Demand Forecasting
Production and Operations Management
Judit Uzonyi-Kecskés
Research Assistant
Department of Management and Corporate Economics
Budapest University of Technology and Economics
[email protected]
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
Forecasting
• What is forecasting?
– 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
Forecasting Methods
• Subjective methods
• Objective methods
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
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
Patterns of Demand
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
Forecasting Stationary Series
• For stationary time series
Dt    t
• Most frequently used methods:
– Moving average
– Simple exponential smoothing
Moving Average
• Forecasting:
1 tN
1
Ft    Di   Dt 1  Dt  2    Dt  N 
N i t 1
N
• 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
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.
Example
The observed demands in the last 7 periods were the
following:
Period
1
2
3
4
5
6
7
Demand
200
250
176
189
224
236
214
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
Example
• Forecast for the third period, if N=2:
1 tN
1
Ft    Di   Dt 1  Dt  2    Dt  N 
N i t 1
N
1
F3   D1  D2  
2
1
  200  250  225
2
• Forecasts for the following periods:
1
1
F4   250  176   213
F6   189  224   206,5
2
2
1
1
F5   176  189   182,5
F7   224  236   236
2
2
1
F8   236  214   225
2
Example
• Multiple-step-ahead forecast
– Last known demands: D6=236 and D7=214.
– Last forecast: F8=225.
• We assume that demand is constant!
F7 ,8  F7 ,9  F7 , 7 n  225
• Suppose that in period 8 we observe a demand of
D8=195, we now need to update the forecasts:
1
F9  F8,9  F8,10  F8,8n   214  195  204,5
2
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
New forecast    last demand  1   last forecast
Simple Exponential Smoothing
• Forecast
Ft    Dt 1  1    Ft 1
• 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
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.
Example
The observed demands in the last 7 periods were the
following:
Period
1
2
3
4
5
6
7
Demand
200
250
176
189
224
236
214
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:
Ft    Dt 1  1     Ft 1
F2    D1  1     F1 
 0.2  200  1  0.2   250 
 40  200  240
Example
F3  0.2  250  0.8  240  242
F4  0.2 176  0.8  242  229
F5  0.2 189  0.8  229  221 F6  0.2  224  0.8  221  222
F7  0.2  236  0.8  222  225 F8  0.2  214  0.8  225  223
Example
• More-step-ahead forecast
– Last known demand: D7=214.
– Last forecast: F8=223.
• We assume that demand is constant!
F7 ,8  F7 ,9  F7 ,7 n  223
• Suppose that in period 8 we observe a demand of
D8=195, we now need to update the forecasts:
F9  F8,9  F8,10  F8,8n  0.2 195  0.8  223  218