1. Forecasting Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

2. 3-2 You should be able to: LO 3.1List features common to all forecasts LO 3.2Explain why forecasts are generally wrong LO 3.3List elements of a good forecast LO 3.4Outline the steps in the forecasting process LO 3.5Summarize forecast errors and use summaries to make decisions LO 3.6Describe four qualitative forecasting techniques LO 3.7Use a naïve method to make a forecast LO 3.8Prepare a moving average forecast LO 3.9Prepare a weighted-average forecast LO 3.10Prepare an exponential smoothing forecast LO 3.11Prepare a linear trend forecast LO 3.12Prepare a trend-adjusted exponential smoothing forecast LO 3.13Compute and use seasonal relatives LO 3.14Compute and use regression and correlation coefficients LO 3.15Construct control charts and use them to monitor forecast errors LO 3.16Describe the key factors and trade-offs to consider when choosing a forecasting technique

3. 3-3 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. 3-4 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. 3-5 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

6. 3-6 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 LO 3.1

7. 3-7 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. LO 3.2

8. 3-8 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 LO 3.3

9. 3-9 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 LO 3.4

10. 3-10 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 LO 3.5

11. 3-11 MAD weights all errors evenly MSE weights errors according to their squared values MAPE weights errors according to relative error LO 3.5

12. 3-12 Period Actual (A) Forecast (F) (A-F) Error |Error|Error 2 [|Error|/Actual]x100 1107110-3392.80% 212512144163.20% 31151123392.61% 4118120-2241.69% 51081091110.93% Sum133911.23% n = 5n-1 = 4n = 5 MADMSEMAPE = 2.6= 9.75= 2.25% LO 3.5

13. 3-13 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 LO 3.6

14. 3-14 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 Sales force 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 0pinions 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 LO 3.6

15. 3-15 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

16. 3-16 Trend Seasonality Cycles Irregular variations Random variation

17. 3-17 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

18. 3-18 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

19. 3-19 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 LO 3.7

20. 3-20 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 LO 3.8

21. 3-21 Technique that averages a number of the most recent actual values in generating a forecast LO 3.8

22. 3-22 As new data become available, the forecast is updated by adding the newest value and dropping the oldest and then re-computing 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 LO 3.8

23. 3-23 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 LO 3.9

24. 3-24 A weighted averaging method that is based on the previous forecast plus a percentage of the forecast error LO 3.10

25. 3-25 Moving Average CCC wishes to forecast the number of incoming calls it receives in a day from the customers of one of its clients, BMI. CCC schedules the appropriate number of telephone operators based on projected call volumes. CCC believes that the most recent 12 days of call volumes (shown on the next slide) are representative of the near future call volumes.

26. 3-26 Moving Average Representative Historical Data DayCallsDayCalls 11597203 22178195 31869188 416110168 517311198 615712159

27. 3-27 Moving Average Use the moving average method with an AP = 3 days to develop a forecast of the call volume in Day 13. F 13 = (168 + 198 + 159)/3 = 175.0 calls

28. 3-28 Weighted Moving Average Use the weighted moving average method with an AP = 3 days and weights of.1 (for oldest datum),.3, and.6 to develop a forecast of the call volume in Day 13. F 13 =.1(168) +.3(198) +.6(159) = 171.6 calls Note: The WMA forecast is lower than the MA forecast because Day 13’s relatively low call volume carries almost twice as much weight in the WMA (.60) as it does in the MA (.33).

29. 3-29 Example: Central Call Center l Exponential Smoothing If a smoothing constant value of.25 is used and the exponential smoothing forecast for Day 11 was 180.76 calls, what is the exponential smoothing forecast for Day 13? F 12 = 180.76 +.25(198 – 180.76) = 185.07 F 13 = 185.07 +.25(159 – 185.07) = 178.55

30. 3-30 Forecast Accuracy - MAD Which forecasting method (the AP = 3 moving average or the  =.25 exponential smoothing) is preferred, based on the MAD over the most recent 9 days? (Assume that the exponential smoothing forecast for Day 3 is the same as the actual call volume.)

