1. Chapter 3
Forecasting

2. Forecast OM is mostly proactive not reactive
It involves structured planning activities
Planning requires data pertaining to the feature
Forecast: A statement about the future
Not necessarily numerical
Weather forecasts

3. Uses of Forecasts Accounting Cost/profit estimates Finance
Cash flow and funding
Human Resources
Hiring/recruiting/training
Marketing
Pricing, promotion, strategy
MIS
IT/IS systems, services
Operations
Schedules, MRP, workloads
Product/service design
New products and services

4. REMARKS
Assume a causal system
Future resembles the past
Forecasts rarely perfect because of randomness
Forecasts more accurate for groups vs. individuals.
Forecasting errors among items in a group usually have a canceling effect.
Extremes in a group cancel each other
Ex. I can forecast the class average from the midterm better than Mrs. X’s individual grade.
Sample variance of {-1,1,-1,1} is 1.
Sample variance of {(-1+1)/2, {(-1+1)/2} is 0.
Forecast accuracy decreases as time horizon for forecasts increases
Ex. I can forecast this year’s class average better than next year’s class average

5. Elements of a Good Forecast
Timely
Accurate
Reliable
Meaningful
Written
Easy to use

6. Steps in the Forecasting Process
Step 1 Determine purpose of forecast
Step 2 Establish a time horizon
Step 3 Select a forecasting technique
Step 4 Gather and analyze data
Step 5 Prepare the forecast
Step 6 Monitor the forecast
“The forecast”

7. Types of Forecasts
Judgmental - Subjective analysis of subjective inputs
Associative models – Analyzes historical data to reveal relationships between (easily or in advance) observable quantities and forecast quantities. Uses this relationship to make predictions.
Time series – Objective analysis historical data assuming the future will be like the past

8. Judgmental Forecasts Executive opinions (long-range planning)
There are factors hard to quantify
Ex: Effects of November 2004 election on new houses built in 2005
Sales force composite
Retailer forecasts for the manufacturer
Consumer surveys
The guy at the mall who asks if you like cherry flavor in your shampoo
Outside opinion
Financial and consulting gurus and companies
Opinions of managers and staff
Delphi method: A series of questionnaires developed sequentially

9. Associative Forecasting
Based on identification of related variables that can be used to predict values of the variable of interest.
Sales of mountain bikes in an area may be related to the percentage of the young population living in that area.
Sales of Harley-Davidson motorbikes is related to mid-aged men population. Average age of H-D owners is 46.
Ice cream sales can be related to temperature
Home depot bases sales forecasts on mortgage refinancing rates, smaller rates imply higher sales.
Changes in Federal Reserve Board’s interest rate leads to certain business activities
House sales
Industrial investments
Increase in energy cost leads to price increases in products and services

10. Associative Forecasting
Find an association between the predictor and the predicted
Predictor variables - used to predict values of variable interest, sometimes called independent variables
Predicted variable = Dependent variable
Regression - technique for fitting a line to a set of points
Linear regression is the most widely used form of regression
The objective is to obtain an equation of a straight line that minimizes the sum of squared vertical deviations of data points from the line.

11. Linear Regression (cont.)
y = a + bx
Where
y = predicted (dependent) variable
x = predictor (independent) variable
b = slope of the line
a = value of y when x = 0 (the height of line at the y intercept)

12. Computing a and b
Given n data points, find the intercept a and the slope b to

13. Linear Model Seems Reasonable
Computed relationship

14. Another Linear Regression Example Variables: Weeks and Sales

15. Linear Trend Calculationb =
5 (2499) -
15(812)
5(55)
225
12495
12180
275
6.3
812 -
6.3(15) a = =
143.5 5
y = t
Sales in week t = t

16. Linear Trend Calculation
y = t
When t = 0, the value of y is and the slope of the line is 6.3. meaning that the value of of y will increase by 6.3 units for each time period. If t = 10, the forecast is (10) = 206.5
Excel example
regression.xls

17. Linear Regression Remember from Statistics
Correlation (r) between variables: The strength and direction of relationships between two variables
1.00 means changes in one variable are always matched by changes in the other, vice versa.
A correlation close to zero means little linear relationship
The square of the correlation coefficient provides a measure of the percentage of variability in the values of y that is explained by the independent variable.(80% or more: the independent variable is a good predictor of the values of dependent variable)

