1. Demand Forecasting Production and Operations Management Judit Uzonyi-Kecskés Ph.D. Student Department of Management and Corporate Economics Budapest University of Technology and Economics uzonyi-kecskes@mvt.bme.hu

2. Topics Introduction Forecasting methods Forecasting stationary series –Moving average (with example) –Simple exponential smoothing (with example) Trend based forecasting methods –Double exponential smoothing (with example) Evaluating forecasts –Analyzing the size of errors (with example) –Analyzing the validity of the forecasting model (with example)

3. Forecasting Find balance of supply and demand Predicting the future Production and service area Application of forecasting results: –Capacity planning –Production scheduling –Inventory control –Materials requirement planning

4. Forecasting Methods Subjective methods Objective methods

5. Subjective Forecasting Methods Based on expert opinion –Personal insight –Panel consensus –Delphi method –Historic analogy Based on customer opinion –Indirectly: Sales force composites –Directly: Market surveys

6. Objective Forecasting Methods Casual models –Analyzing the causes of the demand –Forecasting the demand based on the measure of the causes Time series/projective methods –Analyzing the demand of previous periods –Determining the patterns of the demand –Forecasting the demand based on the information of previous prior periods

7. Patterns of Demand

8. Symbols t: period t (e.g. day, week, month) D t : observation of demand in period t F t,t+τ : forecast in period t for period t+τ F t : forecast for period t S t : constant component in period t G t : trend component in period t Other parameters (e.g. time horizon parameter, smoothing constants)

9. Forecasting Stationary Series For stationary time series Most frequently used methods: –Moving average –Simple exponential smoothing

10. Moving Average Forecasting: N: number of analyzed periods –Large N: more weight on past data forecasts are more stable –Small N: more weight on the current observation of demand forecasts react quickly to changes in the demand

11. Example In a car factory the management observed that the demand for the factory’s car is nearly constant. Therefore they forecast the demand with the help of moving average based on the demand information of the last 2 months.

12. Example The observed demands in the last 7 periods were the following: PeriodDemand 1200 2255 3176 4189 5224 6283 7308

13. Example The observed demand in the first two periods was 200 and 255 cars: –D 1 =200, –D 2 =255. The forecast is based on the demand information of the last 2 months: N=2. The first period when forecast can be performed is period 3: t=3 –D t-1 = D 3-1 =D 2 =255 –D t-N = D 3-2 =D 1 =200

14. Example Forecast for the third period, if N=2: Forecasts for the following periods:

15. Example Multiple-step-ahead forecast –Last known demands: D 6 =283 and D 7 =308. –Last forecast: F 8 =295,5. We assume that demand is constant! Suppose that in period 8 we observe a demand of D 8 =195, we now need to update the forecasts:

16. Exponential Smoothing Forecast is a weighted average Current forecast is based on: –Last forecast –Last value of demand –Smoothing constant (e.g. α, β): 0 ≤ α, β≤ 1

17. Simple Exponential Smoothing Forecast α: smoothing constant (0 ≤ α ≤ 1) –Large α: more weight on the current observation of demand forecasts react quickly to changes in the demand –Small α: more weight on past data forecasts are more stable

18. Example In a car factory the management observed that the demand for the factory’s car is nearly constant. Therefore they forecast the demand with the help of simple exponential smoothing, and they use α=0.1 value as smoothing constant. The forecast for the first period was 250 cars.

19. Example The observed demands in the last 7 periods were the following: PeriodDemand 1200 2250 3176 4189 5224 6283 7308

20. Example The forecast for the first period was 250 cars: F 1 =250. The observed demand in the first period was 200 cars: D 1 =200. Forecast for the second period, if α=0.1:

21. Example

22. More-step-ahead forecast –Last known demand: D 7 =308. –Last forecast: F 8 =245. We assume that demand is constant! Suppose that in period 8 we observe a demand of D 8 =195, we now need to update the forecasts:

23. Comparison of the Two Methods Similarities –Both assume that demand is stationary –Both use a single parameter (N or α) Differences –Number of directly used demand data –Number and weights of indirectly used demand data

24. Trend-based Forecasting Methods For time series containing additive trend Most frequently used methods: –Regression analysis (linear or non-linear) –Double exponential smoothing

25. Double Exponential Smoothing Holt’s method Forecast α, β: smoothing constants (0≤α,β≤1)

26. Example In a furniture factory the management observed that the demand for the factory’s products is progressive and doesn’t show seasonal pattern. Therefore they forecast the demand with the help of Holt’s method, and they use α=0.2 and β=0.1 values as smoothing constants. In period zero the management has the following initial values: S 0 =200 and G 0 =10.

