2. Forecasting

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. Trend component Seasonal peaks Actual demand Demand for product or service Average demand over four years Random variation | | | | 1 2 3 4 Year Forecast Using Different Components

13. Time Series Analysis - Notation • Dt is the actual demand for period t • Ft is the forecast for period t • Ft+k is the forecast made at period t for k periods ahead

14. Moving Average • Ft+1 = (Dt + Dt-1 + …+ Dt-N+1) / N • Ft+2 = (Dt+1 + Dt + …+ Dt-N+2) / N = Ft+1 + (Dt+1 - Dt-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. 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 Example (12 + 13 + 16)/3 = 13 2/3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1/3

17. 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 Example

18. 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 Weights applied: 3, 2, 1 [(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

19. 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 Example

20. Weight Assigned to Most 2nd Most 3rd Most 4th Most 5th Most Recent Recent Recent Recent Recent Smoothing Period Period Period Period Period Constant (a) a(1 - a) a(1 - a)2a(1 - a)3a(1 - a)4 a = .1 .1 .09 .081 .073 .066 a = .5 .5 .25 .125 .063 .031 Exponential Smoothing • Ft+1 = αDt + α(1- α)Dt-1 + α(1- α)2Dt-2 + … • Ft+2 = αDt+1 + α(1- α)Dt + α(1- α)2Dt-1 + … = αDt+1 + (1- α)Ft+1 where 0 < α < 1. (typically, α is 0.1 to 0.3) Better for constant processes

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 a = .20 New forecast = .8 x 142 + .2 x 153 = 144.2 ≈ 144 cars

23. 225 – 200 – 175 – 150 – Actual demand a = .5 Demand a = .1 | | | | | | | | | 1 2 3 4 5 6 7 8 9 Quarter Example

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. • At = αDt + (1- α)(At-1+Bt-1) • Bt = β(At-At-1) + (1- β)Bt-1 • Ft+k = At + kBt

25. Example

26. Seasonal Process • At = αDt/Ct-4 + (1- α)(At-1+Bt-1) • Bt = β(At-At-1) + (1- β)Bt-1 • Ct = γDt/At + (1- γ)Ct-4 • Ft+k = (At + kBt) Ct+k-4

27. Example

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. • Yt = a + bXt where Yt is dependent variable to be solved for and Xt is independent variable. a is interceptand b is slope of the line.

29. Example

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. 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 5.00 175 5.00 2 168 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 175 173.18 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62 MAD 10.31 12.33 MSE 190.82 195.24 MAPE 5.59% 6.76% Example

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.