Course Notes Operations Management Forecasting

3: Forecasting

Charles E. Oyibo

Introduction

A forecast is a statement about the future. Basically, we take two kinds of information into account when (attempting to) make forecasts: (1) current factors or conditions, and (2) past experience in a similar situation.

Forecasts help managers to:

• plan the system, which generally involves long-range plans about the types of products and services to offer, what facilities and equipments to invest in, where to locate, etc.; and
• plan the use of the system, which refers to short-range and intermediate-range planning which involves tasks such as planning inventory and workforce levels, planning purchasing and production, budgeting, and scheduling.

Features Common to All Forecasts

1. Forecasting techniques generally assume that the same underlying causal system that existed in the past will continue to exist in the future. Hence, a manager ought not to delegate forecasting to models or computers and leave it at that. He or she must make accommodations for unplanned occurrences (like weather-related events, tax changes, changes in features or prices of competing products) and should be ready to override forecasts, which assume a stable system
2. Forecasts are rarely perfect; actual results usually differ from predicted values. Because no one can predict precisely how an infinite number of factors can impinge upon the variable in question, and because of the presence of sheer randomness, it is impossible to have a perfect forecast. Allowances should be made for inaccuracies.
3. Forecasts of groups of items tend to be more accurate than forecasts for individual items because forecasting errors among items in a group usually have a canceling effect.
4. Forecast accuracy decreases as the time period covered by the forecast--the time horizon--increases. Generally, short-range forecasts must contend with fewer uncertainties than longer-range forecasts, so they tend to be more accurate.

Elements of a Good Forecast

1. The forecast should be timely. As a certain amount of time is needed to respond to the information contained in a forecast, the forecasting horizon must cover the time necessary to implement possible changes.
2. The forecast should be accurate and the degree of accuracy should be stated. This will enable users to plan for possible errors and will provide a basis for comparing alternative forecasts.
3. The forecast should be reliable; it should work consistently.
4. The forecast should be expressed in meaningful units, depending on the users needs.
5. The forecast should be in writing. In addition to increasing the likelihood that all concerned are using the same information, a written forecast will permit an objective basis for evaluating the forecast once actual results are in.
6. The forecasting technique should be simple to understand and use.

Steps in the Forecasting Process

1. Determine the purpose of the forecast and when it will be needed, the level of detail required, the amount of resources (personnel, computer time, money) that can be justified, and the level of accuracy necessary.
2. Establish a time horizon of the forecast, bearing in mind that accuracy decreases as the time horizon increases.
3. Select a(n appropriate) forecasting technique
4. Gather and analyze relevant data. Identify any assumptions that are made in conjunction with preparing and using the forecast.
5. Prepare the forecast using the selected technique.
6. Monitor the forecast to determine whether it is performing in a satisfactory manner. It it is not, reexamine the method, assumption, validity of data, etc.; modify as needed; prepare a revised forecast.

Approaches to Forecasting

1. Qualitative Approaches, which consist mainly of subjective inputs, and often defy precise numerical description. These involve either the extension of historical data or the development of associative models that attempt to utilize causal (explanatory) variables to make a forecast. Qualitative techniques permit the inclusion of soft information (e.g. human factors, personal opinion, hunches) in the forecasting process.
2. Quantitative Approaches, which consist mainly of analyzing objective, or hard, data. They usually avoid personal biases that sometimes contaminate qualitative methods.

Forecasts Based on Judgment and Opinion

Judgmental forecasts rely on analysis of subjective inputs obtained from various sources, such as consumer surveys, the sales staff, managers and executives, and panels of experts. Often, these sources provide insights that are not otherwise available.

An important approach in this category is the Delphi Method which involves circulating a series of questionnaires among individuals who possess the knowledge and ability to contribute meaningfully. Each new questionnaire is developed using information from the previous one, thus enlarging the scope of information on which participants can base their judgment--the goal being to achieve a consensus forecast.

Forecasts Based on Time Series (Historical) Data

Some forecast techniques simply attempt to project past experiences into the future. These techniques use historical, or time series, data with the assumption that the future will be like the past. Some models attempt to smooth out random variations in historical data; others attempt to identify specific patterns in the data and project or extrapolate those patterns into the future, without trying to identify causes of the patterns.

A time series is a time-ordered sequence of observations taken at regular intervals over a period of time. Analysis of time series data requires the analyst to identify the underlying behavior of the series. The can often be accomplished by merely plotting the data and visually examining the plot. One or more of the following behaviors or patterns might be observed:

1. Trend, a long-term upward or downward movement in the data.
2. Seasonality, short-term, fairly regular variations generally related to factors such as the calendar or time of the day.
3. Cycles, wavelike variations of more than one year's duration often related to a variety of economic, political, and even agricultural conditions.
4. Irregular variations, due to usual circumstances such as severe weather conditions, strikes, or a major change in product or service. These do not reflect typical behavior, and, whenever possible, should be removed from the data.
5. Random variations, residual variations that remain after all other behaviors have been accounted for.

