1. 13 – 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Forecasting 13 For Operations Management, 9e by Krajewski/Ritzman/Malhotra © 2010 Pearson Education Homework: 2, 12, 14, 16 (omit a.)

2. 13 – 2 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Forecasting Forecasts are critical inputs to business plans, annual plans, and budgets Finance, human resources, marketing, operations, and supply chain managers need forecasts to plan: output levels, purchases of services and materials, workforce and output schedules, inventories, and long-term capacities Forecasts are made on many different variables Forecasts are important to managing both processes and managing supply chains

3. 13 – 3 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Forecasting Rarely perfect because of randomness Forecasts more accurate for groups vs. individuals Accuracy decreases as time horizon increases I see that you will get an A this semester.

4. 13 – 4 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Demand Patterns A time series is the repeated observations of demand for a service or product in their order of occurrence There are five basic time series patterns  Horizontal  Trend  Seasonal  Cyclical  Random

5. 13 – 5 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Demand Patterns Quantity Time (a) Horizontal: Data cluster about a horizontal line Figure 13.1 – Patterns of Demand

6. 13 – 6 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Demand Patterns Quantity Time (b) Trend: Data consistently increase or decrease Figure 13.1 – Patterns of Demand

7. 13 – 7 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Demand Patterns Quantity | ||||||||||| Months (c) Seasonal: Data consistently show peaks and valleys Year 1 Year 2 Figure 13.1 – Patterns of Demand

8. 13 – 8 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Demand Patterns Quantity |||||| Years (d) Cyclical: Data reveal gradual increases and decreases over extended periods Figure 13.1 – Patterns of Demand

9. 13 – 9 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Types of Forecasts Judgmental  Uses subjective inputs Time series  Uses historical data assuming the future will be like the past Associative models  Uses explanatory variable(s) to make a forecast regarding a dependent variable

10. 13 – 10 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Judgment Methods Other methods (casual and time-series) require an adequate history file, which might not be available Salesforce estimates Executive opinion is a method in which opinions, experience, and technical knowledge of one or more managers are summarized to arrive at a single forecast Consumer surveys Outside opinion Delphi method

11. 13 – 11 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Judgment Methods Market research is a systematic approach to determine external customer interest through data-gathering surveys Delphi method is a process of gaining consensus from a group of experts while maintaining their anonymity Useful when no historical data are available

12. 13 – 12 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Linear Regression A dependent variable is related to one or more independent variables by a linear equation The independent variables are assumed to “cause” the results observed in the past Simple linear regression model is a straight line Y = a + bX where Y = dependent variable X = independent variable a = Y -intercept of the line b = slope of the line

13. 13 – 13 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Linear Regression Dependent variable Independent variable X Y Estimate of Y from regression equation Regression equation: Y = a + bX Actual value of Y Value of X used to estimate Y Deviation, or error Figure 13.2 – Linear Regression Line Relative to Actual Data

14. 13 – 14 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Linear Regression The sample correlation coefficient, r  Measures the direction and strength of the relationship between the independent variable and the dependent variable.  The value of r can range from –1.00 ≤ r ≤ 1.00 The sample coefficient of determination, r 2  Measures the amount of variation in the dependent variable about its mean that is explained by the regression line  The values of r 2 range from 0.00 ≤ r 2 ≤ 1.00 The standard error of the estimate, s yx  Measures how closely the data on the dependent variable cluster around the regression line

15. 13 – 15 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using Linear Regression EXAMPLE 13.1 The supply chain manager seeks a better way to forecast the demand for door hinges and believes that the demand is related to advertising expenditures. The following are sales and advertising data for the past 5 months: MonthSales (thousands of units)Advertising (thousands of $) 12642.5 21161.3 31651.4 41011.0 52092.0 The company will spend $1,750 next month on advertising for the product. Use linear regression to develop an equation and a forecast for this product.

