Learning Objectives

1. Learning Objectives When you complete this chapter, you should be able to : Identify or Define: • Forecasting • Types of forecasts • Time horizons • Approaches to forecasts

2. Learning Objectives When you complete this chapter, you should be able to : Describe or Explain: • Moving averages • Exponential smoothing • Trend projections • Regression and correlation analysis • Measures of forecast accuracy

3. ?? What is Forecasting? • Process of predicting a future event

4. Forecasting Time Horizons • Short-range forecast • Up to 1 year, generally less than 3 months • Purchasing, job scheduling, workforce levels, job assignments, production levels • Medium-range forecast • 3 months to 3 years • Sales and production planning, budgeting • Long-range forecast • 3+ years • New product planning, facility location, research and development

5. Types of Forecasts • Economic forecasts • Address business cycle – inflation rate, money supply, housing starts, etc. • Technological forecasts • Predict rate of technological progress • Impacts development of new products • Demand forecasts • Predict sales of existing product

6. Strategic Importance of Forecasting • Human Resources – Hiring, training, laying off workers • Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market share • Supply-Chain Management – Good supplier relations and price advance

7. Seven Steps in Forecasting • Determine the use of the forecast • Select the items to be forecasted • Determine the time horizon of the forecast • Select the forecasting model(s) • Gather the data • Make the forecast • Validate and implement results

8. The Realities! • Forecasts are seldom perfect • Most techniques assume an underlying stability in the system • Product family and aggregated forecasts are more accurate than individual product forecasts

9. Forecasting Approaches Qualitative Methods • Used when situation is vague and little data exist • New products • New technology • Involves intuition, experience • e.g., forecasting sales on Internet

10. Forecasting Approaches Quantitative Methods • Used when situation is ‘stable’ and historical data exist • Existing products • Current technology • Involves mathematical techniques • e.g., forecasting sales of color televisions

11. Overview of Qualitative Methods • Jury of executive opinion • Pool opinions of high-level executives, sometimes augment by statistical models • Delphi method • Panel of experts, queried iteratively

12. Overview of Qualitative Methods • Sales force composite • Estimates from individual salespersons are reviewed for reasonableness, then aggregated • Consumer Market Survey • Ask the customer

13. Jury of Executive Opinion • Involves small group of high-level managers • Group estimates demand by working together • Combines managerial experience with statistical models • Relatively quick • ‘Group-think’disadvantage

14. Sales Force Composite • Each salesperson projects his or her sales • Combined at district and national levels • Sales reps know customers’ wants • Tends to be overly optimistic

15. Decision Makers (Evaluate responses and make decisions) Staff (Administering survey) Respondents (People who can make valuable judgments) Delphi Method • Iterative group process, continues until general agreement is reached • 3 types of participants • Decision makers • Staff • Respondents

16. Consumer Market Survey • Ask customers about purchasing plans • What consumers say, and what they actually do are often different • Sometimes difficult to answer

17. Time-Series Models Associative Model Overview of Quantitative Approaches • Naive approach • Moving averages • Exponential smoothing • Trend projection • Linear regression

18. Time Series Forecasting • Set of evenly spaced numerical data • Obtained by observing response variable at regular time periods • Forecast based only on past values • Assumes that factors influencing past and present will continue influence in future

19. Trend Cyclical Seasonal Random Time Series Components

20. Trend component Seasonal peaks Actual demand Demand for product or service Average demand over four years Random variation | | | | 1 2 3 4 Year Components of Demand Figure 4.1

21. Trend Component • Persistent, overall upward or downward pattern • Changes due to population, technology, age, culture, etc. • Typically several years duration

22. Number of Period Length Seasons Week Day 7 Month Week 4-4.5 Month Day 28-31 Year Quarter 4 Year Month 12 Year Week 52 Seasonal Component • Regular pattern of up and down fluctuations • Due to weather, customs, etc. • Occurs within a single year

23. 0 5 10 15 20 Cyclical Component • Repeating up and down movements • Affected by business cycle, political, and economic factors • Multiple years duration • Often causal or associative relationships

24. M T W T F Random Component • Erratic, unsystematic, ‘residual’ fluctuations • Due to random variation or unforeseen events • Short duration and nonrepeating

25. Time-Series Models Associative Model Overview of Quantitative Approaches • Naive approach • Moving averages • Exponential smoothing • Trend projection • Linear regression

26. Naive Approach • Assumes demand in next period is the same as demand in most recent period • e.g., If May sales were 48, then June sales will be 48 • Sometimes cost effective and efficient

27. Time-Series Models Associative Model Overview of Quantitative Approaches • Naive approach • Moving averages • Exponential smoothing • Trend projection • Linear regression

28. ∑ demand in previous n periods n Moving average= Moving Average Method • MA is a series of arithmetic means • Used if little or no trend • Used often for smoothing • Provides overall impression of data over time

29. Actual 3-Month Month Shed Sales Moving Average January 10 February 12 March 13 April 16 May 19 June 23 July 26 10 12 13 (10 + 12 + 13)/3 = 11 2/3 Moving Average Example (12 + 13 + 16)/3 = 13 2/3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1/3

30. Moving Average Forecast 30 – 28 – 26 – 24 – 22 – 20 – 18 – 16 – 14 – 12 – 10 – Actual Sales Shed Sales | | | | | | | | | | | | J F M A M J J A S O N D Graph of Moving Average