Naïve Methods

A naïve forecast uses a single previous value of time series as the basis for a forecast; that is, the forecast for any period equals the previous period's actual value. Naïve methods represent virtually no cost, they are quick and easy to prepare because data analysis is nonexistent, and they are easily understandable. The main disadvantage, obviously, is the methods' inability to provide highly accurate forecasts.

Techniques for Averaging

Averaging techniques smooth fluctuations in a time series because the individual highs and lows (random variation, or noise) in 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. Three techniques for averaging are:

1. Moving Average. Averages a number of the most recent actual data in generating a forecast,
2. Weighted Moving Average. Works like the moving average, but assigns more weight to the most recent values in the time series.
3. Exponential Smoothing. A sophisticated weighted moving average method in which each new forecast is based on the previous forecast plus a percentage of the difference between the forecast and the actual value of the series at that point. That is:
   Next forecast = Previous forecast + α(Actual - Pervious forecast)
   where (Actual - Pervious forecast) represents the forecast error and α is a percentage of the error.

Techniques for Trend

Analysis of tend involves developing an equation that will suitable describe trend (assuming that trend is present in the data). A trend is often linear, but it could also be nonlinear (like parabolic, exponential, and growth trends). There are two important techniques that can be used to develop forecasts when trend is present:

1. Trend Equation. A linear trend equation has the form y_t = a + bt, where t =specified number of time periods from t = 0; y_t = Forecast for period t; a = Value of y_t at t = 0; and b = Slope of the line.
2. Trend-Adjusted Exponential Smoothing. A variation of simple exponential smoothing used when a time series exhibits a trend, it is also called double smoothing to differentiate it from simple exponential smoothing, which is appropriate only when data vary around an average or have step or gradual changes. The trend adjusted factor (TAF) is composed of two elements: a smoothed error and a trend factor:
   TAF_{t + 1} = S_t + T_t , where S_t = Smoothed forecast, T_t = Current trend estimate, and both S_t and T_{t a} are further defined using smoothing constants α and β...

Techniques for Seasonality

Seasonal variations in time series data are regularly repeating upward and downward movements in series values that can be tied to recurring events. The term seasonal variation may refer to regular annual variations; but it is also applied to daily, weekly, monthly, or other regularly recurring patterns in data.

There are two different models of seasonality: additive and multiplicative. In the additive model, seasonality is expressed as a quantity (e.g. 20 units), which is added or subtracted from the series average in order to incorporate seasonality. In the multiplicative model, seasonality is expressed as a percentage of the average (or trend) amount (e.g. 1.10), which is then used to multiply the value of a series to incorporate seasonality. The seasonal percentages in the multiplicative model are referred to as seasonal relatives or seasonal indexes.

Seasonal relatives are used in two different ways in forecasting. One is to deseasonalize data; the other way is to incorporate seasonality in a forecast. Let's defer a more expansive discussion of these topics to an Operations Management textbook.

Techniques for Cycles

Cycles are up and down movements similar to seasonal variations but of longer duration--say, two to six years between peaks. The most commonly used approach to forecasting cycles is explanatory: we search for another variable that relates to, and leads, the variable of interest. E.g. the number of laser printer sales in a given month often is an indicator of demand a few months later for toner cartridges. Thus, if we are able to establish a high correlation with such a leading variable, we can develop an equation that describes the relationship, enabling forecasts to be made. The higher the correlation between the two variables, the more reliable the forecast is likely to be.

Associative Forecasts & Associative Forecasting Techniques

Associative Models use equations that consist of one or more explanatory variable that can be used to predict future demand. For example, demand for a particular product might be related to variable such as price per unit, the amount spent on advertising, as well as specific characteristics of the product.

Associative techniques rely on identifying related variables that can be used to predict the variable of interest. Sales of beef might be related to sale of substitutes like chicken; real estate prices are usually related to property location; crop yields are related to soil condition, etc.

The essence of associative techniques is the development of an equation that summarizes the effect of predictor variables. The primary method of analysis is known as regression.

Simple Linear Regression

The object in linear regression is to obtain an equation of a straight lines that minimizes the sum of the squared vertical deviations of data points from the line. This least squares line has the equation

y_c = a + bx , where

• y_c = Predicted (dependant) variable
• x = Predictor (independent) variable
• b = Slop of the line
• a = Value of y_c when x = 0 (i.e. the height of the line at the y-intercept)

Curvilinear and Multiple Regression Analysis

When nonlinear relationships are present, we employ curvilinear regression; models that involve more than one predictor and require the use of multiple regression analysis. These computations lend themselves more to computers than hand calculation, and would be beyond the scope of this entry.

Summarizing Forecast Accuracy

Two commonly used measures for summarizing historical errors are the mean absolute deviation (MAD) and the mean squared error (MSE). MAD is the average absolute error, and MSE is the average of squared errors.

MAD = Σ |Actual - Forecast| ÷ n

MSE = Σ (Actual - Forecast)² ÷ n

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