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© 2007 Pearson Education
Forecasting
Chapter 13
© 2007 Pearson Education
How Forecasting fits the Operations Management
Philosophy
Operations As a Competitive Weapon
Operations StrategyProject Management Process Strategy
Process AnalysisProcess Performance and Quality
Constraint ManagementProcess LayoutLean Systems
Supply Chain StrategyLocation
Inventory ManagementForecasting
Sales and Operations PlanningResource Planning
Scheduling
© 2007 Pearson Education
Forecasting at Unilever
Customer demand planning (CDP), which is critical to managing value chains, begins with accurate forecasts.
Unilever has a state-of-the-art CDP system that blends historical shipment data with promotional data and current order data.
Statistical forecasts are adjusted with planned promotion predictions.
Forecasts are frequently reviewed and adjusted with point of sale data.
This has enabled Unilever to reduce its inventory and improved its customer service.
© 2007 Pearson Education
Demand Patterns
Time Series: The repeated observations of demand for a service or product in their order of occurrence.
There are five basic patterns of most time series.a. Horizontal. The fluctuation of data around a constant mean.
b. Trend. The systematic increase or decrease in the mean of the series over time.
c. Seasonal. A repeatable pattern of increases or decreases in demand, depending on the time of day, week, month, or season.
d. Cyclical. The less predictable gradual increases or decreases over longer periods of time (years or decades).
e. Random. The unforecastable variation in demand.
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Demand Patterns
Horizontal Trend
Seasonal Cyclical
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Designing the Forecast System
Deciding what to forecast Level of aggregation. Units of measure.
Choosing the type of forecasting method: Qualitative methods
Judgment Quantitative methods
Causal Time-series
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Deciding What To Forecast
Few companies err by more than 5 percent when forecasting total demand for all their services or products. Errors in forecasts for individual items may be much higher.
Level of Aggregation: The act of clustering several similar services or products so that companies can obtain more accurate forecasts.
Units of measurement: Forecasts of sales revenue are not helpful because prices fluctuate. Forecast the number of units of demand then translate
into sales revenue estimates Stock-keeping unit (SKU): An individual item or product
that has an identifying code and is held in inventory somewhere along the value chain.
© 2007 Pearson Education
Choosing the Type ofForecasting Technique
Judgment methods: A type of qualitative method that translates the opinions of managers, expert opinions, consumer surveys, and sales force estimates into quantitative estimates.
Causal methods: A type of quantitative method that uses historical data on independent variables, such as promotional campaigns, economic conditions, and competitors’ actions, to predict demand.
Time-series analysis: A statistical approach that relies heavily on historical demand data to project the future size of demand and recognizes trends and seasonal patterns.
Collaborative planning, forecasting, and replenishment (CPFR): A nine-step process for value-chain management that allows a manufacturer and its customers to collaborate on making the forecast by using the Internet.
© 2007 Pearson Education© 2007 Pearson Education
Demand Forecast Applications
• Causal• Judgment
• Causal• Judgment
• Time series• Causal• Judgment
ForecastingTechnique
• Facility location• Capacity planning• Process management
• Staff planning• Production planning
• Master production scheduling
• Purchasing• Distribution
• Inventory management
• Final assembly scheduling
• Workforce scheduling
• Master production scheduling
Decision Area
• Total sales• Total sales• Groups or families
of products or services
• Individual products or services
Forecast Quality
Long Term(more than 2 years)
Medium Term(3 months– 2 years)
Short Term(0–3 months)
ApplicationTime Horizon
© 2007 Pearson Education
Judgment Methods
Sales force estimates: The forecasts that are compiled from estimates of future demands made periodically by members of a company’s sales force.
Executive opinion: A forecasting method in which the opinions, experience, and technical knowledge of one or more managers are summarized to arrive at a single forecast. Executive opinion can also be used for technological
forecasting to keep abreast of the latest advances in technology.
Market research: A systematic approach to determine external consumer interest in a service or product by creating and testing hypotheses through data-gathering surveys.
Delphi method: A process of gaining consensus from a group of experts while maintaining their anonymity.
© 2007 Pearson Education
Guidelines for Using Judgment Forecasts
Judgment forecasting is clearly needed when no quantitative data are available to use quantitative forecasting approaches.