18. Time series Types of Variations in Time Series Data
Time-ordered sequence of observations taken at regular intervals over a period of time
Future values of the series can be estimated from past values.
Types of Variations in Time Series Data
Trend - long-term movement in data
Seasonality - short-term regular variations in data
Cycles – wavelike variations of long-term
Irregular variations - caused by unusual circumstances
Random variations - caused by chance

19. Forecast Variations Figure 3-1 Trend Cyclical Cycles
Irregular variation
Figure 3-1
Trend
Cyclical
Cycles
Year 01 00 99
Seasonal variations

20. Naïve Forecasts Some notation: Forecast at time t is F(t)
Uses a single previous value of a time series as the basis of a forecast.
Virtually no cost
Data analysis is nonexistent
Easily understandable
Cannot provide high accuracy
If it were true, future will always be the same as the past
Some notation: Forecast at time t is F(t)
Actual observation at time t is A(t)
Today is temperature is 98 F, A(Today)=98
F(Tomorrow)=98
F(Day after)=98

21. Uses for Naïve Forecasts
Stable time series data
Forecast is the same as the last actual observation
F(t) = A(t-1)
Seasonal variations
Forecast is the same as the last actual observation when we were in the same point in the cycle, where a cycle lasts n periods.
F(t) = A(t-n)
Data with trends
There is constant trend, the change from (t-2) to (t-1) will be exactly as the change from (t-1) to (t)
F(t) = A(t-1) + (A(t-1) – A(t-2))

22. week.... Now, next week we should sell....
Naive Forecasts
Uh, give me a minute....
We sold 250 wheels last
week.... Now, next week we should sell....

23. Naïve (Cont.) Check if the resulting accuracy is acceptable
The higher the accuracy, often the higher the cost.
Do we really need our forecast that accurate? Is it worth the additional resources?
Why do you need forecasts for? How critical they are for operations?

24. Time Series Models: Variations What is random and what is not?
Historical data contain random variations or noise
Random variations are caused by relatively unimportant factors.
What is random? Can we not study everything to negligible detail? “God does not roll dices” –A.E.
The objective is to remove all randomness and have real variations.
Minor variations are random and large ones are real.

25. Techniques for Averaging
Moving averages (MA)
Naïve methods just trace the actual data with a lag of one period, F(t)=A(t-1)
They don’t smooth
MA uses a number of the most recent actual data to smooth
Weighted moving averages
Exponential smoothing

26. Simple Moving Average Note the sensitivity of forecasts
Averaging (over time) techniques are used to smooth variations in the data.
Actual
MA(t,5)
MA(t,3)

27. Ex: Three period moving average forecast
Month Demand
MA(6,3) = ( ) / 3 =
If A(6) = 39, then
MA(7,3) = ( ) / 3
= 40.00

28. Weighted average Moving Average
Advantage=Easy to compute and easy to understand
Disadvantage=All values in the average are weighted equally
Weighted Moving Average
Similar to moving average
It assigns more weight to the most recent values in a time series
Idea: most recent observations must be better indicators of the future than older observations

29. Weighted average Month Demand 1 42 2 40 3 43 4 40 5 41 6 39
Compute a weighted average forecast using a weight of 0.4 for the most recent period, 0.3 for the next most recent, 0.2 for the next and 0.1 for the next.
Continuing with the data on the left
F(6) = .40(41)+.30(40)+.20(43)+.10(40)=41.0
If the actual demand for period 6 is 39,
F(7) = .40(39)+.30(41)+.20(40)+.10(43)=40.2
The weighted average is more reflective of the most recent occurrences.

30. Exponential Smoothing
Forecast error:=Actual – Forecast =A(t-1)-F(t-1)
Forecast today=Forecast yesterday+(alpha)*(Forecast error yesterday)
Each new forecast is equal to the previous forecast plus a percentage of the previous error.
Today’s forecast
Depends on yesterday’s (time-wise dependence, strong memory)
But it has to be corrected by forecast error
Therefore, we should give more weight to the more recent time periods when forecasting.
Alpha = smoothing constant = percentage of the forecast error.

