1. 2. Forecasting

2. Forecasting  Using past data to help us determine what we think will happen in the future  Things typically forecasted Demand for products and services Raw material prices Human resources costs Economic forecasts: inflation rates, money supplies, housing starts

3. Why do we forecast?  We forecast as an input to production/services planning, so that we have some idea of demand/resources, etc.  Forecasts drive a lot of decision-making  We should never expect forecasts to be exactly correct, we only hope that they give us a reasonable idea as to what the future holds

4. Laws of Forecasting  Forecasts are always wrong  Detailed forecasts are worse than aggregate forecasts  The further into the future, the less reliable the forecast will be

5. Ranges of Forecasts  Short range less than three months Purchasing, job scheduling, workforce levels should be accurate  Medium range Three months to three years Sales, production planning, budgeting should be good

6. Ranges of Forecasts (Continued)  Long range several years New products, capital expenditure, facility location and expansion hopefully good

7. Types of Forecasting  Qualitative Methods - Subjective estimates of future  Time Series Analysis - using past data to predict future  Causal Relationships - data pattern is explained by various factors

8. Forecasting Sequence  Determine the use of the forecast  Select the items to be forecasted  Determine the time horizon of the forecast  Select the forecasting models  Gather the data  Make the forecast  Validate and implement results

9. Qualitative Forecasting

10. Quantitative Forecasting

11. Components of Data  Average value  Trend - a slow direction/shift  Seasonal influence - sensitivity to time of year  Cyclical elements - high and low points  Random variation (white noise) - unexplainable behavior

12. Forecast Using Different Components Demand for product or service |||| 1234 Year Average demand over four years Seasonal peaks Trend component Actual demand Random variation

13. Time Series Analysis - Notation  D t is the actual demand for period t  F t is the forecast for period t  F t+k is the forecast made at period t for k periods ahead

14. Moving Average  F t+1 = (D t + D t-1 + …+ D t-N+1 ) / N  F t+2 = (D t+1 + D t + …+ D t-N+2 ) / N = F t+1 + (D t+1 - D t-N+1 ) / N  N is the number of averaging periods (typically, N is 5 to 7)  Better for constant processes

15. Effect of Number of Periods  Smaller N is good for quick response, but larger N ignores random fluctuations

16. Example January10 February12 March13 April16 May19 June23 July26 Actual3-Month MonthShed SalesMoving Average (12 + 13 + 16)/3 = 13 2 / 3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1 / 3 101213 (10 + 12 + 13)/3 = 11 2 / 3

17. Example ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Shed Sales 30 30 – 28 28 – 26 26 – 24 24 – 22 22 – 20 20 – 18 18 – 16 16 – 14 14 – 12 12 – 10 10 – Actual Sales Moving Average Forecast

18. Weighted Moving Average January10 February12 March13 April16 May19 June23 July26 Actual3-Month Weighted MonthShed SalesMoving Average [(3 x 16) + (2 x 13) + (12)]/6 = 14 1 / 3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 20 1 / 2 101213 [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights applied: 3, 2, 1

19. Example 30 30 – 25 25 – 20 20 – 15 15 – 10 10 – 5 5 – Sales demand ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Actual sales Moving average Weighted moving average

20. Exponential Smoothing  F t+1 = α D t + α (1- α )D t-1 + α (1- α ) 2 D t-2 + …  F t+2 = α D t+1 + α (1- α )D t + α (1- α ) 2 D t-1 + … = α D t+1 + (1- α )F t+1 where 0 < α < 1. (typically, α is 0.1 to 0.3) Better for constant processes Weight Assigned to Most2nd Most3rd Most4th Most5th Most RecentRecentRecentRecentRecent SmoothingPeriodPeriodPeriodPeriodPeriod Constant(  )  (1 -  )  (1 -  ) 2  (1 -  ) 3  (1 -  ) 4  =.1.1.09.081.073.066  =.5.5.25.125.063.031

21. Effect of α  Larger α gives greater weight to new data  Use small values for  if demand is stable, larger values for  if demand is fluctuating

22. Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast=.8 x 142 +.2 x 153 = 144.2 ≈ 144 cars

23. Example 225 225 – 200 200 – 175 175 – 150 150 – |||||||||123456789123456789|||||||||123456789123456789 Quarter Demand  =.1 Actual demand  =.5

24. Trend Process (Double Exponential Smoothing)  Simple exponential smoothing tends to lag behind a trend. Correct this by estimating the slope and multiply this slope by the number of periods.  A t = α D t + (1- α )(A t-1 +B t-1 )  B t = β (A t -A t-1 ) + (1- β )B t-1  F t+k = A t + kB t

25. Example Period1234567 Demand74798090105142122

26. Seasonal Process  A t = α D t /C t-4 + (1- α )(A t-1 +B t-1 )  B t = β (A t -A t-1 ) + (1- β )B t-1  C t = γ D t /A t + (1- γ )C t-4  F t+k = (A t + kB t ) C t+k-4

27. Example Q -- Y12 Sp6984 Su266310 F188212 W5964 Avg145.5167.5

28. Causal Relationships – Linear (Multiple) Regression Model  A forecasting technique that assumes that the relationship between the dependent and independent variables. Useful if there is a strong relationship and a time lag between variables.  Y t = a + bX t where Y t is dependent variable to be solved for and X t is independent variable. a is intercept and b is slope of the line.

29. Example Period1234567 Demand74798090105142122

30. Forecast Error  Projection of past trends into the future  Bias errors Consistent mistakes causing a forecast to be too high or too low: wrong models, wrong trend line, errors in shifting seasonal demand, undetected trends  Random errors Variations (noise) in a forecast that cannot be explained by the forecast model

31. Forecast Error Measurements  MAD (Mean absolute deviation)  MSE (Mean squared error)  MAPE (Mean absolute percent error)

32. Example RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62 MAD10.3112.33 MSE190.82195.24 MAPE5.59%6.76%

33. Selection of Parameters

34. Video Case Study  Describe three different forecasting applications. Name three other areas in which you think Hard Rock could use forecasting models.  Justify the use of the weighting system used for evaluating managers for annual bonuses.  Name several variables besides those mentioned in the case that could be used as good predictors of daily sales.