Guidelines for the use of judgment to adjust quantitative forecasts to improve forecast quality are as follows:1. Adjust quantitative forecasts when they tend to be
inaccurate and the decision maker has important contextual knowledge.
2. Make adjustments to quantitative forecasts to compensate for specific events, such as advertising campaigns, the actions of competitors, or international developments.
© 2007 Pearson Education
Causal Methods Linear Regression
Causal methods are used when historical data are available and the relationship between the factor to be forecasted and other external or internal factors can be identified.
Linear regression: A causal method in which one variable (the dependent variable) is related to one or more independent variables by a linear equation.
Dependent variable: The variable that one wants to forecast.
Independent variables: Variables that are assumed to affect the dependent variable and thereby “cause” the results observed in the past.
© 2007 Pearson Education
Dep
ende
nt v
aria
ble
Independent variableX
YEstimate ofY fromregressionequation
Actualvalueof Y
Value of X usedto estimate Y
Deviation,or error
{
Causal Methods Linear Regression
Regressionequation:Y = a + bX
Y = dependent variableX = independent variablea = Y-intercept of the lineb = slope of the line
© 2007 Pearson Education
Sales AdvertisingMonth (000 units) (000 $)
1 264 2.52 116 1.33 165 1.44 101 1.05 209 2.0
a = – 8.135b = 109.229Xr = 0.98r2 = 0.96syx= 15.603
The following are sales and advertising data for the past 5 months for brass door hinges. The marketing manager says that next month the company will spend $1,750 on advertising for the product. Use linear regression to develop an equation and a forecast for this product.
Linear Regression Example 13.1
We use the computer to determine the best values of a, b, the correlation coefficient (r), the coefficient of determination (r2), and the standard error of the estimate (syx).
© 2007 Pearson Education
| | | |1.0 1.5 2.0 2.5
Advertising (thousands of dollars)
300 —
250 —
200 —
150 —
100 —
50 —
Sale
s (th
ousa
nds
of u
nits
)
Y = – 8.135 + 109.229X
a = – 8.135b = 109.229Xr = 0.98r2 = 0.96syx= 15.603
Y = a + bX
Linear Regression Line for Example 13.1
Forecast for Month 6: X = $1750, Y = – 8.135 + 109.229(1.75) = 183,016
© 2007 Pearson Education
The production scheduler can use this forecast of 183,016 units to determine the quantity of brass door hinges needed for month 6.
If there are 62,500 units in stock, then the requirement to be filled from production is 183,016 - 62,500 = 120,516 units.
Forecasting Demand for Example 13.1
© 2007 Pearson Education
Time Series Methods
Naive forecast: A time-series method whereby the forecast for the next period equals the demand for the current period, or Forecast = Dt
Simple moving average method: A time-series method used to estimate the average of a demand time series by averaging the demand for the n most recent time periods. It removes the effects of random fluctuation and is most
useful when demand has no pronounced trend or seasonal influences.
…
© 2007 Pearson Education
Forecasting Error
For any forecasting method, it is important to measure the accuracy of its forecasts.
Forecast error is the difference found by subtracting the forecast from actual demand for a given period.Et = Dt - Ft
whereEt = forecast error for period tDt = actual demand for period tFt = forecast for period t
© 2007 Pearson Education
Moving Average Method Example 13.2
a. Compute a three-week moving average forecast for the arrival of medical clinic patients in week 4. The numbers of arrivals for the past 3 weeks were:
PatientWeek Arrivals
1 4002 3803 411
b. If the actual number of patient arrivals in week 4 is 415, what is the forecast error for week 4? c. What is the forecast for week 5?
© 2007 Pearson EducationWeek
450 —
430 —
410 —
390 —
370 —
| | | | | |0 5 10 15 20 25 30
Patie
nt a
rriv
als
Actual patientarrivals
Example 13.2Solution
The moving average method may involve the use of as many periods of past demand as desired. The stability of the demand series generally determines how many periods to include.
© 2007 Pearson Education
Week Arrivals Average1 4002 3803 411 3974 415 4025 ?