16. 13 – 16 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using Linear Regression SOLUTION We used POM for Windows to determine the best values of a, b, the correlation coefficient, the coefficient of determination, and the standard error of the estimate a = b = r = r 2 = s yx = The regression equation is Y = –8.135 + 109.229 X –8.135 109.229 X 0.980 0.960 15.603

17. 13 – 17 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using Linear Regression The regression line is shown in Figure 13.3. The r of 0.98 suggests an unusually strong positive relationship between sales and advertising expenditures. The coefficient of determination, r 2, implies that 96 percent of the variation in sales is explained by advertising expenditures. | 1.02.0 Advertising ($000) 250 – 200 – 150 – 100 – 50 – 0 – Sales (000 units) Brass Door Hinge X X X X X X Data Forecasts Figure 13.3 – Linear Regression Line for the Sales and Advertising Data

18. 13 – 18 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Linear Regression Output

19. 13 – 19 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Linear Regression Assumptions  Variations around the line are random  Deviations around the line normally distributed  Predictions are being made only within the range of observed values  For best results:  Always plot the data to verify linearity  Check for data being time-dependent  Small correlation may imply that other variables are important

20. 13 – 20 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Time Series Methods In a naive forecast the forecast for the next period equals the demand for the current period (F t = D t-1 ) Uh, give me a minute.... We sold 250 wheels last week.... Now, next week we should sell....

21. 13 – 21 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Simple Moving Averages D t = actual demand in period t F t = forecast for period t E t = forecast error in period t n = total number of periods in the average

22. 13 – 22 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Weighted Moving Averages Weights are given; example (.5,.3,.2)

23. 13 – 23 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Exponential Smoothing Premise--The most recent observations might have the highest predictive value.  Therefore, we should give more weight to the more recent time periods when forecasting.

24. 13 – 24 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Exponential Smoothing The emphasis given to the most recent demand levels can be adjusted by changing the smoothing parameter Larger α values emphasize recent levels of demand and result in forecasts more responsive to changes in the underlying average Smaller α values treat past demand more uniformly and result in more stable forecasts Exponential smoothing is simple and requires minimal data When the underlying average is changing, results will lag actual changes

25. 13 – 25 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Including a Trend A trend in a time series is a systematic increase or decrease in the average of the series over time The forecast can be improved by calculating an estimate of the trend Trend-adjusted exponential smoothing requires two smoothing constants

26. 13 – 26 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Including a Trend For each period, we calculate the average and the trend: A t =α(Demand this period) + (1 – α)(Average + Trend estimate last period) = α D t + (1 – α)( A t –1 + T t –1 ) T t =β(Average this period – Average last period) + (1 – β)(Trend estimate last period) = β( A t – A t –1 ) + (1 – β) T t –1 F t +1 = A t + T t where 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, with a value between 0 and 1 =smoothing parameter for the trend, with a value between 0 and 1 F t +1 =forecast for period t + 1

27. 13 – 27 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using Trend-Adjusted Exponential Smoothing EXAMPLE 13.4 Medanalysis, Inc., provides medical laboratory services Managers are interested in forecasting the number of blood analysis requests per week There has been a national increase in requests for standard blood tests Medanalysis recently ran an average of 28 blood tests per week and the trend has been about three additional patients per week This week’s demand was for 27 blood tests We use α = 0.20 and β = 0.20 to calculate the forecast for next week

28. 13 – 28 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 30.2 + 2.8 = 33 blood tests Using Trend-Adjusted Exponential Smoothing SOLUTION If the actual number of blood tests requested in week 2 proved to be 44, the updated forecast for week 3 would be A 0 = 28 patients and T 0 = 3 patients The forecast for week 2 (next week) is A 1 = T 1 = F 2 = 0.20(27) + 0.80(28 + 3) = 30.2 0.20(30.2 – 28) + 0.80(3) = 2.8 A 2 = F 3 = 35.2 + 3.2 = 38.4 or 38 blood tests 0.2(35.2 – 30.2) + 0.80(2.8) = 3.2 0.20(44) + 0.80(30.2 + 2.8) = 35.2 T 2 =

