Forecasting is essential for every organisation and is the basis of corporate long-rung planning. Strategic forecasts are medium and long-term forecasts that are used for decisions related to strategy and aggregate demand. Tactical forecasts are short-term forecasts used for making day-to-day decisions related to meeting demand.
There are four basis types of forecasting: qualitative, time series analysis, causal relationships and simulation. Qualitative techniques are subjective and based on estimates and opinions Time series analysis (focus of this chapter) is a forecast in which past demand data is used to predict future demand. For causal forecasting the linear regression technique is used, which assumes that demand is related to some underlying factor(s) in the environment. Simulation models allow the forecaster to run through a range of assumptions about the condition of the forecast.
Demand for products/services can be broken down into six components in most cases: average demand for the period, a trend, seasonal element, cyclical elements, random variation and autocorrelation (see exhibit 3.1). Cyclical influence on demand may come from occurrences as political elections, war or economic conditions. Random variation is caused by chance events. Autocorrelation denotes the persistence of occurrence. Trend lines are the usual starting point in developing a forecast. Exhibit 3.2 illustrates the four common types of trends.
Time series forecasting models try to predict the future based on past data. Exhibit 3.3 shows the time series models of this chapter. Short-term refers to under three months, medium term to three months to two years and long-term to greater than two years. Which model a company uses depends on the time horizon to forecast, data availability, the required accuracy, the size of the forecasting budget and the availability of qualified personnel. Other issues as the firm’s degree of flexibility are also important. The consequence of a bad forecast also needs to be taken into consideration.
When the demand for a product is constant, and there are no seasonal characteristics, the moving average can be used: a forecast based on average past demand. See exhibit 3.4 for an example. Selecting the period length should be dependent on how the forecast is going to be used. The formula:
Ft= (At-1+ At-2+ At-3+ … + At-n) / n
Ft = forecast for the coming period
n = number of periods to be averaged
At-n = actual occurrences in the past period/past two periods/etc.
The main disadvantage in calculating a moving average is that all individual elements must be carried as data because a new forecast period involves adding new data and removing earlier data.
A weigthed moving average allows any weights to be placed on each element, provided that the sum of all weights equals 1. By forecasting this way with past data, more recent data is given more significance than older data. The formula is:
Ft= w1At-1+ w2At-2+ … + wnAt-n
wn = weight to be given to the actual occurrence for the period t-n
n = total number of prior periods in the forecast
The major drawback of using these two methods is the need to continually carry a large amount of historical data. Exponential smoothing uses weights for past data that decrease exponentially (1 – α) for each past period. This is the most used technique for forecasting. It is easily to use, the forecasts are surprisingly accurate and little computation is necessary to use the model. Three pieces of data are needed to forecast the future:
The most recent forecast;
The actual demand that occurred for the forecast period;
A smoothing constant alpha (α): the parameter in the exponential smoothing equation that controls the speed of reaction to differences between forecasts and actual demand. This is determined by both the nature of the product and the manager’s sense of what constitues a good response rate. The more rapid the growth, the higher the reaction rate should be.
Ft= Ft-1+ α (At-1 – Ft-1)
Ft = the exponentially smoothed forecast for period t
Ft-1 = the exponentially smoothed forecast made for the prior period
At-1 = the actual demand in the prior period
α = the desired response rate, or smoothing constant
This equation states that the new forecast is equal to the old forecast plus a portion of the error (the difference between the previous forecast and what actually occurred).
An upward or downward trend in data collected over a sequence of time periods causes the exponential forecast to always lag behind (be above or below) the actual occurrence. By adding another constant, the smoothing constant delta (δ), this trend can be corrected somewhat. Both alpha and delta reduce the impact of the error that occurs between the actual and the forecast. The formulas to compute the forecast including trend (FIT) are:
Ft= FITt-1+ α (At-1 – FITt-1)
Tt= Tt-1+ δ (Ft – FITt-1)
FITt= Ft+ Tt
Ft = the exponentially smoothed forecast that does not include trend for period t
Tt = the exponentially smoothed trend for period t
FITt(-1) = the forecast including trend for period t or the prior period
At-1 = the actual demand for the prior period
These equations need to be taken step for step to make an exponential forecast that includes trend. See example 3.1 for an example.
