1. Demand Forecasting Production and Operations Management
Judit Uzonyi-Kecskés
Research Assistant
Department of Management and Corporate Economics
Budapest University of Technology and Economics

2. Topics Importance of demand forecasting Forecasting methods
Forecasting stationary series (with examples)
Moving average
Simple exponential smoothing
Trend based forecasting methods (with example)
Double exponential smoothing
Seasonal series - Winters model
Evaluating forecasts (with example)
Analyzing the size of errors
Analyzing the validity of the forecasting model

3. Forecasting What is forecasting? Where can be apply?
Predicting the future + information
Where can be apply?
Business/Non- business
Production/ Service
Why is it important?
Risky decison need information
Implication every aspect of operation
Find balance of supply and demand

4. Forecasting Methods
Subjective methods
Objective methods

5. Subjective Forecasting Methods
Based on expert opinion
Personal insight
Panel consensus
Delphi method
Historic analogy
Based on customer opinion
Indirectly: Sales force composites
Directly: Market surveys

6. Objective Forecasting Methods
Casual models
Analyzing the causes of the demand
Forecasting the demand based on the measure of the causes
Time series/projective methods
Analyzing the demand of previous periods
Determining the patterns of the demand
Forecasting the demand based on the information of previous prior periods

7. Patterns of Demand

8. Symbols t: period t (e.g. day, week, month)
Dt: observation of demand in period t
Ft,t+τ: forecast in period t for period t+τ
Ft: forecast for period t

9. Forecasting Stationary Series
For stationary time series
Most frequently used methods:
Moving average
Simple exponential smoothing

10. Moving Average Forecasting: N: number of analyzed periods Large N:
more weight on past data
forecasts are more stable
Small N:
more weight on the current observation of demand
forecasts react quickly to changes in the demand

11. Example
In a car factory the management observed that the demand for the factory’s car is nearly constant. Therefore they forecast the demand with the help of moving average based on the demand information of the last 2 months.

12. Example The observed demands in the last 7 periods were the following:1
200 2
250 3
176 4
189 5
224 6
236 7
214

13. Example
The observed demand in the first two periods was 200 and 250 cars:
D1=200,
D2=250.
The forecast is based on the demand information of the last 2 months: N=2.
The first period when forecast can be performed is period 3: t=3
Dt-1= D3-1 =D2=250
Dt-N= D3-2 =D1=200

14. Example Forecast for the third period, if N=2:
Forecasts for the following periods:

15. Example Multiple-step-ahead forecast
Last known demands: D6=236 and D7=214.
Last forecast: F8=225.
We assume that demand is constant!
Suppose that in period 8 we observe a demand of D8=195, we now need to update the forecasts:

16. Exponential Smoothing
Forecast is a weighted average
Current forecast is based on:
Last forecast
Last value of demand
Smoothing constant (e.g. α, β):
0 ≤ α, β≤ 1

17. Simple Exponential Smoothing
Forecast
α: smoothing constant (0 ≤ α ≤ 1)
Large α:
more weight on the current observation of demand
forecasts react quickly to changes in the demand
Small α:
more weight on past data
forecasts are more stable

18. Example
In a car factory the management observed that the demand for the factory’s car is nearly constant. Therefore they forecast the demand with the help of simple exponential smoothing, and they use α=0.2 value as smoothing constant. The forecast for the first period was 250 cars.

19. Example The observed demands in the last 7 periods were the following:1
200 2
250 3
176 4
189 5
224 6
236 7
214

20. Example The forecast for the first period was 250 cars: F1=250.
The observed demand in the first period was 200 cars: D1=200.
Forecast for the second period, if α=0.1:

21. Example

22. Example More-step-ahead forecast Last known demand: D7=214.
Last forecast: F8=223.
We assume that demand is constant!
Suppose that in period 8 we observe a demand of D8=195, we now need to update the forecasts:

23. Comparison of the Two Methods
Similarities
Both assume that demand is stationary
Both use a single parameter (N or α)
Differences
Number of directly used demand data
Number and weights of indirectly used demand data

24. Trend examples in real life

25. Trend-based Forecasting Methods
For time series containing additive trend
Most frequently used methods:
Regression analysis (linear or non-linear)
Double exponential smoothing

26. Double Exponential Smoothing
Holt’s method
Forecast
α, β: smoothing constants (0≤α,β≤1)

27. Example
In a furniture factory the management observed that the demand for the factory’s products is progressive and doesn’t show seasonal pattern. Therefore they forecast the demand with the help of Holt’s method, and they use α=0.4 and β=0.5 values as smoothing constants. In period zero the management has the following initial values: S0=200 and G0=10.

28. Example The observed demands in the last 7 periods were the following:1
210 2
220 3
260 4
298 5
353

29. Example The initial values: S0=200 and G0=10.
The observed demand in the first period was 200: D1=210.
Forecast for the second period, if α=0.2; β=0.1:

30. Example
Further steps:

31. Example

32. Example Multiple-step-ahead forecast Last known demand: D5=353.
Last data of forecasting: S5=320, G5=35, F6=355.
Forecast for the next 4 periods from period 7:
There also can be need to update forecasts.