1. Forecasting to account for seasonality Regularly repeating movements that can be tied to recurring events (e.g. winter) in a time series that varies around an average, it is expressed as a value of deviation from the average if the time series exhibits trend, seasonality is expressed in terms of the trend value

2. Seasonal Relative An index you calculate which can then be multiplied by the value of a series to incorporate seasonality e.g. Chocolate sales: February seasonal relative may be 1.2 “120% of the monthly average”; June’s may be.85 “85% of the monthly average” use of relatives assists capacity planning, scheduling

3. Naïve Forecasting incorporating seasonality Refer to the forecast of the same season e.g. Snow tires sales naïve forecasting- when forecasting for 4Q 2000, it’s more valuable to look at 4Q 1999 than 3Q 1999

4. Seasonal Relatives- doing the math 2 approaches: 1) remove seasonality from the data: gives you greater understanding of the non- seasonal ( trend or average) components (e.g. “What is the underlying trend in demand for chocolate?”) 2) incorporate seasonality into the data: useful when time series has both trend and seasonal components “What is the forecast for chocolate given trend and seasonality?”

5. 1) obtain trend estimates using trend equation 2) add seasonality by multiplying estimates by seasonal relative (index) Example: predict demand in period 6 (4Q 1999) given that trend is represented by Y t =350-2.5T and seasonal relatives are Q1=1.5; Q2=.8; Q3=1.1; Q4=.6 Solution: Y t =350-2.5(6)= 335 335*.6= 201 Incorporating seasonality You try: forecast period 7 Y t =350-2.5(7)= 332.5 332.5*1.5= 498.75

6. Computing Seasonal Relatives 1) Create a centered moving average (# of periods needed = # of seasons involved) Here, let’s assume 3 seasons for a Symphony Orchestra. 1100 2115(100+115+85)/3 =100 385(115+85+106)/3= 102 4106 2) Compute the index perdemand ctd mvg avgrelative 2115100115/100=1.15 38510285/102=.83 “The time series data at period 2 is 15 percent above average at that point”

7. Techniques for cyclical demand Seek to locate the variable that causes the cyclical change (e.g. new home construction and mortgage rates) use simple or multiple regression to summarize the effects of this predictor variable(s) software such as SPSS available to do multiple regression analysis

8. Accuracy and control of forecasts Principle: “sell” other stakeholders on the validity of your analysis by reporting on it Question: “Is the forecast in bounds or out of bounds?” So you set the “boundaries” then compare your data remember that Error = Actual - Forecast e t =A t -F t

9. Summarizing forecast error Mean Absolute Deviation computes the absolute value of sum of the errors MAD =  |Actual- Forecast | / n use MAD to compare forecasts. Lower value is better. Peractualfcst1 error |error |fcst 2 error |error | 12172152221700 2213216-33216-33 32162151121600 4210214-44216-66 521321122214-11 62192145521455  317-515 MAD= 17/6=2.83MAD- 15/6= 2.5

10. MSE- Mean Squared Error Takes into account variation of the errors MSE =  (Actual- Forecast ) 2 / n-1 Peractualfcst1 error error 2 121721524 2213216-39 321621511 4210214-416 521321124 6219214525  359MSE= 59/5= 11.8

11. Setting limits and monitoring forecasts: reasons for error Variable omission, shift, or new variable appearance (e.g. government regulation in sale of term life insurance) Uncontrollable events Incorrect use of technique or results misinterpreted (e.g. new industry doesn’t yet understand trend of product “Internet anything”) random variations “noise”

12. Setting your “boundaries” and monitoring forecasts using control charts Assumes forecast errors are randomly distributed around a mean of 0; distribution of errors is normal (I.e. +/-1S captures about 67% of data; +/- 2S captures 95%; 3S 99% How to do it: 1) ensure average error is approximately zero, to ensure forecast is not biased 2) Set 2S control limits (2S is generally accepted) 3) compare your errors to 2S value. This ensures 95% of the time your forecast is “in control”

13. In our example…. Peractualfcst1 error error 2 121721524 2213216-39 321621511 4210214-416 521321124 6219214525  359 MSE= 59/5= 11.8 Step 1: Ensure average error is approximately zero. Sum of errors/n= 3/6 =.5 OK Step 2: 2s= 2* the Square Root of (  e 2 / n-1) = 2* 3.4 = 6.8 Step 3: Compare your error values to +/- 6.8

14. Selecting a forecasting technique Cost/ benefit analysis What’s the “political” environment Choose based on time horizon SHORT= moving averages, exponential smoothing techniques LONG= qualitative techniques need to be included due to amount of macro variables Turn over stones. Use multiple techniques and see how they compare

15. What if we can’t rely on long term forecasts? Shorten the lead time your company needs to react to forecasts. Fulfillment companies may use and expandable/contractible shipping and warehouse team to more quickly react to forecast upturns and downturns. This is fundamentally a strategic decision: if our industry is too complex to rely on long term forecasts, we need to design systems that are more nimble This may also be a staff training issue. Cross training allows more nimble operation, at a cost