31. Weightedmoving average ∑(weight for period n) x (demand in period n) ∑ weights = Weighted Moving Average • Used when trend is present • Older data usually less important • Weights based on experience and intuition

32. Weights Applied Period 3 Last month 2 Two months ago 1 Three months ago 6 Sum of weights Actual 3-Month Weighted Month Shed Sales Moving Average January 10 February 12 March 13 April 16 May 19 June 23 July 26 10 12 13 [(3 x 13) + (2 x 12) + (10)]/6 = 121/6 Weighted Moving Average [(3 x 16) + (2 x 13) + (12)]/6 = 141/3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 201/2

33. Weighted moving average 30 – 25 – 20 – 15 – 10 – 5 – Actual sales Sales demand Moving average | | | | | | | | | | | | J F M A M J J A S O N D Moving Average And Weighted Moving Average Figure 4.2

34. Time-Series Models Associative Model Overview of Quantitative Approaches • Naive approach • Moving averages • Exponential smoothing • Trend projection • Linear regression

35. Exponential Smoothing New forecast = last period’s forecast + a(last period’s actual demand – last period’s forecast) Ft = Ft – 1 +a(At – 1 - Ft – 1) where Ft = new forecast Ft – 1 = previous forecast a = smoothing (or weighting) constant (0  a  1)

36. Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20

37. New forecast = 142 + .2(153 – 142) Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20

38. Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = 142 + .2(153 – 142) = 142 + 2.2 = 144.2 ≈ 144 cars

39. Exponential Smoothing • Form of weighted moving average • Weights decline exponentially • Most recent data weighted most • Requires smoothing constant () • Ranges from 0 to 1 • Subjectively chosen • Involves little record keeping of past data

40. 225 – 200 – 175 – 150 – Actual demand a = .5 Demand a = .1 | | | | | | | | | 1 2 3 4 5 6 7 8 9 Quarter Impact of Different 

41. Choosing  The objective is to obtain the most accurate forecast no matter the technique We generally do this by selecting the model that gives us the lowest forecast error Forecast error = Actual demand - Forecast value = At - Ft

42. Mean Absolute Deviation (MAD) • Mean Squared Error (MSE) MAD = ∑ |actual - forecast| n ∑(forecast errors)2 n MSE = Common Measures of Error

43. Mean Absolute Percent Error (MAPE) n i = 1 100 ∑ |actuali - forecasti|/actuali n MAPE = Common Measures of Error

44. Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloadeda = .10 a = .10 a = .50 a = .50 1 180 175 5 175 5 2 168 176 8 178 10 3 159 175 16 173 14 4 175 173 2 166 9 5 190 173 17 170 20 6 205 175 30 180 25 7 180 178 2 193 13 8 182 178 4 186 4 84 100 Comparison of Forecast Error

45. Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonage with for with for Quarter Unloadeda = .10 a = .10 a = .50 a = .50 ∑ |deviations| n MAD = For a = .10 1 180 175 5 175 5 2 168 176 8 178 10 3 159 175 16 173 14 4 175 173 2 166 9 5 190 173 17 170 20 6 205 175 30 180 25 7 180 178 2 193 13 8 182 178 4 186 4 84 100 = 84/8 = 10.50 For a = .50 = 100/8 = 12.50 Comparison of Forecast Error

46. Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonage with for with for Quarter Unloadeda = .10 a = .10 a = .50 a = .50 For a = .10 = 1,558/8 = 194.75 1 180 175 5 175 5 2 168 176 8 178 10 3 159 175 16 173 14 4 175 173 2 166 9 5 190 173 17 170 20 6 205 175 30 180 25 7 180 178 2 193 13 8 182 178 4 186 4 84 100 MAD 10.50 12.50 For a = .50 = 1,612/8 = 201.50 ∑(forecast errors)2 n MSE = Comparison of Forecast Error

47. n i = 1 100 ∑ |deviationi|/actuali n MAPE = Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonage with for with for Quarter Unloadeda = .10 a = .10 a = .50 a = .50 For a = .10 1 180 175 5 175 5 2 168 176 8 178 10 3 159 175 16 173 14 4 175 173 2 166 9 5 190 173 17 170 20 6 205 175 30 180 25 7 180 178 2 193 13 8 182 178 4 186 4 84 100 MAD 10.50 12.50 MSE 194.75 201.50 = 45.62/8 = 5.70% For a = .50 = 54.8/8 = 6.85% Comparison of Forecast Error

48. Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloadeda = .10 a = .10 a = .50 a = .50 1 180 175 5 175 5 2 168 176 8 178 10 3 159 175 16 173 14 4 175 173 2 166 9 5 190 173 17 170 20 6 205 175 30 180 25 7 180 178 2 193 13 8 182 178 4 186 4 84 100 MAD 10.50 12.50 MSE 194.75 201.50 MAPE 5.70% 6.85% Comparison of Forecast Error

49. Time-Series Models Associative Model Overview of Quantitative Approaches • Naive approach • Moving averages • Exponential smoothing • Trend projection • Linear regression

50. ^ y = a + bx ^ where y = computed value of the variable to be predicted (dependent variable) a = y-axis intercept b = slope of the regression line x = the independent variable (in this case time) Trend Projections Fitting a trend line to historical data points to project into the medium-to-long-range Linear trends can be found using the least squares technique