1. Chapter 5 Forecasting

2. Eight Steps to Forecasting 1. Determine the use of the forecast—what objective are we trying to obtain? 2. Select the items or quantities that are to be forecasted. 3. Determine the time horizon of the forecast—is it 1 to 30 days (short term), 1 month to 1 year (medium term), or more than 1 year (long term)? 4. Select the forecasting model or models. 5. Gather the data or information needed to make the forecast. 6. Validate the forecasting model. 7. Make the forecast. 8. Implement the results. Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-2 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

3. Types of Forecasts To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-3 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

4. Time-Series Models Time-series models attempt to predict the future by using historical data. In other words, time-series models look at what has happened over a period of time and use a series of past data to make a forecast. The time-series models we examine in this chapter are Moving average Exponential smoothing, Trend projections, and Decomposition. Regression analysis can be used in trend projections and is one type of decomposition model. The primary emphasis of this chapter is time series forecasting. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-4 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

5. Causal Models Causal models incorporate the variables or factors that might influence the quantity being forecasted into the forecasting model. For example, daily sales of a cola drink might depend on the season, the average temperature, the average humidity, whether it is a weekend or a weekday, and so on. Causal models may also include past sales data as time-series models do, but they include other factors as well. These include Linear regression analysis Multiple regression analysis To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-5 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

6. Qualitative Models Qualitative models attempt to incorporate judgmental or subjective factors into the forecasting model. Opinions by experts, individual experiences and judgments, and other subjective factors may be considered. Qualitative models are especially useful when subjective factors are expected to be very important or when accurate quantitative data are difficult to obtain. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-6 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

7. Delphi method. This iterative group process allows experts, who may be located in different places, to make forecasts. There are three different types of participants in the Delphi process: decision makers, staff personnel, and respondents. The decision making group usually consists of 5 to 10 experts who will be making the actual forecast. The staff personnel assist the decision makers by preparing, distributing, collecting, and summarizing a series of questionnaires and survey results. The respondents are a group of people whose judgments are valued and are being sought. This group provides inputs to the decision makers before the forecast is made. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-7 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

8. Jury of executive opinion This method takes the opinions of a small group of high-level managers, often in combination with statistical models, and results in a group estimate of demand. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-8 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

9. Sales force composite In this approach, each salesperson estimates what sales will be in his or her region; these forecasts are reviewed to ensure that they are realistic and are then combined at the district and national levels to reach an overall forecast. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-9 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

10. Consumer market survey This method solicits input from customers or potential customers regarding their future purchasing plans. It can help not only in preparing a forecast but also in improving product design and planning for new products. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-10 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

11. Scatter Diagrams and Time Series A scatter diagram helps to obtain ideas about a relationship. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-11 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

12. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-12 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

13. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-13 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

14. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-14 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

15. Measures of Forecast Accuracy To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-15 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Forecast error = Actual value - Forecast value This is computed by taking the sum of the absolute values of the individual forecast errors and dividing by the numbers of errors (n): Mean Absolute Deviation (MAD).

16. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-16 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

17. Mean Squared Error (MSE), It is the average of the squared errors To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-17 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

18. Mean Absolute Percent Error (MAPE) The MAPE is the average of the absolute values of the errors expressed as percentages of the actual values. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-18 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

19. Components of a Time Series 1. Trend (T) is the gradual upward or downward movement of the data over time. 2. Seasonality (S) is a pattern of the demand fluctuation above or below the trend line that repeats at regular intervals. 3. Cycles (C) are patterns in annual data that occur every several years. They are usually tied into the business cycle. 4. Random variations (R) are “blips” in the data caused by chance and unusual situations; they follow no discernible pattern. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-19 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

20. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-20 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

21. Moving Averages To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-21 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

22. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-22 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

23. WEIGHTED MOVING AVERAGE To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-23 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

24. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-24 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

25. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-25 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

26. Exponential Smoothing Exponential smoothing is a type of moving average technique, which involves little record keeping of past data. The exponential smoothing approach has been applied successfully by banks, manufacturing companies, wholesalers, and other organizations. The exponential smoothing formula is as follow: To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-26 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

27. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-27 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

28. Example In January, a demand for 142 of a certain car model for February was predicted by a dealer. Actual February demand was 153 autos. Using a smoothing constant of we can forecast the March demand using the exponential smoothing model. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-28 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

29. SELECTING THE SMOOTHING CONSTANT The appropriate value of the smoothing constant can make the difference between an accurate forecast and an inaccurate forecast. In picking a value for the smoothing constant, the objective is to obtain the most accurate forecast. Several values of the smoothing constant may be tried, and the one with the lowest MAD could be selected. This is analogous to how weights are selected for a weighted moving average forecast. Some forecasting software automatically select the best smoothing constant. QM for Windows displays the MAD that obtains values of ranging from 0 to 1 in increments of 0.01. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-29 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

30. Example To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-30 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

31. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-31 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

32. EXPONENTIAL SMOOTHING WITH TREND ADJUSTMENT The averaging or smoothing forecasting techniques are useful when a time series has random component, but these techniques are not suitable to respond trends. The idea is to develop an exponential smoothing forecast and then adjust this for trend. Two smoothing constants, and are used in this model, and both of these values must be between 0 and 1. The level of the forecast is adjusted by multiplying the first smoothing constant, by the most recent forecast error and adding it to the previous forecast. The trend is adjusted by multiplying the second smoothing constant, by the most recent error or excess amount in the trend. A higher value gives more weight to recent observations and thus responds more quickly to changes in the patterns. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-32 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

33. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-33 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

34. Example: Midwestern Manufacturing’s Demand To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-34 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

35. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-35 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

36. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-36 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

37. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-37 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

38. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-38 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Trend Projection Trend projections are used to forecast time-series data that exhibit a linear trend.  Least squares may be used to determine a trend projection for future forecasts.  Least squares determines the trend line forecast by minimizing the mean squared error between the trend line forecasts and the actual observed values.  The independent variable is the time period and the dependent variable is the actual observed value in the time series.

39. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-39 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Trend Projection (continued) The formula for the trend projection is: Y = b + b X where: Y = predicted value b1 = slope of the trend line b0 = intercept X = time period (1,2,3…n) 0 1

40. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-40 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Midwestern Manufacturing Trend Projection Example Midwestern Manufacturing Company’s demand for electrical generators over the period of 2004 – 2010 is given below.

41. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-41 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

42. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-42 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Midwestern Manufacturing Company Trend Solution Sales = 56.71 + 10.54 (time)

43. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-43 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Midwestern Manufacturing’s Trend

44. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-44 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Seasonal Variations Seasonal indices can be used to make adjustments in the forecast for seasonality.  A seasonal index indicates how a particular season compares with an average season.  The seasonal index can be found by dividing the average value for a particular season by the average of all the data.

45. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-45 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

46. Now suppose we expected the third year’s annual demand for answering machines to be 1,200 units, which is 100 per month. We would not forecast each month to have a demand of 100, but we would adjust these based on the seasonal indices as follows: To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-46 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

47. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-47 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

48. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-48 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Eichler Supplies: Seasonal Index Example MonthSales Demand Average Two-Year Demand Average Monthly Demand Seasonal Index Year 1 Year 2 80100 90940.957 758580940.851 809085940.904 90110100941.064 Jan Feb Mar Apr May115131123941.309 … …………… Total Average Demand 1,128 Seasonal Index: = Average 2 -year demand/Average monthly demand

49. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-49 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Seasonal Variations with Trend Steps of Multiplicative Time-Series Model 1. Compute the CMA for each observation. 2.Compute seasonal ratio (observation/CMA). 3. Average seasonal ratios to get seasonal indices. 4. If seasonal indices do not add to the number of seasons, multiply each index by (number of seasons)/(sum of the indices). Centered Moving Average (CMA) is an approach that prevents a variation due to trend from being incorrectly interpreted as a variation due to the season.

50. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-50 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

51. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-51 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Turner IndustriesSeasonal Variations with Trend Turner Industries Seasonal Variations with Trend Turner Industries’ sales figures are shown below with the CMA and seasonal ratio. CMA (qtr 3 / yr 1 ) =.5(108) + 125 + 150 + 141+.5(116) 4 Seasonal Ratio = Sales Qtr 3 = 150 CMA 132

52. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-52 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

53. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-53 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decomposition Method with Trend and Seasonal Components Decomposition is the process of isolating linear trend and seasonal factors to develop more accurate forecasts. There are five steps to decomposition: 1.Compute the seasonal index for each season. 2.Deseasonalize the data by dividing each number by its seasonal index. 3.Compute a trend line with the deseasonalized data. 4.Use the trend line to forecast. 5.Multiply the forecasts by the seasonal index.

54. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-54 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Turner Industries: Decomposition Method Turner Industries has noticed a trend in quarterly sales figures. There is also a seasonal component. Below is the seasonal index and deseasonalized sales data. * This value is derived by averaging the season rations for each quarter. Refer to slide 5-37. Seasonal Index for Qtr 1 = 0.851+0.848 = 0.85 2 108 0.85 =

55. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-55 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Turner Industries: Decomposition Method Using the deseasonalized data, the following trend line was computed: Sales = 124.78 + 2.34X

56. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-56 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Turner Industries: Decomposition Method Using the trend line, the following forecast was computed: Sales = 124.78 + 2.34X For period 13 (quarter 1/ year 4): Sales = 124.78 + 2.34 (13) = 155.2 (before seasonality adjustment) After seasonality adjustment: Sales = 155.2 (0.85) = 131.92 Seasonal index for quarter 1

57. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-57 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decomposition of Time-Series: Two Models Additive model assumes demand is the summation of the four components. The underlying level of the series fluctuates but the magnitude of the seasonal spikes remains approximately stable Tool: Regression demand = T + S + C + R

58. Decomposition of Time-Series: Two Models Multiplicative model assumes demand is the product of the four components. As the underlying level of the series changes, the magnitude of the seasonal fluctuations varies as well. Tool: Decomposition demand = T * S * C * R

59. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-59 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Multiple Regression with Trend and Seasonal Components Multiple regression can be used to develop an additive decomposition model. One independent variable is time.  Seasons are represented by dummy independent variables. Y = a + b X + b X + b X + b X Where X = time period X = 1 if quarter 2 = 0 otherwise X = 1 if quarter 3 = 0 otherwise X = 1 if quarter 4 = 0 otherwise 1 1 2 2 3 3 4 4 12341234

60. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-60 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Monitoring and Controlling Forecasts Tracking signals measure how well predictions fit actual data. + 2 MADs are the control Limits or 89% Errors 1 MAD is 0.8 St dev.

61. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-61 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Monitoring and Controlling Forecasts