27. Example The observed demands in the last 7 periods were the following: PeriodDemand 1210 2270 3291 4160 5303

28. Example The initial values: S 0 =200 and G 0 =10. The observed demand in the first period was 200: D 1 =210. Forecast for the second period, if α=0.2; β=0.1:

29. Example Further steps:

30. Example

31. Multiple-step-ahead forecast –Last known demand: D 5 =303. –Last data of forecasting: S 5 =263, G 5 =11, F 8 =274. –Forecast for the next 4 periods from period 7: –There also can be need to update forecasts.

32. Evaluating Forecasts There are almost always errors in forecasts –Random effects, noises –Inappropriate forecasting methods Analysis of –the size of forecasting errors –the validity of forecasting models

33. Forecast Error Difference between the forecasted value for a period and the actual demand for the same period Covers only one period Does not give information about the acceptability of the forecasting method

34. Mean Error The average error during a term of n periods Positive and negative errors cancel each other Measures bias: –If ME is positive, the forecast is over-estimated –If ME is negative, the forecast is under-estimated

35. Absolute Error Measures Measures of forecasts accuracy during n periods Mean absolute error Mean squared error Positive and negative errors cannot cancel each other Do not give information about the relative size of error

36. Mean Absolute Percentage Error Arithmetical average of percentage error of n periods Gives information about the average, relative size of the absolute error observed during several periods

37. Example A hotel makes the following forecasts for rooms needed for a month and compares these with actual bookings. PeriodDemandForecast 1100110 2130169 3150135 4140168 5110121

38. Example First determine the forecast error in each period PeriodDemandForecastError 1100110 213016939 3150135-15 414016828 511012111

39. Example Determine the presented error measures after period 5 (t=5, T=4)

40. Example

41. Validity of Forecasting Method Analyzing the validity of the forecasting method used Signs that forecast –is inappropriate –will be inappropriate in the immediate future Tracking signal will be used Monitoring –the size of tracking signal values –the tendency of tracking signal values

42. Tracking Signal Moving sum of forecast error in period t Mean absolute error in period t Tracking signal in period t

43. Monitoring the Tracking Signal Monitoring size Monitoring tendency –Tracking signal diagram –Typical patterns: Small-scale, random alternating near to zero Increasing trend Decreasing trend

44. Example We have the following forecast and demand data. Evaluate the validity of forecast model. PeriodDemandForecast 1100110 2 126130 3 124120 4 129125 5 135115

45. Example Determine the value of tracking signal in each period PeriodDtDt FtFt etet MSFE t |et||et|MAE t TS t 1100110 2 12613044441 3 124120-40440 4 129125-4 44 5 135115-20-24208-3

46. Example Draw the tracking signal diagram Evaluate the validity of forecasting method applied –Only few data were available –Does not step out of control borders –Decreasing trend, systematic undervaluation –There is a negative trend instead of constant demand, there is a constant demand instead of positive trend, etc.

47. Possible questions in the exam Name subjective forecasting methods In which life cycle period are subjective/objective methods used? Name the similarities/differences between moving average and exponential smoothing. Name differences between forecasts made by simple exponential smoothing(moving average) with a small and a large α (N) value? Name three different forecasting errors

48. Possible exercises in the exam Give forecast using moving average Give forecast using exponential smoothing Determine the values of simple error / mean error / absolute mean error You can find examples for these in the presentation!

49. 1. Exercise for extra points The demand for a product is constant. Make forecasts for periods 3 and 4. Use moving average method. N=2. Make forecasts for periods 2,3 and 4. Use exponential smoothing. α=0.3 Give a multiple-step-ahead forecast for period 7 from period 4. Period1234 Demand140150200220

50. 2. Exercise for extra points Use double exponential smoothing with smoothing constants α=0.1 and β=0.1, and initial values S0=50, G0=10. Give one-period-ahead forecasts for the following time series: Period12345 Demand5568757780