Example 13.2 Solution continued
Forecast for week 5 is the average of the arrivals for weeks 2,3 and 4
Forecast error for week 4 is 18. It is the difference between the actual arrivals (415) for week 4 and the average of 397 that was used as a forecast for week 4. (415 – 397 = 18)
Forecast for week 4 is the average of the arrivals for weeks 1,2 and 3
F4 = 411 + 380 + 4003
a.
c. b.
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Comparison of 3- and 6-Week MA Forecasts
Week
Patie
nt A
rriv
als
Actual patient arrivals
3-week moving average forecast
6-week moving average forecast
© 2007 Pearson Education
Application 13.1
We will use the following customer-arrival data in this moving average application:
© 2007 Pearson Education© 2007 Pearson Education
Application 13.1a Moving Average Method
F5 D4 D3 D2
3790 810 740
3780
780 customer arrivals
F6 D5 D4 D3
3805 790 810
3801.667
802 customer arrivals
© 2007 Pearson Education
Weighted Moving Averages
Weighted moving average method: A time-series method in which each historical demand in the average can have its own weight; the sum of the weights equals 1.0.
Ft+1 = W1Dt + W2Dt-1 + …+ WnDt-n+1
© 2007 Pearson Education© 2007 Pearson Education
Application 13.1b Weighted Moving Average
F5 W1D4 W2D3 W3D2 0.50 790 0.30 810 0.20 740 786
786 customer arrivals
F6 W1D5 W2D4 W3D3 0.50 805 0.30 790 0.20 810 801.5
802 customer arrivals
© 2007 Pearson Education
Exponential Smoothing
Ft+1 = (Demand this period) + (1 – )(Forecast calculated last period) = Dt + (1–)Ft
Or an equivalent equation: Ft+1 = Ft + (Dt – Ft )Where alpha (is a smoothing parameter with a value between 0 and 1.0Exponential smoothing is the most frequently used formal forecasting method because of its simplicity and the small amount of data needed to support it.
Exponential smoothing method: A sophisticated weighted moving average method that calculates the average of a time series by giving recent demands more weight than earlier demands.
© 2007 Pearson Education
Reconsider the medical clinic patient arrival data. It is now the end of week 3. a. Using = 0.10, calculate the exponential smoothing forecast for week 4.
Ft+1 = Dt + (1-)Ft
F4 = 0.10(411) + 0.90(390) = 392.1b. What is the forecast error for week 4 if the actual demand turned out to be 415?
E4 = 415 - 392 = 23c. What is the forecast for week 5?
F5 = 0.10(415) + 0.90(392.1) = 394.4
Exponential SmoothingExample 13.3
Week Arrivals1 4002 3803 4114 4155 ?
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Application 13.1c Exponential Smoothing
Ft1 Ft Dt Ft 783 0.20 790 783 784.4
784 customer arrivals
Ft1 Ft Dt Ft 784.4 0.20 805 784.4 788.52
789 customer arrivals
© 2007 Pearson Education
Trend-Adjusted Exponential Smoothing
A trend in a time series is a systematic increase or decrease in the average of the series over time. Where a significant trend is present, exponential smoothing
approaches must be modified; otherwise, the forecasts tend to be below or above the actual demand.
Trend-adjusted exponential smoothing method: The method for incorporating a trend in an exponentially smoothed forecast. With this approach, the estimates for both the average and
the trend are smoothed, requiring two smoothing constants. For each period, we calculate the average and the trend.
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Ft+1 = At +Tt
where At = Dt + (1 – )(At-1 + Tt-1) Tt = (At – At-1) + (1 – )Tt-1
At = exponentially smoothed average of the series in period tTt = exponentially smoothed average of the trend in period t = smoothing parameter for the average = smoothing parameter for the trendDt = demand for period tFt+1 = forecast for period t + 1
Trend-Adjusted Exponential Smoothing Formula
© 2007 Pearson Education
A0 = 28 patients and Tt = 3 patientsAt = Dt + (1 – )(At-1 + Tt-1)
A1= 0.20(27) + 0.80(28 + 3) = 30.2
Tt = (At – At-1) + (1 – )Tt-1
T1 = 0.20(30.2 – 2.8) + 0.80(3) = 2.8
Ft+1 = At + Tt
F2 = 30.2 + 2.8 = 33 blood tests
Trend-Adjusted Exponential Smoothing
Example 13.4 Medanalysis ran an average of 28 blood tests per week during the past four weeks. The trend over that period was 3 additional patients per week. This week’s demand was for 27 blood tests. We use = 0.20 and = 0.20 to calculate the forecast for next week.
