1. © 2007 Pearson Education Forecasting Chapter 13

2. © 2007 Pearson Education 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

3. © 2007 Pearson Education 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.

4. © 2007 Pearson Education Choosing the Type of Forecasting 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.

5. © 2007 Pearson Education Demand Forecast Applications Causal Judgment Causal Judgment Time series Causal Judgment Forecasting Technique 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 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) Application Time Horizon

6. © 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.

7. © 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.

8. © 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. E t = D t - F t where E t = forecast error for period t D t = actual demand for period t F t = forecast for period t

9. © 2007 Pearson Education 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. Et2nEt2n MSE = MAD =  |E t | n CFE =  Et

10. © 2007 Pearson Education MAPE =  [ |E t | / 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.

11. © 2007 Pearson Education Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) 1200225-25 625 2512.5% 224022020 400 208.3 330028515 225 155.0 4270290–20 400 207.4 5230250–20 400 208.7 626024020 400 207.7 7210250–40 1600 4019.0 827524035 1225 3512.7 Total–15 5275 19581.3% 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.

12. © 2007 Pearson Education Example 13.6 Forecast Error Measures CFE = – 15 Cumulative forecast error (bias): E = = – 1.875 – 15 8 Average forecast error (mean bias): MSE = = 659.4 5275 8 Mean squared error:  = 27.4 Standard deviation: MAD = = 24.4 195 8 Mean absolute deviation: MAPE = = 10.2% 81.3% 8 Mean absolute percent error: Tracking signal = = = -0.6148 CFE MAD -15 24.4

13. © 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.

14. © 2007 Pearson Education Dependent variable Independent variable X Y Estimate of Y from regression equation Actual value of Y Value of X used to estimate Y Deviation, or error { Causal Methods Linear Regression Regression equation: Y = a + bX Y = dependent variable X = independent variable a = Y-intercept of the line b = slope of the line

15. © 2007 Pearson Education SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 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

16. © 2007 Pearson Education SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 a = Y – b X b =b =b =b =  XY – n XY  X 2 – n X 2 Example 13.1 Regression equation for forecast = Y = a + bx, where Causal Methods Linear Regression Example 13.1 Causal Methods Linear Regression

17. © 2007 Pearson Education Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 Example 13.1 a = Y – b X b =b =b =b =  XY – n XY  X 2 – n X 2 Causal Methods Linear Regression Example 13.1 Causal Methods Linear Regression

18. © 2007 Pearson Education a = Y – b X b =b =b =b = 1560.8 – 5(1.64)(171) 14.90 – 5(1.64) 2 Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 Example 13.1 Causal Methods Linear Regression Example 13.1 Causal Methods Linear Regression

19. © 2007 Pearson Education a = Y – b X b = 109.229 Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 Example 13.1 Causal Methods Linear Regression Example 13.1 Causal Methods Linear Regression

20. © 2007 Pearson Education a = 171 – 109.229(1.64) b = 109.229 Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 Example 13.1 Causal Methods Linear Regression Example 13.1 Causal Methods Linear Regression

21. © 2007 Pearson Education a = – 8.136 b = 109.229 Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 Y = – 8.136 + 109.229(X) Example 13.1 Causal Methods Linear Regression Example 13.1 Causal Methods Linear Regression

22. © 2007 Pearson Education a = - 8.136 b = 109.229 Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 Y = – 8.136 + 109.229(X) Sales (thousands of units) |||| 1.01.52.02.5 Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Figure 13.3 Causal Methods Linear Regression Example 13.1 Causal Methods Linear Regression

23. © 2007 Pearson Education Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 n  XY –  X  Y [ n  X 2 – (  X) 2 ][ n  Y 2 – (  Y) 2 ] r =r =r =r = Example 13.1 Causal Methods Linear Regression Example 13.1 Causal Methods Linear Regression

24. © 2007 Pearson Education Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 r = 0.98 r 2 = 0.96 Example 13.1 Causal Methods Linear Regression Example 13.1 Causal Methods Linear Regression

25. © 2007 Pearson Education Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 r = 0.98 r 2 = 0.96 Forecast for Month 6: Advertising expenditure = $1750 Y = - 8.136 + 109.229(1.75) Y = - 8.136 + 109.229(1.75) Example 13.1 Causal Methods Linear Regression Example 13.1 Causal Methods Linear Regression

26. © 2007 Pearson Education Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 r = 0.98 r 2 = 0.96 Forecast for Month 6: Advertising expenditure = $1750 Y = 183.015 or 183,015 hinges Y = 183.015 or 183,015 hinges Example 13.1 Causal Methods Linear Regression Example 13.1 Causal Methods Linear Regression

27. © 2007 Pearson Education Components of a Time Series  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.Trend. The systematic increase or decrease in the mean of the series over time. b.Seasonal. A repeatable pattern of increases or decreases in demand, depending on the time of day, week, month, or season. c.Cyclical. The less predictable gradual increases or decreases over longer periods of time (years or decades). d.Random. The unforecastable variation in demand.

28. © 2007 Pearson Education Demand Patterns HorizontalTrend SeasonalCyclical

29. © 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 = D t  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. …

30. © 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: Patient WeekArrivals 1400 2380 3411 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?

31. © 2007 Pearson Education Week 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — |||||| 051015202530 Patient arrivals Actual patient arrivals Example 13.2 Solution 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.

32. © 2007 Pearson Education WeekArrivalsAverage 1400 2380 3411397 4415402 5? 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 =F4 =F4 =F4 = 411 + 380 + 400 3 a. c. b.

