest is to develop a future estimate of demand.
2. The WMA model should only be used for random variation. Patterns such as trend and/or seasonal variation require that other models be used.
3. Your future forecasts should be limited to one or two periods. Going any further takes you too far away from the historical data used to develop the forecast.
427

20. Simple Exponential Smoothing
This is a variation of the weighted moving average model.
Weights are determined by an exponential function which declines as the data gets older.
The formula: Ft+1 = aAt + (1 – a)Ft
Where Ft+1 = forecast for next period
a = smoothing constant (0 < a < 1)
At = current period’s actual demand
Ft = current period’s forecast
Simple Exponential Smoothing
Simple exponential smoothing is a variation of the weighted moving average model in which data points are weighted by an exponential function, which declines, as the data gets older. The simple exponential smoothing function can be shown as:
New forecast = alpha (current demand) + (1-alpha)(current forecast)
where alpha is a weight, or smoothing constant, between 0 and 1.
Mathematically, the simple exponential smoothing formula is written as:
Ft+1 = alpha At + (1-alpha)Ft
where Ft+1 = forecast for next period
Alpha = smoothing constant (0  alpha  1)
At = current period’s actual demand
Ft = current period’s forecast
The concept behind simple exponential smoothing is not complex. The latest estimate of demand is equal to a percentage of our current demand and a percentage of the current forecast.
Selecting a smoothing constant is basically a matter of judgment or trial and error, using forecast errors to guide your decision. The goal is to select a smoothing constant that balances the benefits of smoothing random variations with the benefits of responding to real changes in the data.
Using extreme values of alpha is not advisable. If alpha were set equal to 1, the latest forecast would be equal to the last actual value – making the model very responsive, but not stable, if there is any random variation in the data. If alpha were set equal to zero, the new forecast is equal to the old forecast – a result that is unhelpful if there are real changes in demand.
The smoothing constant, alpha, is generally in the range from .05 to .50 for business application. It can be changed to give more weight to recent data (when alpha is high) or more weight to past data (when alpha is low).
An initial (starting) forecast must be developed. You can estimate a value, or you can use a technique such as SMA or WMA to develop the starting forecast. If you intend to estimate a value, we would suggest that your estimate be close to the earliest actual value.

21. Example 3 – Simple Exponential Smoothing Illustration
(Let us continue with the same problem as we had in Example 1.) Market Mixer, Inc. sells can openers. Monthly sales for an eight-month period were as follows:
Month Sales Month Sales
Forecast next month’s sales using exponential smoothing with alpha (a) = 0.30 and the first (starting) forecast = 450.
Solution:
Period Sales Exponential Smoothing Forecast
(.30*450) + ( )*450 = 450
(.30*425) + ( )*450 = 443
(.30*445) + ( )*443 = 443
(.30*435) + ( )*443 = 441
(.30*460) + ( )*441 = 447
(.30*455) + ( )*447 = 449
(.30*430) + ( )*449 = 443
(.30*420) + ( )*443 =
Example 3 – Simple Exponential Smoothing Illustration
Comments:
1. Any forecasts beyond Period 9 will have the same value as the Period 9 forecast, i.e., 436.
3. The higher the value of a, the quicker the reaction to changes in the data and the less the smoothing.
Simple Exponential Smoothing Illustration
The Problem
The data for this problem illustration is the same as for the SMA and WMA illustrations. By doing this, we can compare forecasts and errors thus drawing some conclusions about the adequacy of the models.
The sales data does have random variation, so a Simple Exponential Smoothing model is appropriate. The challenge for us: select the weight for alpha.
The Solution
We chose am alpha equal to 0.30 and a starting forecast of Because the starting forecast is equal to the starting sales value, the second forecast will be equal to the first one.
We should also note that with simple exponential smoothing, there is no choice as to where we start the forecasts. Unlike SMA and WMA, where forecasts can begin wherever we want, in simple exponential smoothing the first forecast must be in the same period as the first sales period.
The first forward forecast is for Period 9 and has a value of 436, by forecasts beyond Period 0 will be equal to the Period 9 forecast until new sales data comes into play.
Tips ‘n Hints
1. Back forecasts are necessary; you can’t pick your point at which to start these forecasts – they must start at the first actual sales point.
2. The Simple Exponential Smoothing model should only be used for random variation. Any other patterns require alternate models. Fortunately, or otherwise, there are other exponential smoothing models that can handle patterns such as trend or seasonal variation.
3. Forward forecasts should be limited to one or a very few future periods. Going any farther is likely to lose the connection you have with the historical data.
436