1. The Importance of Forecasting in POM
Chapter 3
The Importance of Forecasting in POM

2. Assumes causal system past ==> future
Forecasts rarely perfect because of randomness
Forecasts more accurate for groups vs. individuals
Forecast accuracy decreases as time horizon increases
I see that you will get an A this semester.

3. 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”

4. The Importance of Forecasting in P.O.M

5. Factors Influencing Demand
Business Cycle
Product Life Cycle
Testing and Introduction
Rapid Growth
Maturity
Decline
Phase Out

6. Factors Influencing Demand
Other Factors
Competitor’s efforts and prices
Customer’s confidence and attitude

7. Who makes the sales forecast?
Sales Personnel
32%
Marketing Personnel
29%

8. Reliance on Forecasting

9. A Classification of Forecasting Methods:

10. Judgmental Forecasts Executive opinions Sales force opinions
Consumer surveys
Outside opinion
Delphi method
Opinions of managers and staff
Achieves a consensus forecast

11. Statistical Forecasting: Time Series Model

12. Time Series Forecasting -- using the Past to Develop Future Estimates

13. Time Series Forecasts Trend - long-term movement in data
Seasonality - short-term regular variations in data
Cycle – wavelike variations of more than one year’s duration
Irregular variations - caused by unusual circumstances
Random variations - caused by chance

14. Forecast Variations Trend Cycles Irregular variation 90 89 88
Seasonal variations

15. Naive Forecasts Uh, give me a minute.... We sold 250 wheels last
week.... Now, next week we should sell....
The forecast for any period equals the previous period’s actual value.

16. Naïve Forecasts Simple to use Virtually no cost
Quick and easy to prepare
Data analysis is nonexistent
Easily understandable
Cannot provide high accuracy
Can be a standard for accuracy

17. Uses for Naïve Forecasts
Stable time series data
F(t) = A(t-1)
Seasonal variations
F(t) = A(t-n)
Data with trends
F(t) = A(t-1) + (A(t-1) – A(t-2))

18. Short Run Forecasts
Moving Average Method
Exponential Smoothing

19. Moving Average Method
This method consists of computing an average of the most recent n data values in the time series. This average is then used as a forecast for the next period.
Moving average =  (most recent n data values) n
Moving average usually tends to eliminate the seasonal and random components.

21. Moving Average Method
The larger the averaging period, n, the smoother the forecast.
The ultimate selection of an averaging period would depend upon management needs.

22. Simple Moving Average
Actual
MA5
MA3
High AP forecast has a low impulse response and a high noise dampening ability.

24. Weighted Moving Average Method
Weighted moving average – More recent values in a series are given more weight in computing the forecast.

25. Exponential Smoothing
It is a forecasting technique that uses a smoothed value of time series in one period to forecast the value of time series in the next period. The basic model is as follows:
Ft+1 = aYt + (1-a)Ft
Where:
Ft+1= the forecast of time series for period t+1
Yt = the actual value of the time series in period t
Ft = the forecast of time series for period t
a = the smoothing constant 0£a£1

26. Example 3 - Exponential Smoothing
F2 = F1+.1(A1-F1)
= 42+.1(42-42) = 42
F3 = F2+.1(A2-F2)
= 42+.1(40-42) = 41.8

27. Week 8
102 9
110 10 90 11
105 12 95 13
115 14
120 15 80 16 17
100
Total Errors
133.9
124.4
126
Actual Demand
Forecasts
a = .1
a = .2
a = .3
Forecast Error
Forecast Error
Forecast Error
MAD=13.39
MAD=12.44
MAD=12.60
The smoothing constant a = .2 gives slightly better accuracy when compared to a = .1, and a = .3.

