1. MS 401 - Production and Service Systems Operations Forecasting
Murat Kaya
FENS, Sabanci University

2. Predicting the Future
“My concern is with the future since I plan to spend the rest of my life there” C. F. Kettering
Hertz: How many cars will be rented during March 2008?
Apple: How many iPod Nano 8GB will be sold in 2008?
Why is it important to know the answers to these questions?

3. If Forecasting Fails
Cisco could not forecast the demand for networking equipment correctly
result: lost $2.5 billion due to unsold products
Volvo – Green car example (mid 1990s)
excessive amount of green color cars in the middle of the year
to sell these cars, marketing offered special promotions and discounts

4. Forecasts Forecast: An estimate of the future level of some variable
Characteristics of Forecasts
They are usually wrong
the planning systems that use forecasts should be robust
A good forecast is more than a single number
include some measure of anticipated error
Aggregate forecasts are more accurate
The longer the forecast horizon, the less accurate the forecast will be
Forecasts should not be used to the exclusion of known information
some information may not be present in the past history

5. Time Series Methods
Time series: A collection of observations of some economic or physical phenomenon drawn at discrete points in time
The idea: Information can be inferred from the pattern of past observations and can be used to forecast the future value of the series
Patterns in time series
trend: tendency of a time series to exhibit a stable pattern of growth or decline
seasonality: having a pattern that repeats in fixed intervals
cycles: similar to seasonality, but the length and the magnitude of the cycle may vary
randomness: when there is no recognizable pattern to the data

6. Time Series Patterns
Copyright © 2001 by The McGraw-Hill Companies, Inc

7. Evaluating Forecasts

8. Random versus Biased Forecast Errors
Copyright © 2001 by The McGraw-Hill Companies, Inc

9. Forecasting Stationary Time Series
Stationary time series: Each observation can be represented by a constant plus a random fluctuation
Two methods
moving averages (MA)
exponential smoothing (ES)

10. Moving Averages (MA)
A moving average of order N is the arithmetic average of the most recent N observations
When calculating the forecast for the following period (period t+1), we do not need to recalculate the N-period average because
Example 2.2

11. Moving Average Lags Behind the Trend

12. Exponential Smoothing (ES)
The current forecast is the weighted average of the current observation of demand and the last forecast
High α: forecast reacts better, however it is less stable

13. Weights in Exponential Smoothing
Copyright © 2001 by The McGraw-Hill Companies, Inc

14. Exponential Smoothing with Different α Values
Copyright © 2001 by The McGraw-Hill Companies, Inc

15. The forecasts are quite stable due to low α
Example 2.3 from Nahmias
Observed number of failures:
200, 250, 175, 186, 225, 285,
Assume F1 was (we need a starting value)
Using α=0.1
The forecasts are quite stable due to low α

16. In-Class Exercise
Handy, Inc. produces a calculator that experienced the following monthly sales history for the first four months of the year:
Jan:23.3; Feb: 72.3; March: ; April: 15.5
If the forecast for January was 25, determine the one-step-ahead forecasts for February, March, April and May using exponential smoothing with α=0.15
Repeat the calculations using α=0.40
Compute the MSEs for the forecasts in parts (a) and (b)

17. Solution - 1
Ft = Dt (1-)Ft-1

18. Solution - 2

19. Similarities Between Moving Averages and Exponential Smoothing
Stationary demand assumption
can also handle shifts in demand (will adjust)
Single parameter: N, α
small N or large α results in
greater weight on current data
more responsive forecasts
Not effective in catching trends
both lag behind trends

20. Differences Between Moving Averages and Exponential Smoothing
ES assigns weight to all past data points
MA uses only the latest N
ES requires only the latest data point
MA requires to save N past data points

21. Forecasting Time Series with Trend
Two methods
regression analysis (we will not cover)
fits a straight line to a set of data
double exponential smoothing (Holt’s method)
simultaneous smoothing on the series and the trend

22. Double Exponential Smoothing Using Holt’s Method
Intercept
Slope
Initialization issue: The best way is to use some initial period data to estimate the initial intercept (S0) and slope (G0)

23. Example 2.5 from Nahmias
Observed number of failures: 200, 250, 175, 186, 225, 285, 305, 190
Assume S0 = 200, G0 = Use α=0.1, β=0.1 t
Ft-1,t (forecasted)
Dt (actual)
St (intercept)
Gt (slope)
---
200.0
10.0 1
210.0
200
209.0
9.9 2
218.9
250
222.0
10.2 3
232.2
175
226.5
9.6 4
236.1
186 … 5
240.3
225 6
247.7
285
Multi-step ahead forecast: F2,5=S2+(3)G2=222+(3)(10.2)=252.6

24. Forecasting Seasonal Series
A seasonal series is a series that has a pattern repeating every N periods (length of the season)
Note that this is different than using “season” to refer to a time of the year
To model seasonality, use seasonal factors:
ct represents the average amount that the demand in the tth period of the season is above or below the overall average
We will study the Winter’s method
triple exponential smoothing

25. Winter’s Method: Seasonal Series with Increasing Trend
Copyright © 2001 by The McGraw-Hill Companies, Inc

26. Winter’s Method
Assume a model of the form
Trend
Seasonal factors

27. Winter’s Method: Initialization Procedure
Check Nahmias, page 85 for details
Use at least two seasons of data (2N data)
Calculate the sample means for the two seasons V1, V2
Calculate the initial slope estimate G0
Calculate the initial intercept estimate S0
Calculate the initial seasonal factors
find the average of each seasonal factor
normalize the seasonal factors (so that they sum up to 1)

28. Example 2.8 from Nahmias The data set: 10, 20, 26, 17, 12, 23, 30, 22
Initialize
Suppose that at time t=1, we observe D1=16. Update the equations using α=0.2, β=0.1, γ=0.1
Suppose that we observe one full year of demand given by D1=16, D2=33, D3=34, D4=26. Update the equations again
Season 1
Season 2

29. Seasonal Demand, No Trend
Copyright © 2001 by The McGraw-Hill Companies, Inc

30. Affecting the Demand
“The best way to forecast the future is to create it”
Peter Drucker
“Forecasting the demand” versus “demand planning”, or “demand management”
Firms can “affect” their demand through their actions
promotions
sales effort
Encourages the retailers / wholesalers to “forward buy”
What are the effects of past promotions in the health of forecasting data?

31. Some Practical Issues Sales data versus demand data
how can a firm capture “lost sales” ?
Forecasting demand for a new product is difficult
will it generate demand, or will it steal demand from existing products?
Forecasting assumes that history represents future. What if there are some external changes?
a new competitor
Slow-moving items are hard to forecast
sparse data