Chapter 4
Random variations
"Blips" in the data caused by chance and unusual situations. They follow no discernible pattern, so they cannot be predicted.
Trend projection
A time-series forecasting method that fits a trend line to a series of historical data points and then projects the line into the future for forecasts.
Qualitative forecasts
AKA subjective forecasts. Incorporate such factors as the decision maker's intuition, emotions, personal experiences, and value system in reaching a forecast.
The forecast is the only estimate of demand until
Actual demand becomes known.
Economic forecasts
Address the business cycle by predicting inflation rates, money supplies, housing starts, and other planning indicators.
When α reaches the extreme of 1.0, then
All the older values drop out, and the forecast becomes identical to the naive model mentioned previously in this chapter.
Adaptive forecasting/smoothing
An approach to exponential smoothing forecast in which the smoothing constant is automatically changed to keep errors to a minimum.
Multiple regression
An associative forecasting method with more than one independent variable.
Good forecasts are
An essential part of efficient service and manufacturing operations.
Due to special demand patterns, many service firms
Maintain records of sales, noting not only the day of the week but also unusual events, including the weather, so that patterns and correlations that influence demand can be developed.
Moving average formula
Moving average=∑demand in previous n periods/n n is the number of periods in the moving average.
Basic exponential smoothing formula
New forecast=Last period's forecast+ α (Last period's actual demand − Last period's forecast) α 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.
Quantitative forecasts
Use a variety of mathematical models that rely on historical data and/or associative variables to forecast demand.
Moving average forecast
Uses a number of historical actual data values to generate a forecast. This approach is useful if we can assume that market demands will stay fairly steady over time.
The smoothing constant, α, is generally in the range from _______ for business applications.
.05 to .50
Three steps to compute a trend-adjusted forecast
1. Compute Ft, the exponentially smoothed forecast average for period t. 2. Compute the smoothed trend, Tt. 3. Calculate the forecast including trend, FITt, by the forecast including trend formula .
Seven basic steps of forecasting
1. Determine the use of the forecast 2. Select the items to be forecasted 3. Determine the time horizon of the forecast 4. Select the forecasting model(s) 5. Gather the data needed to make the forecas 6. Make the forecast. 7. Validate and implement the results
Three major types of forecasts in planning future operations
1. Economic forecasts 2. Technological forecasts 3. Demand forecasts
Here are the steps we will follow for a company that has "seasons" of 1 month
1. Find the average historical demand each season (or month in this case) by summing the demand for that month in each year and dividing by the number of years of data available. For example, if, in January, we have seen sales of 8, 6, and 10 over the past 3 years, average January demand equals (8+6+10)/3=8(8+6+10)/3=8 units. 2. Compute the average demand over all months by dividing the total average annual demand by the number of seasons. For example, if the total average demand for a year is 120 units and there are 12 seasons (each month), the average monthly demand is 120/12=120/12= 10 units. 3. Compute a seasonal index for each season by dividing that month's historical average demand (from Step 1) by the average demand over all months (from Step 2). For example, if the average historical January demand over the past 3 years is 8 units 8 units and the average demand over all months is 10 units, the seasonal index for January is 8/10=.80.8/10=.80. Likewise, a seasonal index of 1.20 for February would mean that February's demand is 20% larger than 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.
Medium- and long-range forecasts are distinguished from short-range forecasts by three features
1. First, intermediate and long-range forecasts deal with more comprehensive issues supporting management decisions regarding planning and products, plants, and processes. Implementing some facility decisions, such as GM's decision to open a new Brazilian manufacturing plant, can take 5 to 8 years from inception to completion. 2. Second, short-term forecasting usually employs different methodologies than longer-term forecasting. Mathematical techniques, such as moving averages, exponential smoothing, and trend extrapolation (all of which we shall examine shortly), are common to short-run projections. Broader, less quantitative methods are useful in predicting such issues as whether a new product, like the optical disk recorder, should be introduced into a company's product line. 3. Finally, as you would expect, short-range forecasts tend to be more accurate than longer-range forecasts. Factors that influence demand change every day. Thus, as the time horizon lengthens, it is likely that forecast accuracy will diminish. It almost goes without saying, then, that sales forecasts must be updated regularly to maintain their value and integrity. After each sales period, forecasts should be reviewed and revised.
Moving averages present three problems
1. Increasing the size of n (the number of periods averaged) does smooth out fluctuations better, but it makes the method less sensitive to changes in the data. 2. Moving averages cannot pick up trends very well. Because they are averages, they will always stay within past levels and will not predict changes to either higher or lower levels. That is, they lag the actual values. 3. Moving averages require extensive records of past data.