28. Picking a Smoothing Constant
 .1
.4
Actual

30. Forecast Accuracy
Error - difference between actual value and predicted value
Mean Absolute Deviation (MAD)
Average absolute error
Mean Squared Error (MSE)
Average of squared error
Mean Absolute Percent Error (MAPE)
Average absolute percent error

31. MAD, MSE, and MAPE  Actual  forecast MAD = n MSE = Actual forecast)- 1 2   n (
MAPE =
Actual
forecast  n
/ Actual*100) (

32. Example 10

33. Controlling the Forecast
Control chart
A visual tool for monitoring forecast errors
Used to detect non-randomness in errors
Forecasting errors are in control if
All errors are within the control limits
No patterns, such as trends or cycles, are present

34. Sources of Forecast errors
Model may be inadequate
Irregular variations
Incorrect use of forecasting technique

35. Tracking Signal  Tracking signal = (Actual - forecast) MAD
Ratio of cumulative error to MAD
Tracking signal =
(Actual -
forecast)
MAD 
Bias – Persistent tendency for forecasts to be
Greater or less than actual values.

36. Common Nonlinear Trends
Parabolic
Exponential
Growth

37. Trend Projection

38. Trend Projection  (t – Ft)2
The approach used to determine the linear function that best approximates the trend is the least – squared method. The objective is to determine the value of a and b that minimize:
 (t – Ft)2
Where:
t = actual value of time series in period
Ft = forecast value in period t
n = number of period n
t=r

39. Linear Trend Equation Ft = a + bt Ft = Forecast for period t
t = Specified number of time periods
a = Value of Ft at t = 0
b = Slope of the line

40. Calculating a and b b = n
(ty) - t y 2 ( t) a 

41. Linear Trend Equation Example

42. Linear Trend Calculation
y = t a =
812 -
6.3(15) 5 b
5 (2499)
15(812)
5(55)
225
12495
12180
275
6.3
143.5

43. Casual Forecasting Models
Regression
Correlation Coefficient
Coefficient of Determination
Multiple Regression
Autogressive Model
Stepwise Regression

44. Associative Forecasting
Regression - technique for fitting a line to a set of points
Least squares line - minimizes sum of squared deviations around the line

45. Causal Forecasting Models (Regression)
Regression analysis is a statistical technique that can be used to develop an equation to estimate mathematically how two or more variables are related.
Y = bo + b1x
b1 = n xy – x y
n x2 – ( x)2
bo = y - b1x     

46. Linear Model Seems Reasonable
Computed relationship
A straight line is fitted to a set of sample points.

49. Correlation Coefficient
The coefficient of correlation, r, explains the relative importance of the association between y and x. The range of r is from -1 to +1.
r = n xy - x y______________
 [ n x2 – ( x)2][n y2 -( y)2]
Although the coefficient of correlations is helpful in establishing confidence in our predictive model, terms such as strong, moderate, and weak are not very specific measures of a relationship.       

52. Coefficient of Determination
The coefficient of determination, r2, is the square of the coefficient of correlation.
This measure indicates the percent of variation in y that is explained by x.

53. Multiple Regression
Multiregression analysis is used when two or more independent variables are incorporated into the analysis.
In forecasting the sale of refrigerators, we might select independent variable such as:
Y= annual sales in thousands of units
X1 = price in period t
X2 = total industry sales in period t-1
X3 = number of building permits for new houses in period t-1

54. Multiple Regression X4 = population forecast for period t
X5 = advertising budget for period t
Y = bo +b1X1+b2X2+b3X3+b4X4+b5X5

55. Autogressive Models
Regression models where the independent variables are previous values of the same time series
Yt = bo+b1Yt-1+b2Yt-2+b3Yt-3

56. Stepwise Regression
In regular multiple regression analysis, all the independent variables are entered into the analysis concurrently.
In stepwise regression analysis, independent variables will be selected for entry into the analysis on the basis of their explanatory (discriminatory) power.

57. Choosing a Forecasting Technique
No single technique works in every situation
Two most important factors
Cost
Accuracy
Other factors include the availability of:
Historical data
Computers
Time needed to gather and analyze the data
Forecast horizon

58. Exponential Smoothing

59. Linear Trend Equation

60. Simple Linear Regression