© 2007 Pearson Education
| | | | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
80 —
70 —
60 —
50 —
40 —
30 —
Patie
nt a
rriv
als
Week
Actual blood test requests
Trend-adjusted forecast
Example 13.4 Medanalysis Trend-Adjusted Exponential Smoothing
© 2007 Pearson Education© 2007 Pearson Education
Forecast for Medanalysis Using the Trend-Adjusted Exponential Smoothing Model
© 2007 Pearson Education
Application 13.2
The forecaster for Canine Gourmet dog breath fresheners estimated (in March) the sales average to be 300,000 cases sold per month and the trend to be +8,000 per month.
The actual sales for April were 330,000 cases. What is the forecast for May, assuming = 0.20 and = 0.10?
© 2007 Pearson Education© 2007 Pearson Education
Application 13.2 Solution
thousand
thousand
To make forecasts for periods beyond the next period, multiply the trend estimate by the number of additional periods, and add the result to the current average
© 2007 Pearson Education
Seasonal Patterns Seasonal patterns are regularly repeated upward
or downward movements in demand measured in periods of less than one year. An easy way to account for seasonal effects is to use one
of the techniques already described but to limit the data in the time series to those time periods in the same season.
If the weighted moving average method is used, high weights are placed on prior periods belonging to the same season. Multiplicative seasonal method is a method whereby
seasonal factors are multiplied by an estimate of average demand to arrive at a seasonal forecast.
Additive seasonal method is a method whereby seasonal forecasts are generated by adding a constant to the estimate of the average demand per season.
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Multiplicative Seasonal Method
Step 1: For each year, calculate the average demand for each season by dividing annual demand by the number of seasons per year.
Step 2: For each year, divide the actual demand for each season by the average demand per season, resulting in a seasonal index for each season of the year, indicating the level of demand relative to the average demand.
Step 3: Calculate the average seasonal index for each season using the results from Step 2. Add the seasonal indices for each season and divide by the number of years of data.
Step 4: Calculate each season’s forecast for next year.
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Quarter Year 1 Year 2 Year 3 Year 41 45 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215
Total 1000 1200 1800 2200
Using the Multiplicative Seasonal Method
Example 13.5: Stanley Steemer, a carpet cleaning company needs a quarterly forecast of the number of customers expected next year. The business is seasonal, with a peak in the third quarter and a trough in the first quarter.
Forecast customer demand for each quarter of year 5, based on an estimate of total year 5 demand of 2,600 customers.
Demand has been increasing by an average of 400 customers each year. The forecast demand is found by extending that trend, and projecting an annual demand in year 5 of 2,200 + 400 = 2,600 customers.
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Example 13.5 OM Explorer Solution
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Application 13.3 Multiplicative Seasonal Method
1320/4 quarters = 330
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Comparison of Seasonal Patterns
Multiplicative pattern Additive pattern
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Measures of Forecast Error
Cumulative sum of forecast errors (CFE): A measurement of the total forecast error that assesses the bias in a forecast.
Mean squared error (MSE): A measurement of the dispersion of forecast errors.
Mean absolute deviation (MAD): A measurement of the dispersion of forecast errors.
Standard deviation (): A measurement of the dispersion of forecast errors.
Et2
nMSE =
MAD =|Et |n
= (Et – E )2
n – 1
CFE = Et
© 2007 Pearson Education
MAPE = [ |Et | / Dt ](100)
n
Measures of Forecast Error
Mean absolute percent error (MAPE): A measurement that relates the forecast error to the level of demand and is useful for putting forecast performance in the proper perspective.
Tracking signal: A measure that indicates whether a method of forecasting is accurately predicting actual changes in demand.
Tracking signal = CFEMAD
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Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)1 200 225 -25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
Calculating Forecast Error Example 13.6
The following table shows the actual sales of upholstered chairs for a furniture manufacturer and the forecasts made for each of the last eight months. Calculate CFE, MSE, MAD, and MAPE for this product.