Four different qualitative forecasting techniques
1. Jury of executive opinion 2. Delphi method 3. Sales force composite 4. Market survey
Five quantitative forecasting methods
1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend progression 5. Linear regression
Three categories of future time horizons
1. Short-range forecast 2. Medium-range forecast 3. Long-range forecast
Focus forecasting is based on two principles
1. Sophisticated forecasting models are not always better than simple ones. 2. There is no single technique that should be used for all products or services.
Four components of a time series
1. Trend 2. Seasonality 3. Cycles 4. Random variations
Using the least-squares method implies that we have met three requirements
1. We always plot the data because least-squares data assume a linear relationship. If a curve appears to be present, curvilinear analysis is probably needed. 2. We do not predict time periods far beyond our given database. For example, if we have 20 months' worth of average prices of Microsoft stock, we can forecast only 3 or 4 months into the future. Forecasts beyond that have little statistical validity. Thus, you cannot take 5 years' worth of sales data and project 5 years into the future. The world is too uncertain. 3. Deviations around the least-squares line are assumed to be random and normally distributed, with most observations close to the line and only a smaller number farther out.
Taco Bell found that
A 6-week moving average was the forecasting technique that minimized its mean squared error (MSE) of these quarter-hour forecasts.
Bias error
A consistent tendency for forecasts to be greater or less than the actual values (that is, for a high absolute cumulative error).
Seasonality
A data pattern that repeats itself after a period of days, weeks, months, or quarters.
Effective planning in both the short run and long run depends on
A forecast of demand for the company's products.
Market survey
A forecasting method that solicits input from customers or potential customers regarding future purchasing plans.
Sales force composite
A forecasting technique based on salespersons' estimates of expected sales.
Naive approach forecasting
A forecasting technique that assumes that demand in the next period is equal to demand in the most recent period. It turns out that for some product lines, this approach is the most cost-effective and efficient objective forecasting model.
Jury of executive opinion
A forecasting technique that uses the opinion of a small group of high-level managers to form a group estimate of demand.
Delphi method
A forecasting technique using a group process that allows experts to make forecasts.
The value of the trend-smoothing constant, β, resembles the α constant because
A high β is more responsive to recent changes in trend. A low β gives less weight to the most recent trends and tends to smooth out the present trend.
Mean absolute deviation (MAD)
A measure of the overall forecast error for a model.
Coefficient of correlation
A measure of the strength of the relationship between two variables. Usually identified as r, this value can be any number between +1 and −1.
Standard error of the estimate
A measure of variability around the regression line - its standard deviation.
Tracking signal
A measurement of how well a forecast is predicting actual values.
A time series is based on
A sequence of evenly spaced (weekly, monthly, quarterly, and so on) data points.
The MSE tends to accentuate
Large deviations because of the squared term.
Negative signals mean that demand is
Less than forecast.
High values of α are chosen when the underlying average is
Likely to change.
Small deviations are okay, but positive and negative errors should
Balance one another so that the tracking signal centers closely around zero.
CPFR
Collaborative Planning, Forecasting, and Replenishment
Technological forecasts
Concerned with rates of technological progress, which can result in the birth of exciting new products, requiring new plants and equipment.
Mean absolute deviation (MAD) formula
MAD=∑|Actual − Forecast|/n
Mean absolute percent error (MAPE) formula
MAPE=[∑100|Actual−Forecast|/Actual]/n
Mean squared error (MSE) formula
MSE=∑(Forecast errors)^2/n
Regression lines are not "cause-and-effect" relationships. They merely
Describe the relationships among variables.
Exponentially smoothed forecast average (Ft) formula
Exponentially smoothed forecast average (Ft)=α(Actual demand last period)+(1−α)(Forecast last period + Trend estimate last period) α= smoothing constant for the average (0≤α≤1)
Exponentially smoothed trend (Tt) formula
Exponentially smoothed trend (Tt)=β(Forecast this period − Forecast last period)+(1−β)(Trend estimate last period) β= smoothing constant for the trend (0≤β≤1)
Low values of α are used when the underlying average is
Fairly stable.
Standard deviation of the regression formula
Sy,x=sqrt(∑y^2−a∑y−b∑xy/n−2)
Simple exponential smoothing is often referred to as
First-order smoothing.
Forecast error formula
Forecast error=Actual demand − Forecast value
Forecast including trend formula
Forecast including trend (FITt)=Exponentially smoothed forecast average (Ft)+ Exponentially smoothed trend (Tt)
Focus forecasting
Forecasting that tries a variety of computer models and selects the best one for a particular application.
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.
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.
Medium-range 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.
What are some aspects of supply chain management that depend on accurate forecasts?
Good supplier relations and the ensuing advantages in product innovation, cost, and speed to market.
Positive tracking signals indicate that demand is
Greater than forecast.
Short-range 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.
What are some aspects of human resources management that depend on accurate forecasts?
Hiring, training, and laying off workers.
Associative models
Incorporate the variables or factors that might influence the quantity being forecast. Linear regression forecasting method falls into this category.
