![© McGraw Hill 37
Forecast Error Calculation
LO 3.5
Period
Actual
(A)
Forecast
(F)
(A − F)
Error |Error| Error2 [|Error|/Actual] × 100
1 107 110 −3 3 9 2.80%
2 125 121 4 4 16 3.20%
3 115 112 3 3 9 2.61%
4 118 120 −2 2 4 1.69%
5 108 109 1 1 1 0.93%
Sum 13 39 11.23%
n = 5 n − 1 = 4 n = 5
MAD MSE MAPE
= 2.6 = 9.75 = 2.25%](https://image.slidesharecdn.com/500215757-stevenson-14e-chap003-ppt-accessible-copy-250117024108-23f3a9ae/85/Forecasting-Operating-Management-Stevenson-37-320.jpg)
Forecasting Operating Management Stevenson
- 1. © McGraw Hill 1 Chapter 3 Forecasting Operations Management FOURTEENTH EDITION William J. Stevenson © 2021 McGraw Hill. All rights reserved. Authorized only for instructor use in the
- 2. © McGraw Hill 2 Chapter 3: Learning Objectives You should be able to: LO 3.1 List features common to all forecasts LO 3.2 Explain why forecasts are generally wrong LO 3.3 List the elements of a good forecast LO 3.4 Outline the steps in the forecasting process LO 3.5 Summarize forecast errors and use summaries to make decisions LO 3.6 Describe four qualitative forecasting techniques LO 3.7 Use a naïve method to make a forecast LO 3.8 Prepare a moving average forecast LO 3.9 Prepare a weighted-average forecast LO 3.10 Prepare an exponential smoothing forecast LO 3.11 Prepare a linear trend forecast LO 3.12 Prepare a trend-adjusted exponential smoothing forecast LO 3.13 Compute and use seasonal relatives LO 3.14 Compute and use regression and correlation coefficients LO 3.15 Construct control charts and use them to monitor forecast errors LO 3.16 Describe the key factors and trade-offs to consider when choosing a forecasting technique
- 3. © McGraw Hill 3 Forecast LO 3.1 Forecast – a statement about the future value of a variable of interest We make forecasts about such things as weather, demand, and resource availability Forecasts are important to making informed decisions
- 4. © McGraw Hill 4 Two Important Aspects of Forecasts LO 3.1 Expected level of demand The level of demand may be a function of some structural variation such as trend or seasonal variation Accuracy Related to the potential size of forecast error
- 5. © McGraw Hill 5 Forecasts in Business Organizations LO 3.1 Accounting. New product/process cost estimates, profit projections, cash management. Finance. Equipment/equipment replacement needs, timing and amount of funding/borrowing needs. Human resources. Hiring activities, including recruitment, interviewing, and training; layoff planning, including outplacement counseling. Marketing. Pricing and promotion, e-business strategies, global competition strategies. MIS. New/revised information systems, internet services. Operations. Schedules, capacity planning, work assignments and workloads, inventory planning, make-or-buy decisions, outsourcing, project management. Product/service design. Revision of current features, design of new products or services.
- 6. © McGraw Hill 6 Forecast Uses LO 3.1 Plan the system Generally involves long-range plans related to: • Types of products and services to offer • Facility and equipment levels • Facility location Plan the use of the system Generally involves short- and medium-range plans related to: • Inventory management • Workforce levels • Purchasing • Production • Budgeting • Scheduling
- 7. © McGraw Hill 7 Features Common to All Forecasts LO 3.1 1. Techniques assume some underlying causal system that existed in the past will persist into the future 2. Forecasts are not perfect 3. Forecasts for groups of items are more accurate than those for individual items 4. Forecast accuracy decreases as the forecasting horizon increases
- 8. © McGraw Hill 8 Forecasts Are Not Perfect LO 3.2 Forecasts are not perfect: • Because random variation is always present, there will always be some residual error, even if all other factors have been accounted for.
