Central Luzon State University
Science City of Muñoz 3120
Nueva Ecija, Philippines
Instructional Module for the Course
MNGT 3108: Operations Management
Module 4
Forecasting
In this module, we will examine different types of forecasts
and present a variety of forecasting models. We will also provide an
overview of business sales forecasting and describe how to prepare,
monitor, and judge the accuracy of a forecast.
Objectives:
Upon completion of this module, you are expected to:
1. Explain forecasting and its characteristics
2. List the elements of a good forecast.
3. Outline the steps in the forecasting process.
4. Evaluate at least three qualitative forecasting techniques
and the advantages and disadvantages of each.
5. Compare and contrast qualitative and quantitative
approaches to forecasting.
6. Describe averaging techniques, trend and seasonal
techniques, and regression analysis, and solve typical
problems.
7. Explain three measures of forecast accuracy.
8. Understand the standard error of the estimate.
A. Forecasting
Heizer & Render (2014) states that good forecasts are an essential part of an
efficient service and manufacturing operations. Forecasting is the art and science
of predicting future events. Forecasting may involve taking historical data (such as
past sales) and projecting them into the future with a mathematical model. It may
be a subjective or an intuitive prediction. It may be based on demand-driven data,
such as customer plans to purchase, and projecting them into the future. Or the
forecast may involve a combination of these, that is, a mathematical model
adjusted by a manager’s good judgment.
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A forecast is usually classified by the future time horizon that it covers. Time
horizons fall into three categories:
a. Short-range forecast: This forecast has a time span of up to 1 year but is
generally less than 3 months. It is used for planning purchasing, job
scheduling, workforce levels, job assignments, and production levels.
b. Medium-range forecast: A medium-range, or intermediate, forecast
generally spans from 3 months to 3 years. It is useful in sales planning,
production planning and budgeting, cash budgeting, and analysis of
various operating plans.
c. Long-range forecast: Generally 3 years or more in time span, long-range
forecasts are used in planning for new products, capital expenditures,
facility location or expansion, and research and development.
Organizations use three major types of forecasts in planning future
operations:
a. Economic forecasts address the business cycle by predicting inflation rates,
money supplies, housing starts, and other planning indicators.
b. Technological forecasts are concerned with rates of technological progress,
which can result in the birth of exciting new products, requiring new plants
and equipment.
c. Demand forecasts are projections of demand for a company’s products or
services. Forecasts drive decisions, so managers need immediate and
accurate information about real demand. They need demand-driven
forecasts, where the focus is on rapidly identifying and tracking customer
desires. These forecasts may use recent point-of-sale (POS) data, retailer
generated reports of customer preferences, and any other information that
will help to forecast with the most current data possible. Demand driven
forecasts drive a company’s production, capacity, and scheduling systems
and serve as inputs to financial, marketing, and personnel planning. In
addition, the payoff in reduced inventory and obsolescence can be huge
(pp. 108-109).
B. Strategic Importance of Forecasting
Good forecasts are of critical importance in all aspects of a business: The forecast is
the only estimate of demand until actual demand becomes known. Forecasts of demand
therefore drive decisions in many areas. Let’s look at the impact of product demand
forecast on three activities:
a. Supply-Chain Management
Good supplier relations and the ensuing advantages in product innovation,
cost, and speed to market depend on accurate forecasts.
b. Human Resources
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Hiring, training, and laying off workers all depend on anticipated demand.
If the human resources department must hire additional workers without
warning, the amount of training declines, and the quality of the workforce
suffers.
c. Capacity
When capacity is inadequate, the resulting shortages can lead to loss of
customers and market share. On the other hand, when excess capacity
exists, costs can skyrocket (pp. 108-110).
C. Elements of a Good Forecast
A properly prepared forecast should fulfill certain requirements:
1. The forecast should be timely. Usually, a certain amount of time is needed
to respond to the information contained in a forecast. For example, capacity
cannot be expanded overnight, nor can inventory levels be changed
immediately. Hence, 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. A technique that
sometimes provides a good forecast and sometimes a poor one will leave
users with the uneasy feeling that they may get burned every time a new
forecast is issued.
4. The forecast should be expressed in meaningful units. Financial planners
need to know how many dollars will be needed, production planners need
to know how many units will be needed, and schedulers need to know what
machines and skills will be required. The choice of units depends on user
needs.
5. The forecast should be in writing. Although this will not guarantee that all
concerned are using the same information, it will at least increase the
likelihood of it. In addition, 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. Users
often lack confidence in forecasts based on sophisticated techniques; they
do not understand either the circumstances in which the techniques are
appropriate or the limitations of the techniques.
7. Misuse of techniques is an obvious consequence. Not surprisingly, fairly
simple forecasting techniques enjoy widespread popularity because users
are more comfortable working with them.
8. The forecast should be cost-effective: The benefits should outweigh the
costs (Stevenson, 2012, p.76).
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D. Seven Steps in Forecasting System
There are six basic steps in the forecasting process:
1. Determine the purpose of the forecast. How will it be used and when will
it be needed? This step will provide an indication of the level of detail
required in the forecast, the amount of resources that can be justified,
and the level of accuracy necessary.
2. Establish a time horizon. The forecast must indicate a time interval,
keeping in mind that accuracy decreases as the time horizon increases.
3. Obtain, clean, and analyze appropriate data. Obtaining the data can
involve significant effort. Once obtained, the data may need to be
“cleaned” to get rid of outliers and obviously incorrect data before
analysis.
4. Select a forecasting technique.
5. Make the forecast.
6. Monitor the forecast. A forecast has to be monitored to determine
whether it is performing in a satisfactory manner. If it is not, reexamine
the method, assumptions, and validity of data, and so on; modify as
needed; and prepare a revised forecast (Stevenson, 2012, p.77).
E. Forecasting Approaches
There are two general approaches to forecasting, just as there are two ways
to tackle all decision modeling. One is a quantitative analysis; the other is a
qualitative approach.
Quantitative forecasts use a variety of mathematical models that rely on
historical data and/or associative variables to forecast demand. Subjective or
qualitative forecasts incorporate such factors as the decision maker’s intuition,
emotions, personal experiences, and value system in reaching a forecast. Some
firms use one approach and some use the other. In practice, a combination of
the two is usually most effective.
Qualitative Methods
We consider four different qualitative forecasting techniques:
1. Jury of executive opinion: Under this method, the opinions of a group of
high-level experts or managers, often in combination with statistical models,
are pooled to arrive at a group estimate of demand. Bristol-Myers Squibb
Company, for example, uses 220 well-known research scientists as its jury
of executive opinion to get a grasp on future trends in the world of medical
research.
2. Delphi method: There are three different types of participants in the Delphi
method: decision makers, staff personnel, and respondents. Decision
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makers usually consist of a group of 5 to 10 experts who will be making the
actual forecast. Staff personnel assist decision makers by preparing,
distributing, collecting, and summarizing a series of questionnaires and
survey results. The respondents are a group of people, often located in
different places, whose judgments are valued. This group provides inputs
to the decision makers before the forecast is made. The state of Alaska, for
example, has used the Delphi method to develop its long range economic
forecast. A large part of the state’s budget is derived from the million-plus
barrels of oil pumped daily through a pipeline at Prudhoe Bay. The large
Delphi panel of experts had to represent all groups and opinions in the state
and all geographic areas.
3. Sales force composite: In this approach, each salesperson estimates what
sales will be in his or her region. These forecasts are then reviewed to
ensure that they are realistic. Then they are combined at the district and
national levels to reach an overall forecast. A variation of this approach
occurs at Lexus, where every quarter Lexus dealers have a “make meeting.”
At this meeting, they talk about what is selling, in what colors, and with
what options, so the factory knows what to build.
4. Market survey: This method solicits input from customers or potential
customers regarding future purchasing plans. It can help not only in
preparing a forecast but also in improving product design and planning for
new products. The consumer market survey and sales force composite
methods can, however, suffer from overly optimistic forecasts that arise
from customer input.
Quantitative Methods
Five quantitative forecasting methods, all of which use historical data. They fall
into two categories:
1. Time-series models predict on the assumption that the future is a function
of the past. In other words, they look at what has happened over a period
of time and use a series of past data to make a forecast. If we are predicting
sales of lawn mowers, we use the past sales for lawn mowers to make the
forecasts.
a. Naïve Approach
b. Moving Averages
c. Exponential Smoothing
2. Associative models, such as linear regression, incorporate the variables or
factors that might influence the quantity being forecast. For example, an
associative model for lawn mower sales might use factors such as new
housing starts, advertising budget, and competitors’ prices (Heizer & Render,
2014, p. 111-112).
d. Trend Projection
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e. Linear Regression
F. Time Series Forecasting
Heizer & Render (2014) describes that a time series is based on a sequence of evenly
spaced (weekly, monthly, quarterly, and so on) data points. Forecasting time-series data
implies that future values are predicted only from past values and that other variables, no
matter how potentially valuable, may be ignored.
Analyzing time series means breaking down past data into components and then
projecting them forward. A time series has four components:
a. Trend is the gradual upward or downward movement of the data over time. Changes
in income, population, age distribution, or cultural views may account for
movement in trend.
b. Seasonality is a data pattern that repeats itself after a period of days, weeks, months,
or quarters.
c. Cycles are patterns in the data that occur every several years. They are usually tied
into the business cycle and are of major importance in short-term business analysis
and planning. Predicting business cycles is difficult because they may be affected
by political events or by international turmoil.
d. Random variations are “blips” in the data caused by chance and unusual situations.