33. © 2007 Pearson Education Comparison of 3- and 6-Week MA Forecasts Week Patient Arrivals Actual patient arrivals 3-week moving average forecast 6-week moving average forecast

34. © 2007 Pearson Education Application 13.1  We will use the following customer-arrival data in this moving average application:

35. © 2007 Pearson Education Application 13.1a Moving Average Method 780 customer arrivals 802 customer arrivals

36. © 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. F t+1 = W 1 D t + W 2 D t-1 + …+ W n D t-n+1

37. © 2007 Pearson Education Application 13.1b Weighted Moving Average 786 customer arrivals 802 customer arrivals

38. © 2007 Pearson Education Exponential Smoothing  F t+1 =  (Demand this period) + (1 –  )(Forecast calculated last period)  =  D t + (1–  )F t  Or an equivalent equation: F t+1 = F t +  (D t – F t )  is a smoothing parameter with a value between 0 and 1.0 Where alpha (  is a smoothing parameter with a value between 0 and 1.0 Exponential 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.

39. © 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. F t+1 =  D t + (1-  )F t F 4 = 0.10(411) + 0.90(390) = 392.1 b. What is the forecast error for week 4 if the actual demand turned out to be 415? E 4 = 415 - 392 = 23 c. What is the forecast for week 5? F 5 = 0.10(415) + 0.90(392.1) = 394.4 Exponential Smoothing Example 13.3 WeekArrivals 1400 2380 3411 4415 5?

40. © 2007 Pearson Education Application 13.1c Exponential Smoothing 784 customer arrivals 789 customer arrivals

41. © 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.

42. © 2007 Pearson Education F t+1 = A t +T t where A t =  D t + (1 –  )(A t-1 + T t-1 ) T t =  (A t – A t-1 ) + (1 –  )T t-1 A t = exponentially smoothed average of the series in period t T t = exponentially smoothed average of the trend in period t  = smoothing parameter for the average  = smoothing parameter for the trend D t = demand for period t F t+1 = forecast for period t + 1 Trend-Adjusted Exponential Smoothing Formula

43. © 2007 Pearson Education A 0 = 28 patients and T t = 3 patients A t =  D t + (1 –  )(A t-1 + T t-1 ) A 1 = 0.20(27) + 0.80(28 + 3) = 30.2 T t =  (A t – A t-1 ) + (1 –  )T t-1 T 1 = 0.20(30.2 – 2.8) + 0.80(3) = 2.8 F t+1 = A t + T t F 2 = 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.

44. © 2007 Pearson Education ||||||||||||||| 0123456789101112131415 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 30 — Patient arrivals Week Actual blood test requests Trend-adjusted forecast Example 13.4 Medanalysis Trend-Adjusted Exponential Smoothing

45. © 2007 Pearson Education Forecast for Medanalysis Using the Trend-Adjusted Exponential Smoothing Model

46. © 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?

47. © 2007 Pearson Education Application 13.2 Solution 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

48. © 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.

49. © 2007 Pearson Education 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.

50. © 2007 Pearson Education QuarterYear 1Year 2Year 3Year 4 14570100100 2335370585725 35205908301160 4100170285215 Total1000120018002200 Total1000120018002200 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.

51. © 2007 Pearson Education Example 13.5 OM Explorer Solution

52. © 2007 Pearson Education Application 13.3 Multiplicative Seasonal Method 1320/4 quarters = 330

53. © 2007 Pearson Education Comparison of Seasonal Patterns Multiplicative patternAdditive pattern

54. © 2007 Pearson Education Tracking Signal Tracking signal: A measure that indicates whether a method of forecasting is accurately predicting actual changes in demand. Tracking signal = CFE t MAD t

55. © 2007 Pearson Education % of area of normal probability distribution within control limits of the tracking signal Control Limit SpreadEquivalentPercentage of Area (number of MAD)Number of  within Control Limits 57.62 76.98 89.04 95.44 98.36 99.48 99.86 ± 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.

56. © 2007 Pearson Education Tracking signal = CFEMAD +2.0 +2.0 — +1.5 +1.5 — +1.0 +1.0 — +0.5 +0.5 — 0 0 — –0.5 –0.5 — –1.0 –1.0 — –1.5 –1.5 — ||||| 0510152025 Observation number Observation number Tracking signal Control limit Out of control Computer Support Computer support, such as OM Explorer, makes error calculations easy when evaluating how well forecasting models fit with past data.

57. © 2007 Pearson Education Results Sheet Moving Average Forecast for 7/17/06

58. © 2007 Pearson Education Results Sheet Weighted Moving Average Forecast for 7/17/06

59. © 2007 Pearson Education Results Sheet Exponential Smoothing Forecast for 7/17/06

60. © 2007 Pearson Education Results Sheet Trend-Adjusted Exponential Smoothing Forecast for 7/17/06 Forecast for 7/24/06 Forecast for 7/31/06 Forecast for 8/7/06 Forecast for 8/14/06 Forecast for 8/21/06

61. © 2007 Pearson Education 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 bias 2.minimizing MAPE, MAD, or MSE 3.meeting managerial expectations of changes in the components of demand 4.minimizing the forecast error last period

62. © 2007 Pearson Education Using Multiple Techniques RResearch during the last two decades suggests that combining forecasts from multiple sources often produces more accurate forecasts. CCombination forecasts: Forecasts that are produced by averaging independent forecasts based on different methods or different data or both. FFocus forecasting: A method of forecasting that selects the best forecast from a group of forecasts generated by individual techniques. T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.

63. © 2007 Pearson Education 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.

64. © 2007 Pearson Education Denver Air-Quality Discussion Question 1 250 250 – 225 225 – 200 200 – 175 175 – 150 150 – 125 125 – 100 100 – 75 75 – 50 50 – 25 25 –0 |||||||||||||| 2225283136912151821142730 Year 2 Year 1 JulyAugust Date Visibility rating