- 9. © McGraw Hill 9 Elements of a Good Forecast LO 3.3 The forecast • Should be timely • Should be accurate • Should be reliable • Should be expressed in meaningful units • Should be in writing • Technique should be simple to understand and use • Should be cost-effective
- 10. © McGraw Hill 10 Steps in the Forecasting Process LO 3.4 1. Determine the purpose of the forecast 2. Establish a time horizon 3. Obtain, clean, and analyze appropriate data 4. Select a forecasting technique 5. Make the forecast 6. Monitor the forecast errors
- 11. © McGraw Hill 11 Forecasting Approaches LO 3.6 Qualitative forecasting Qualitative techniques permit the inclusion of soft information such as: • Human factors • Personal opinions • Hunches These factors are difficult, or impossible, to quantify Quantitative forecasting These techniques rely on hard data Quantitative techniques involve either the projection of historical data or the development of associative methods that attempt to use causal variables to make a forecast
- 12. © McGraw Hill 12 Qualitative Forecasts LO 3.6 Forecasts that use subjective inputs such as opinions from consumer surveys, sales staff, managers, executives, and experts Executive opinions • A small group of upper-level managers may meet and collectively develop a forecast Salesforce opinions • Members of the sales or customer service staff can be good sources of information due to their direct contact with customers and may be aware of plans customers may be considering for the future Consumer surveys • Since consumers ultimately determine demand, it makes sense to solicit input from them • Consumer surveys typically represent a sample of consumer opinions Other approaches • Managers may solicit opinions from other managers or staff people or outside experts to help with developing a forecast • The Delphi method is an iterative process intended to achieve a consensus
- 13. © McGraw Hill 13 Time-Series Forecasts LO 3.6 Forecasts that project patterns identified in recent time-series observations Time-series – a time-ordered sequence of observations taken at regular time intervals Assume that future values of the time-series can be estimated from past values of the time-series
- 14. © McGraw Hill 14 Time-Series Behaviors LO 3.6 Trend Seasonality Cycles Irregular variations Random variation
- 15. © McGraw Hill 15 Trends and Seasonality LO 3.6 Trend A long-term upward or downward movement in data • Population shifts • Changing income Seasonality Short-term, fairly regular variations related to the calendar or time of day Restaurants, service call centers, and theaters all experience seasonal demand
- 16. © McGraw Hill 16 Cycles and Variations LO 3.6 Cycle Wavelike variations lasting more than one year • These are often related to a variety of economic, political, or even agricultural conditions Irregular variation Due to unusual circumstances that do not reflect typical behavior • Labor strike • Weather event Random Variation Residual variation that remains after all other behaviors have been accounted for
- 17. © McGraw Hill 17 Time-Series Forecasting - Naïve Forecast LO 3.7 Naïve forecast Uses a single previous value of a time series as the basis for a forecast • The forecast for a time period is equal to the previous time period’s value Can be used with • A stable time series • Seasonal variations • Trend
- 18. © McGraw Hill 18 Time-Series Forecasting - Averaging LO 3.7 These techniques work best when a series tends to vary about an average Averaging techniques smooth variations in the data They can handle step changes or gradual changes in the level of a series Techniques 1. Moving average 2. Weighted moving average 3. Exponential smoothing
- 19. © McGraw Hill 19 Moving Average 1 LO 3.8 Technique that averages a number of the most recent actual values in generating a forecast where 1 2 1 MA n t i i t n t t t n A A A A F n n − = − − − + + + = = = Forecast for time period MA period moving average Actual value in period Number of periods in the moving average t n t i F t n A t i n − = = = − =