31. 3-31 AP = 3  =.25 DayCallsForec.|Error|Forec.|Error| 4161187.326.3186.025.0 5173188.015.0179.86.8 6157173.316.3178.121.1 7203163.739.3172.830.2 8195177.717.3180.414.6 9188185.03.0184.04.0 10168195.327.3185.017.0 11198183.714.3180.817.2 12159184.725.7185.126.1 MAD20.518.0

32. 3-32 A simple data plot can reveal the existence and nature of a trend Linear trend equation LO 3.11

33. 3-33 Slope and intercept can be estimated from historical data LO 3.11

34. 3-34 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 LO 3.13

35. 3-35 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 (e.g., 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 LO 3.13

36. 3-36 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 LO 3.14

37. 3-37 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 (i.e., the least squares criterion) LO 3.14

38. 3-38 LO 3.14

39. 3-39 Correlation, r A measure of the strength and direction of relationship between two variables Ranges between -1.00 and +1.00 r 2, 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 LO 3.14

40. 3-40 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 LO 3.14

41. 3-41 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 LO 3.14

42. 3-42 Select a representative historical data set. Develop a seasonal index for each season. Use the seasonal indexes to deseasonalize the data. Perform lin. regr. analysis on the deseasonalized data. Use the regression equation to compute the forecasts. Use the seas. indexes to reapply the seasonal patterns to the forecasts.

43. 3-43 Seasonalized Times Series Regression Analysis An analyst at CPC wants to develop next year’s quarterly forecasts of sales revenue for CPC’s line of Epsilon Computers. She believes that the most recent 8 quarters of sales (shown on the next slide) are representative of next year’s sales.

44. 3-44 Seasonalized Times Series Regression Analysis Representative Historical Data Set YearQtr.($mil.)YearQtr.($mil.) 117.4218.3 126.5227.4 134.9235.4 1416.12418.0

45. 3-45 Seasonalized Times Series Regression Analysis Compute the Seasonal Indexes Quarterly Sales YearQ1Q2Q3Q4Total 17.46.54.916.134.9 28.37.45.418.039.1 Totals15.713.910.334.174.0 Qtr. Avg.7.856.955.1517.059.25 Seas.Ind..849.751.5571.8434.000

46. 3-46 Seasonalized Times Series Regression Analysis Deseasonalize the Data Quarterly Sales YearQ1Q2Q3Q4 18.728.668.808.74 29.789.859.699.77

47. 3-47 Seasonalized Times Series Regression Analysis Perform Regression on Deseasonalized Data Yr.Qtr.xyx 2 xy 1118.7218.72 1228.66417.32 1338.80926.40 1448.741634.96 2159.782548.90 2269.853659.10 2379.694967.83 2489.776478.16 Totals3674.01204341.39

48. 3-48 Seasonalized Times Series Regression Analysis Perform Regression on Deseasonalized Data Y = 8.357 + 0.199X

49. 3-49 Seasonalized Times Series Regression Analysis Compute the Deseasonalized Forecasts Y 9 = 8.357 + 0.199(9) = 10.148 Y 10 = 8.357 + 0.199(10) = 10.347 Y 11 = 8.357 + 0.199(11) = 10.546 Y 12 = 8.357 + 0.199(12) = 10.745 Note: Average sales are expected to increase by.199 million (about $200,000) per quarter.

50. 3-50 Seasonalized Times Series Regression Analysis Seasonalize the Forecasts Seas.Deseas.Seas. Yr.Qtr.IndexForecastForecast 31.84910.1488.62 32.75110.3477.77 33.55710.5465.87 341.84310.74519.80

51. 3-51 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 LO 3.15

52. 3-52 LO 3.15

53. 3-53 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 LO 3.16

54. 3-54 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