The smoothing constants need to be given a value between 0 and 1. Typically, values are used for alpha and delta in the range of .1 to .3. The values depend on how much random variation there is in demand and how steady the trend factor is.
Regression is a functional relationship between two or more correlated variables. It is used to predict one variable, given the other. The data should be plotted first to see if they appear linear. Linear regression refers to a special class of regression where the relationship between variables forms a straight line. Form of the formula: Y = a + bt, where Y is the value of the dependent variable that we are solving for, a is the Y intercept, b is the slope and t is an index for the time period. Linear regression is useful for long-term forecasting of major occurrences and aggregate planning. The biggest drawback of using linear regression forecasting is that past data and future projections are assumed to fall in about a straight line. However, it can still be used for both time series forecasting and causal relationship forecasting. See example 3.2 for an example.
A time series is chronologically ordered data that may contain one or more components of demand: trend, seasonal, cyclical, autocorrelation and random. Decomposition of a time series means identifying and separating the time series data into these components. The trend and seasonal component are relatively easy to identify, while cycles, autocorrelation and random components are much harder to identify.
There are two types of seasonal variation:
Additive seasonal variation: assumes that the seasonal amount is a constant, no matter what the trend or average amount is. See exhibit 3.9A for an example.
Forecast including trend and seasonal = Trend + Seasonal
Multiplicative seasonal variation: the trend is multiplied by the seasonal factors. See exhibit 3.9B.
Forecasting including trend and seasonal = Trend x Seasonal factor
A seasonal factor is the amount of correction needed in a time series to adjust for the season of the year. Example 3.3 and example 3.4 shows how seasonal indexes are determined and used to forecast.
Using least squares regression can also do decomposition. The process is as follow:
Decompose the time series into its components:
Find seasonal component;
Deseasonalize the demand;
Find trend component.
Forecast future values of each component:
Project trend component into the future;
Multiply trend component by seasonal component.
Exhibit 3.11 shows an example of this process.
The forecast error is the difference between actual demand and what was forecast. These errors are called residuals. There are two factors that need to be discussed:
Sources of error: errors can come from a variety of sources. Errors can be classified as bias or random. Bias errors occur when a consistent mistake is made, for example by using the wrong variables. Random errors cannot be explained by the forecast model being used.
Measurement of error: there are terms to describe the degree of error: standard error, mean squared error (or variance) and mean absolute deviation. De mean absolute deviation (MAD) is the average of the absolute value of the actual forecast error. It measures the dispersion of some observed value from some expected value.
MAD = () / n
t = period number
At = actual demand for the period t
Ft = forecast demand for the period t
n = total number of periods
| | = the absolute value
When the errors that occur in the forecast are normally distributed (the usual case), the MAD relates to the standard deviation as:
1 standard deviation = x MAD, or approximately 1.25 MAD
1 MAD = approximately 0.8 standard deviation
Another measure of error is the mean absolute percent error (MAPE). This measures the average error as a percentage of average demand.
MAPE = MAD / Average demand
A tracking signal (TS) is a measurement that indicates whether the forecast average is keeping pace with any genuine upward or downward changes in demand. This is used to detect forecast bias. See also exhibit 3.14 and exhibit 3.15.
TS = RSFE / MAD
RSFE = the running sum of forecast errors, considering the nature of the error
MAD = the average of all the forecast errors, the average of the absolute deviations
Causal relationship forecasting involves using independent variables other than time to predict future demand. See example 3.5 for an example.
Multiple regression analysis is another forecasting method, in which a number of variables are considered, together with the effects of each on the item of interest.
S = B + Bm (M) + Bh(H) + Bi(I) + Bt(T)
S = gross sales for year
B = base sales, a starting point from which other factors have influence
M/H/I = other factors, such as marriages during the year/housing starts/etc.
T = time trend (first year = 1, second year =2, etc.)
Next to these quantitative methods of forecasting, there are also qualitative forecasting techniques. The knowledge of experts is important, while it requires much judgement. Examples are market research, panel consensus, historical analogy and the Delphi method. Collaborative Planning, Forecasting and Replenishment (CPFR) is a Web-based tool used to coordinate forecasting, production and purchasing in a firm’s supply chain. See exhibit 3.17. The five steps are:
Creation of a front-end partnership agreement;
Joint business planning;
Development of demand forecasts;
Sharing forecasts;
Inventory replenishment.