- 20. © McGraw Hill 20 Moving Average 2 LO 3.7 As new data become available, the forecast is updated by adding the newest value and dropping the oldest and then recomputing the average The number of data points included in the average determines the model’s sensitivity Fewer data points used—more responsive More data points used—less responsive
- 21. © McGraw Hill 21 Weighted Moving Average LO 3.9 The most recent values in a time series are given more weight in computing a forecast The choice of weights, w, is somewhat arbitrary and involves some trial and error where 1 1 ( ) ( ) ( ) t t t t t t n t n F w A w A w A − − − − = + + + 1 1 weight for period , weight for period 1, etc. the actual value for period , the actual value for period 1, etc. t t t t w t w t A t A t − − = = − = = −
- 22. © McGraw Hill 22 Exponential Smoothing LO 3.10 A weighted averaging method that is based on the previous forecast plus a percentage of the forecast error where 1 1 1 ( ) t t t t F F A F − − − = + − 1 1 Forecast for period Forecast for the previous period Smoothing constant Actual demand or sales for the previous period t t t F t F A − − = = = =
- 23. © McGraw Hill 23 Linear Trend LO 3.11 A simple data plot can reveal the existence and nature of a trend Linear trend equation where t F a bt = + Forecast for period Value of at 0 Slope of the line Specified number of time periods from 0 t t F t a F t b t t = = = = = =
- 24. © McGraw Hill 24 Estimating Slope and Intercept LO 3.11 Slope and intercept can be estimated from historical data where ( ) 2 2 or n ty t y b n t t y b t a y bt n − = − − = − Number of periods Value of the time series n y = =
- 25. © McGraw Hill 25 Trend-Adjusted Exponential Smoothing1 LO 3.12 The trend adjusted forecast consists of two components Smoothed error Trend factor where 1 TAFt t t S T + = + Previous forecast plus smoothed error Current trend estimate t t S T = =
- 26. © McGraw Hill 26 Trend-Adjusted Exponential Smoothing2 LO 3.12 Alpha and beta are smoothing constants Trend-adjusted exponential smoothing has the ability to respond to changes in trend 1 1 1 1 TAF TAF ( TAF ) (TAF TAF ) t t t t t t t t t t t t S T S A T T T + − − − = + = + − = + − −
- 27. © McGraw Hill 27 Techniques for Seasonality LO 3.12 Seasonality – regularly repeating movements in series values that can be tied to recurring events Expressed in terms of the amount that actual values deviate from the average value of a series Models of seasonality • Additive • Seasonality is expressed as a quantity that gets added to or subtracted from the time-series average in order to incorporate seasonality • Multiplicative • Seasonality is expressed as a percentage of the average (or trend) amount which is then used to multiply the value of a series in order to incorporate seasonality
- 28. © McGraw Hill 28 Seasonal Relatives LO 3.13 Seasonal relatives The seasonal percentage used in the multiplicative seasonally adjusted forecasting model Using seasonal relatives To deseasonalize data • Done in order to get a clearer picture of the nonseasonal (for example, trend) components of the data series • Divide each data point by its seasonal relative To incorporate seasonality in a forecast 1. Obtain trend estimates for desired periods using a trend equation 2. Add seasonality by multiplying these trend estimates by the corresponding seasonal relative
- 29. © McGraw Hill 29 Associative Forecasting Techniques LO 3.14 Associative techniques are based on the development of an equation that summarizes the effects of predictor variables Predictor variables – variables that can be used to predict values of the variable of interest • Home values may be related to such factors as home and property size, location, number of bedrooms, and number of bathrooms
- 30. © McGraw Hill 30 Simple Linear Regression LO 3.14 Regression – a technique for fitting a line to a set of data points Simple linear regression – the simplest form of regression that involves a linear relationship between two variables • The object of simple linear regression is to obtain an equation of a straight line that minimizes the sum of squared vertical deviations from the line (that is, the least squares criterion)