29. 13 – 29 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using Trend-Adjusted Exponential Smoothing 30.20 + 2.84 = 33.04 –430.20 35.23 2.84 3.28 28.00 + 3.00 = 31.00 35.23 + 3.28 = 38.51 38.21 + 3.22 = 41.43 40.14 + 2.96 = 43.10 45.08 + 3.36 = 48.44 46.35 + 2.94 = 49.29 50.83 + 3.25 = 54.08 55.46 + 3.52 = 58.98 54.99 + 2.72 = 57.71 57.17 + 2.62 = 59.79 58.63 + 2.38 = 61.01 59.21 + 2.02 = 61.23 60.99 + 1.97 = 62.96 62.37 + 1.86 = 64.23 10.96 –1.51 –6.43 9.90 –10.44 7.71 6.92 –19.98 –2.71 –5.79 –9.01 –1.23 –2.96 10.77 38.21 40.14 45.08 46.35 50.83 55.46 54.99 57.17 58.63 59.21 60.99 62.37 66.38 3.22 2.96 3.36 2.94 3.25 3.52 2.72 2.62 2.38 2.02 1.97 1.86 2.29 TABLE 13.1| FORECASTS FOR MEDANALYSIS USING THE TREND-ADJUSTED EXPONENTIAL | SMOOTHING MODEL Calculations to Forecast Arrivals for Next Week WeekArrivals Smoothed Average Trend Average Forecast for This WeekForecast Error 02828.003.00 127 244 337 435 553 638 757 861 939 1055 1154 1252 1360 1460 1575

30. 13 – 30 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using Trend-Adjusted Exponential Smoothing Week (t)DtChangeAtTtFt 028 28.003.00 12730.202.8431.00 2441735.233.2833.04 337-738.213.2238.51 435-240.142.9641.43 5531845.083.3643.10 638-1546.352.9448.44 7571950.833.2549.29 861455.463.5254.08 939-2254.992.7258.99 10551657.172.6257.72 115458.632.3859.79 1252-259.212.0261.02 1360860.991.9761.24 1460062.371.8662.96 15751566.382.2964.23 Smoothing Parameters Alpha0.23.13 Beta0.2 Smoothing Constants Tt=estimate of the trend for period t At=exponentially smoothed average of the series in period t exponentially smoothed forecast Ft=TA-ES Forecast for period t

31. 13 – 31 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. |||||||||||||||| 0123456789101112131415 80 – 70 – 60 – 50 – 40 – 30 – Patient arrivals Week Actual blood test requests Trend-adjusted forecast Using Trend-Adjusted Exponential Smoothing Figure 13.5 – Trend-Adjusted Forecast for Medanalysis

32. 13 – 32 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 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 α = 0.20 and β = 0.10?

33. 13 – 33 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Seasonal Patterns Seasonal patterns are regularly repeated upward or downward movements in demand measured in periods of less than one year Account for seasonal effects by using one of the techniques already described but to limit the data in the time series to those periods in the same season This approach accounts for seasonal effects but discards considerable information on past demand

34. 13 – 34 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 1.For each year, calculate the average demand for each season by dividing annual demand by the number of seasons per year 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 3.Calculate the average seasonal index for each season using the results from Step 2 4.Calculate each season’s forecast for next year Multiplicative Seasonal Method Multiplicative seasonal method, whereby seasonal factors are multiplied by an estimate of the average demand to arrive at a seasonal forecast

35. 13 – 35 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. The manager wants to forecast customer demand for each quarter of year 5, based on an estimate of total year 5 demand of 2,600 customers Using the Multiplicative Seasonal Method EXAMPLE 13.5 The manager of the Stanley Steemer carpet cleaning company needs a quarterly forecast of the number of customers expected next year. The carpet cleaning business is seasonal, with a peak in the third quarter and a trough in the first quarter. Following are the quarterly demand data from the past 4 years: QuarterYear 1Year 2Year 3 Year 4 14570100 2335370585725 35205908301160 4100170285215 Total1000120018002200

36. 13 – 36 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using the Multiplicative Seasonal Method

37. 13 – 37 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using the Multiplicative Seasonal Method Year1Year2Year3Year4Yr5Forecast Q14570100 132.82 Q2335370585725843.62 Q352059083011601300.03 Q4100170285215323.52 Totals10001200180022002600 Average250300450550650 SFYr1SFYr2SFYr3SFYr4AvgSF Q10.180.230.220.180.20 Q21.341.231.301.321.30 Q32.081.971.842.112.00 Q40.400.570.630.390.50

38. 13 – 38 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Measures of Forecast Error Et2nEt2n MSE = |Et |n|Et |n MAD = (  | E t |/ D t ) (100) n MAPE =

39. 13 – 39 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Measures of Forecast Error Simple Moving Average Weighted Moving Average Exponential Smoothing MAD Results

40. 13 – 40 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Measures of Forecast Error Simple Moving Average Weighted Moving Average MSE Results

41. 13 – 41 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Measures of Forecast Error MAPE Results Simple Moving Average Weighted Moving Average