© 2007 Pearson Education© 2007 Pearson Education
Example 13.6 Forecast Error Measures
CFE = – 15Cumulative forecast error (bias):
E = = – 1.875– 15 8Average forecast error (mean bias):
MSE = = 659.45275
8Mean squared error:
= 27.4Standard deviation:
MAD = = 24.41958
Mean absolute deviation:
MAPE = = 10.2%81.3%8
Mean absolute percent error:
Tracking signal = = = -0.6148 CFEMAD
-1524.4
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% of area of normal probability distribution within control limits of the tracking signal
Control Limit Spread Equivalent Percentage of Area(number of MAD) Number of within Control Limits
57.6276.9889.0495.4498.3699.4899.86
± 0.80± 1.20± 1.60± 2.00± 2.40± 2.80± 3.20
± 1.0± 1.5± 2.0± 2.5± 3.0± 3.5± 4.0
Forecast Error Ranges
Forecasts stated as a single value can be less useful because they do not indicate the range of likely errors. A better approach can be to provide the manager with a forecasted value and an error range.
© 2007 Pearson Education
Tracking signal = CFEMAD
+2.0 —
+1.5 —
+1.0 —
+0.5 —
0 —
–0.5 —
–1.0 —
–1.5 —| | | | |
0 5 10 15 20 25 Observation number
Trac
king
sig
nal
Control limit
Control limitOut of control
Computer Support
Computer support, such as OM Explorer, makes error calculations easy when evaluating how well forecasting models fit with past data.
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OM Solver Output for Medical Clinic Patient Arrivals
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Results SheetMoving Average
Forecast for 7/17/06
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Results SheetWeighted Moving Average
Forecast for 7/17/06
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Results SheetExponential Smoothing
Forecast for 7/17/06
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Results SheetTrend-Adjusted
Exponential Smoothing
Forecast for 7/17/06 Forecast for 7/24/06Forecast for 7/31/06Forecast for 8/7/06Forecast for 8/14/06Forecast for 8/21/06
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Criteria for Selecting Time-Series Methods
Forecast error measures provide important information for choosing the best forecasting method for a service or product.
They also guide managers in selecting the best values for the parameters needed for the method: n for the moving average method, the weights for the weighted
moving average method, and for exponential smoothing. The criteria to use in making forecast method and parameter
choices include 1. minimizing bias2. minimizing MAPE, MAD, or MSE3. meeting managerial expectations of changes in the
components of demand4. minimizing the forecast error last period
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Using Multiple Techniques
Research during the last two decades suggests that combining forecasts from multiple sources often produces more accurate forecasts.
Combination forecasts: Forecasts that are produced by averaging independent forecasts based on different methods or different data or both.
Focus forecasting: A method of forecasting that selects the best forecast from a group of forecasts generated by individual techniques. The forecasts are compared to actual demand, and the
method that produces the forecast with the least error is used to make the forecast for the next period. The method used for each item may change from period to period.
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Forecasting as a Process
The forecast process itself, typically done on a monthly basis, consists of structured steps. They often are facilitated by someone who might be called a demand manager, forecast analyst, or demand/supply planner.
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Some Principles for the Forecasting Process•Better processes yield better forecasts.•Demand forecasting is being done in virtually every company.
The challenge is to do it better than the competition.•Better forecasts result in better customer service and lower
costs, as well as better relationships with suppliers and customers.
•The forecast can and must make sense based on the big picture, economic outlook, market share, and so on.
•The best way to improve forecast accuracy is to focus on reducing forecast error.
•Bias is the worst kind of forecast error; strive for zero bias.•Whenever possible, forecast at higher, aggregate levels.
Forecast in detail only where necessary.•Far more can be gained by people collaborating and
communicating well than by using the most advanced forecasting technique or model.
© 2007 Pearson Education
Denver Air-Quality Discussion Question 1
250 –
225 –
200 –
175 –
150 –
125 –
100 –
75 –
50 –
25 –
0 | | | | | | | | | | | | | |22 25 28 31 3 6 9 12 15 18 21 14 27 30
Year 2
Year 1
July AugustDate
Visi
bilit
y ra
ting