- 31. © McGraw Hill 31 Least Squares Line LO 3.14 where and where e y a bx = + = Predicted (dependent) variable = Predictor (independent) variable = Slope of the line = Value of when 0 (that is, the height of the line at the intercept) c c y x b a y x y = ( ) ( )( ) ( ) ( ) 2 2 or n xy x y b n x x y b x a y bx n − = − − = − Number of paired observations n =
- 32. © McGraw Hill 32 Correlation Coefficient LO 3.14 Correlation, r A measure of the strength and direction of relationship between two variables Ranges between −1.00 and +1.00 r2, square of the correlation coefficient A measure of the percentage of variability in the values of y that is “explained” by the independent variable Ranges between 0 and 1.00 ( ) ( )( ) ( ) ( ) ( ) ( ) 2 2 2 2 n xy x y r n x x n y y − = − −
- 33. © McGraw Hill 33 Simple Linear Regression Assumptions LO 3.14 1. Variations around the line are random 2. Deviations around the average value (the line) should be normally distributed 3. Predictions are made only within the range of observed values
- 34. © McGraw Hill 34 Issues to Consider: LO 3.14 Always plot the line to verify that a linear relationship is appropriate The data may be time-dependent If they are • use analysis of time series • use time as an independent variable in a multiple regression analysis A small correlation may indicate that other variables are important
- 35. © McGraw Hill 35 Forecast Accuracy and Control LO 3.5 Allowances should be made for forecast errors It is important to provide an indication of the extent to which the forecast might deviate from the value of the variable that actually occurs Forecast errors should be monitored Error = Actual − Forecast If errors fall beyond acceptable bounds, corrective action may be necessary
- 36. © McGraw Hill 36 Forecast Accuracy Metrics LO 3.5 MAD weights all errors evenly MSE weights errors according to their squared values MAPE weights errors according to relative error t t Actual Forecast MAD n − = ( ) 2 t t Actual Forecast MSE 1 n − = − t t t Actual Forecast 100 Actual MAPE n − =
- 37. © McGraw Hill 37 Forecast Error Calculation LO 3.5 Period Actual (A) Forecast (F) (A − F) Error |Error| Error2 [|Error|/Actual] × 100 1 107 110 −3 3 9 2.80% 2 125 121 4 4 16 3.20% 3 115 112 3 3 9 2.61% 4 118 120 −2 2 4 1.69% 5 108 109 1 1 1 0.93% Sum 13 39 11.23% n = 5 n − 1 = 4 n = 5 MAD MSE MAPE = 2.6 = 9.75 = 2.25%
- 38. © McGraw Hill 38 Monitoring the Forecast LO 3.15 Tracking forecast errors and analyzing them can provide useful insight into whether forecasts are performing satisfactorily Sources of forecast errors: The model may be inadequate due to a. omission of an important variable b. a change or shift in the variable the model cannot handle c. the appearance of a new variable Irregular variations may have occurred Random variation Control charts are useful for identifying the presence of non- random error in forecasts Tracking signals can be used to detect forecast bias
- 39. © McGraw Hill 39 Control Chart Construction LO 3.15 1. Compute the MSE. 2. Estimate of standard deviation of the distribution of errors where z = Number of standard deviations from the mean Access the text alternative for slide images. MSE s = 3. UCL: 0 MSE 4. LCL: 0 MSE z z + −
- 40. © McGraw Hill 40 Choosing a Forecasting Technique LO 3.16 Factors to consider Cost Accuracy Availability of historical data Availability of forecasting software Time needed to gather and analyze data and prepare a forecast Forecast horizon
- 41. © McGraw Hill 41 Operations Strategy LO 3.16 The better forecasts are, the more able organizations will be to take advantage of future opportunities and reduce potential risks A worthwhile strategy is to work to improve short-term forecasts • Accurate up-to-date information can have a significant effect on forecast accuracy: • Prices • Demand • Other important variables Reduce the time horizon forecasts have to cover Sharing forecasts or demand data through the supply chain can improve forecast quality
- 42. Because learning changes everything.® www.mheducation.com © 2021 McGraw Hill. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw Hill.