They follow no discernible pattern, so they cannot be predicted.
These are the following approach in forecasting time series:
1. Naive Approach
The simplest way to forecast is to assume that demand in the next period
will be equal to demand in the most recent period.
2. Moving Averages
A moving-average forecast uses a number of historical actual data values to
generate a forecast. Moving averages are useful if we can assume that market
demands will stay fairly steady over time. Mathematically, the simple moving
average (which serves as an estimate of the next period’s demand) is expressed
as:
∑(demand in previous period)
Moving Average = n
When a detectable trend or pattern is present, weights can be used to place
more emphasis on recent values. This practice makes forecasting techniques
more responsive to changes because more recent periods may be more heavily
weighted. Choice of 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 month or period is weighted too heavily, the forecast may
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reflect a large unusual change in the demand or sales pattern too quickly. A
weighted moving average may be expressed mathematically as:
∑((Weight for previous n)(𝐷𝑒𝑚𝑎𝑛𝑑 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑛)
Weighted Moving Average = ∑(𝑊𝑒𝑖𝑔ℎ𝑡𝑠)
3. Exponential Smoothing
Exponential smoothing is another weighted-moving-average forecasting
method. It involves very little record keeping of past data and is fairly easy to
use. The basic exponential smoothing formula can be shown as follows: where
a is a weight, or smoothing constant , chosen by the forecaster, that has a value
greater than or equal to 0 and less than or equal to 1. Equation can be written
mathematically as:
𝐹𝑡 = 𝐹𝑡−1 +α (𝐴𝑡−1 − 𝐹𝑡−1)
Simple exponential smoothing, the technique is like any other moving-
average technique. It fails to respond to trends. Other forecasting techniques
that can deal with trends are certainly available. However, because exponential
smoothing is such a popular modeling approach in business, let us look at it in
more detail.
To improve our forecast, let us illustrate a more complex exponential
smoothing model, one that adjusts for trend. The idea is to compute an
exponentially smoothed average of the data and then adjust for positive or
negative lag in trend. The new formula is:
𝐹𝐼𝑇𝑡 = 𝐹𝑡 + 𝑇𝑡
With trend-adjusted exponential smoothing, estimates for both the
average and the trend are smoothed. This procedure requires two smoothing
constants: a for the average and b for the trend. We then compute the
average and trend each period:
𝐹𝑡 = α (𝐴𝑡−1 ) + (1- α) ( 𝐹𝑡−1 + 𝑇𝑡−1 )
𝑇𝑡 = ẞ ( 𝐹𝑡 - 𝐹𝑡−1 ) + (1 - ẞ) 𝑇𝑡−1
4. Trend Projections
This technique fits a trend line to a series of historical data points and then
projects the slope of the line into the future for medium- to long-range forecasts.
Several mathematical trend equations can be developed (for example,
exponential and quadratic), but in this section, we will look at linear (straight-
line) trends only.
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If we decide to develop a linear trend line by a precise statistical method,
we can apply the least-squares method. This approach results in a straight line
that minimizes the sum of the squares of the vertical differences or deviations
from the line to each of the actual observations.
A least-squares line is described in terms of its y -intercept (the height at
which it intercepts the y -axis) and its expected change (slope). If we can
compute the y -intercept and slope, we can express the line with the following
equation:
ŷ = a + bx
Statisticians have developed equations that we can use to find the values of
a and b for any regression line. The slope b is found by:
∑ xy−nxy
̅̅̅̅
b= ∑ x2 −nx̅2
We can compute the y -intercept a as follows:
a = 𝑦̅ − 𝑏𝑥̅
5. Seasonal Variations in Data
Seasonal variations in data are regular movements in a time series that
relate to recurring events such as weather or holidays. Similarly, understanding
seasonal variations is important for capacity planning in organizations that
handle peak loads. The presence of seasonality makes adjustments in trend-line
forecasts necessary. Seasonality is expressed in terms of the amount that actual
values differ from average values in the time series. Analyzing data in monthly
or quarterly terms usually makes it easy for a statistician to spot seasonal
patterns.
Seasonal indices can then be developed by several common methods. In
what is called a multiplicative seasonal model, seasonal factors are multiplied
by an estimate of average demand to produce a seasonal forecast. Our
assumption in this section is that trend has been removed from the data.
Otherwise, the magnitude of the seasonal data will be distorted by the trend.
Here are the steps we will follow for a company that has “seasons” of 1
month:
1. Find the average historical demand each season (quarter, month, or weeks,
etc.) by summing the demand for that month in each year and dividing by
the number of years of data available.
2. Compute the average demand over all months by dividing the total average
annual demand by the number of seasons.