31. Exponential Smoothing as an Weighted Average
Idea--The most recent observations might have the highest predictive value along with the most recent forecast errors. Let us balance them:

32. Example of Exponential Smoothing
Forecasts made in a period and the period has the same color

33. Picking a Smoothing Constant: Responsiveness vs. Smoothing
The quickness of forecast adjustment to error is determined by the smoothing constant.
The closer the alpha is to zero, the slower the forecast will be to adjust to forecast errors.
Conversely, the closer the value of alpha is to 1.00, the greater the responsiveness to the actual observations and the less the smoothing
Select a smoothing constant that balances the benefits of responding to real changes if and when they occur.

34. Picking a Smoothing Constant Sensitivity of Forecasts
Actual
 0.1
0.4
Excel example
exponential-smoothing.xls

35. Techniques for trend Develop an equation that will describe trend
The trend component may be linear or it may not
Linear trend: t Y
b is similar to the slope. However, since it is calculated with the variability of the data in mind, its formulation is not as straight-forward as our usual notion of slope.
Yt = a + bt

36. Common Nonlinear Trends
Parabolic
Exponential
Growth
Figure 3-5

37. Adjusting for Trend with Double Exponential Smoothing
Simple exponential smoothing with no trend
Add forecasted trend
This time trend is also smoothed, note that previous trend (of t-1) and current trend (of t) appear in the smoothing formula:
See Table 3-2 for an exercise

38. Techniques for seasonality
Regularly repeating upward or downward movements in time series values
Seasonality: weather variations, vacations and holidays
Seasonality: Expressed in terms of the amount that actual values deviate from the average value of the series
Seasonality is expressed as a percentage of the average amount
seasonal percentages = seasonal relatives = seasonal indices

39. Different models of seasonality
Seasonal relative = 1.45 for the quantity of television sold in August at Circuit City, meaning that TV sales for that month are 45% above the monthly average.
Seasonal factor=0.60 for the number of notebooks sold at the UTD bookstore in April, meaning that notebook sales are 40% below the monthly average.
Seasonal indices are your vehicle to travel between the seasonal and deseasonal worlds.

40. Use Seasonality Indices to Deseasonalize and Seasonalize
Inputs
Analyze
Output t t t
Deseasonalize historical observations
Divide them by seasonal indices
Make the analysis = Generate forecasts
Seasonalize forecasts
Multiply them by seasonal indices
Excel example
seasonalforecast.xls

41. Measurement is the first step to improve an activity
Forecast Accuracy
Measurement is the first step to improve an activity
What value of smoothing constant is good?
Accuracy measurement is a vital aspect of forecasting
Impossible to correctly predict future values
Important to include an indication of how big the forecast deviate from the actual values

42. Forecast Accuracy
Error - difference between actual value and predicted value
Mean absolute deviation (MAD)
Average absolute error (weights all errors evenly)
Mean squared error (MSE)
Average of squared error (weights errors according to their squared values)
Tracking signal
Ratio of cumulative error and MAD

43. MAD & MSE

44. Compare the accuracy of alternative
Use for MAD & MSE
Compare the accuracy of alternative
forecasting methods using MAD and MSE.
parameter (such as alpha) values used in forecasting
by using MAD and MSE
Determine which method yields the lowest MAD or MSE for a given set of data.

45. Controlling the quality of forecast
Necessary to monitor forecast to ensure that the forecast is performing adequately
This is accomplished by comparing forecast errors to predetermined values
Errors that fall within the limits are considered acceptable
Errors outside either limit indicates that corrective action is needed.
Tracking signal values are compared to predetermined limits (+4,-4) based on judgment and experience
Upper and lower limits for individual forecast errors are calculated using control chart techniques. We will learn about control charts in quality chapters.

46. Choosing a forecasting technique No single technique works best in every situation
The forecast horizon
Forecasting frequency
Forecasting is not free
Consider cost and accuracy
Weigh cost-accuracy trade-offs carefully
Forecast detail, part / product level?
Availability of
historical data
computers
able users / decision makers

47. Choosing a forecasting technique (cont.)
Moving Averages and Exponential Smoothing are short range techniques. They produce forecast for the next period
Trend equations are used for much longer time horizons.
More than one forecasting techniques might be used to increase confidence.

48. Summary We studied the steps of forecasting
We examined three forecasting techniques:
Judgmental
Associative
Time Series
We learned about seasonality, trend, cyclical data
Discussed monitoring forecast accuracy