The seven steps of forecasting present a systematic way of
Initiating, designing, and implementing a forecasting system.
Bernard Smith
Inventory manager for American Hardware Supply, coined the term focus forecasting.
Once a forecast has been completed,
It should not be forgotten.
Cycles
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 these is difficult because they may be affected by political events or by international turmoil.
Firms like Taco Bell now use
Point-of-sale computers that track sales every quarter hour.
Time-series models
Predict on the assumption that the future is a function of the past. Four quantitative forecasting methods fall into this category: 1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend progression
Demand forecasts
Projections of demand for a company's products or services. 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. These 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.
Two general approaches to forecasting
Quantitative and qualitative
Seasonal variations in data
Regular movements in a time series that relate to recurring events such as weather or holidays.
Least-squares method
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.
Multiplicative seasonal model
Seasonal factors are multiplied by an estimate of average demand to produce a seasonal forecast.
Trend-adjusted smoothing is called
Second-order smoothing or double smoothing.
How does capacity management depend on accurate forecasts?
Shortages can lead to loss of customers and market share. On the other hand, when excess capacity exists, costs can skyrocket.
Perhaps the easiest measure to interpret
The MAPE
If the human resources department must hire additional workers without warning,
The amount of training declines, and the quality of the workforce suffers.
Seasonality is expressed in terms of
The amount that actual values differ from average values in the time series.
Forecasting
The art and science of predicting future events.
Mean absolute percent error (MAPE)
The average of the absolute differences between the forecast and actual values, expressed as a percent of actual values.
Mean squared error (MSE)
The average of the squared differences between the forecasted and observed values.
Trend
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 this.
coefficient of determination
The square of the coefficient of correlation—namely, r^2. The value of r^2 will always be a positive number in the range 0≤r^2≤1.0≤r2≤1. r^2 is the percent of variation in the dependent variable (y) that is explained by the regression equation.
Values of β can be found by
The trial-and-error approach or by using sophisticated commercial forecasting software, with the MAD used as a measure of comparison.
A problem with both the MAD and MSE
Their values depend on the magnitude of the item being forecast.
How do firms decide what the upper and lower tracking limits should be?
They try to find reasonable values—in other words, limits not so low as to be triggered with every small forecast error and not so high as to allow bad forecasts to be regularly overlooked. One MAD is equivalent to approximately .8 standard deviations, ±2 MADs =± 1.6 standard deviations, ± 3 MADs =± 2.4 standard deviations, and ± 4 MADs =± 3.2 standard deviations. This fact suggests that for a forecast to be "in control," 89% of the errors are expected to fall within ± 2 MADs, 98% within ± 3 MADs, or 99.9% within ± 4 MADs.
Forecasting in the service sector presents some unusual challenges. A major technique in the retail sector to combat some of these challenges is
Tracking demand by maintaining good short-term records.
Tracking signal formula
Tracking signal=Cumulative error/MAD
Simple exponential smoothing fails to respond to
Trends
Because there are limits to what can be expected from forecasts,
We develop error measures.
Using MSE as the measure of forecast error typically indicates that
We prefer to have several smaller deviations rather than even one large deviation.
Weighted moving average formula
Weighted moving average=∑ ((Weight for period n)(Demand in period n))/∑ Weights
Exponential smoothing
Weighted-moving-average forecasting method. It involves very little record keeping of past data and is fairly easy to use.
α gives more weight to recent data
When α is high.
α gives more weight to past data
When α is low.
Y-intercept formula
a=ȳ−bx̅
Slope of the regression line formula
b=∑(xy−nx̅ȳ)/∑(x^2−nx̅^2) b= slope of the regression line ∑= summation sign x= known values of the independent variable y= known values of the dependent variable x̅= average of the x-values ȳ= average of the y-values n= number of data points or observations
Coefficient of correlation formula
r=n∑xy−∑x∑y/sqrt[n∑x^2−(∑x)^2][n∑y^2−(∑y)^2]
Multiple regression formula
ŷ=a+b1x1+b2x2y^=a+b1x1+b2x2 ŷ= dependent variable, sales a= a constant, the y intercept x1 and x2= values of the two independent variables, area payroll and interest rates, respectively b1 and b2= coefficients for the two independent variables
Linear regression formula
ŷ=a+bx ŷ (called "y hat")= computed value of the variable to be predicted (called the dependent variable) a= y-axis intercept b= slope of the regression line (or the rate of change in y for given changes in x) x= the independent variable (which in this case is time)
Realities of forecasting
•Outside factors that we cannot predict or control often impact the forecast. •Most forecasting techniques assume that there is some underlying stability in the system. •Consequently, some firms automate their predictions using computerized forecasting software, then closely monitor only the product items whose demand is erratic. •Both product family and aggregated forecasts are more accurate than individual product forecasts.