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3. Compute a seasonal index for each season by dividing that season’s historical
average demand by the average demand over all months.
4. Estimate next year’s total annual demand.
5. Divide this estimate of total annual demand by the number of seasons, then
multiply it by the seasonal index for each month. This provides the seasonal
forecast (pp. 112-127).
G. Associative Forecasting
1. Regression Analysis for Forecasting
Unlike time-series forecasting, associative forecasting models usually
consider several variables that are related to the quantity being predicted. Once
these related variables have been found, a statistical model is built and used
to forecast the item of interest. This approach is more powerful than the time-
series methods that use only the historical values for the forecast variable.
We can use the same mathematical model that we employed in the least-
squares method of trend projection to perform a linear-regression analysis. The
dependent variables that we want to forecast will still be ŷ. But now the
independent variable, x, need no longer be time. We use the equation:
ŷ = a + bx
2. Correlation Coefficients for Regression Lines
The regression equation is one way of expressing the nature of the
relationship between two variables. Regression lines are not “cause-and-effect”
relationships. They merely describe the relationships among variables. The
regression equation shows how one variable relates to the value and changes
in another variable.
Another way to evaluate the relationship between two variables is to
compute the coefficient of correlation. This measure expresses the degree or
strength of the linear relationship. To compute r, we use much of the same
data needed earlier to calculate a and b for the regression line. The rather
lengthy equation for r is:
n ∑ xy − ∑ x ∑ y
r= 2 2
√[n ∑ x2 − (∑ x) ] [n ∑ y2 − (∑ y) ]
Although the coefficient of correlation is the measure most commonly used
to describe the relationship between two variables, another measure does
exist. It is called the coefficient of determination and is simply the square of
the coefficient of correlation—namely, r2. The value of r2 will always be a
positive number in the range 0 … r2 … 1. The coefficient of determination is
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the percent of variation in the dependent variable (y) that is explained by the
regression equation.
3. Multiple-Regression Analysis
Multiple regression is a practical extension of the simple regression model
we just explored. It allows us to build a model with several independent
variables instead of just one variable. The proper equation would be (Heizer &
Render, 2014, pp. 131-137):
ŷ = a + 𝑏1 𝑥1 + 𝑏2 𝑥2
H. Measuring Forecast Error (Time Series)
The overall accuracy of any forecasting model—moving average, exponential
smoothing, or other—can be determined by comparing the forecasted values with
the actual or observed values. If F t denotes the forecast in period t , and A t
denotes the actual demand in period t , the forecast error (or deviation) is defined
as:
Forecast Error = Actual demand – Forecast value
Several measures are used in practice to calculate the overall forecast error.
These measures can be used to compare different forecasting models, as well as
to monitor forecasts to ensure they are performing well. Three of the most popular
measures are mean absolute deviation (MAD), mean squared error (MSE), and
mean absolute percent error (MAPE).
a. Mean Absolute Deviation
Mean Absolute Deviation the first measure of the overall forecast error for
a model is the mean absolute deviation (MAD). This value is computed by
taking the sum of the absolute values of the individual forecast errors
(deviations) and dividing by the number of periods of data (n):
∑[Forecast Error]
MAD = n
b. Mean Squared Error
The mean squared error (MSE) is a second way of measuring overall
forecast error. MSE is the average of the squared differences between the
forecasted and observed values. Its formula is:
∑(Forecast Error)2
MSE = n
c. Mean Absolute Percent Error
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A problem with both the MAD and MSE is that their values depend on the
magnitude of the item being forecast. If the forecast item is measured in
thousands, the MAD and MSE values can be very large. To avoid this problem,
we can use the mean absolute percent error (MAPE). This is computed as the
average of the absolute difference between the forecasted and actual values,
expressed as a percentage of the actual values. That is, if we have forecasted
and actual values for n periods, the MAPE is calculated as (Heizer & Render,
2014, pp. 117-120):
∑(|Actualt −Forecastt |⁄Actualt ) 100
MAPE = n
I. Standard Error of Estimate (Associative)
To measure the accuracy of the regression estimates, we must compute the
standard error of the estimate, 𝑆𝑦,𝑥 . This computation is called the standard
deviation of the regression: It measures the error from the dependent variable, y,
to the regression line, rather than to the mean. (Heizer & Render, 2014, pp. 138).
∑ 𝑦 2 −𝑎 ∑ 𝑦−𝑏 ∑ 𝑥𝑦
𝑆𝑦,𝑥 = √ 𝑛−2
References
Heizer, J., & Render, B. (2014). Operations Management, Sustainability and
Supply Chain Management Global Edition (11th ed.). Pearson
Education Inc.
Stevenson, W. (2012). Operations Management (11th ed.). McGraw-Hill
Companies, Inc.
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