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

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

3. Forecasting What is forecasting? –Predicting the future + information Where can be apply? –Business/Non- business –Production/ Service Why is it important? –Risky decison need information –Implication every aspect of operation –Find balance of supply and demand

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

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 2250 3176 4189 5224 6236 7214

13. Example The observed demand in the first two periods was 200 and 250 cars: –D 1 =200, –D 2 =250. 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 =250 –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 =236 and D 7 =214. –Last forecast: F 8 =225. 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=0.2 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 6236 7214

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 =214. –Last forecast: F 8 =223. 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: