Demand Forecasting Production and Operations Management Judit Uzonyi-Kecskés Research Assistant Department of Management and Corporate Economics Budapest University of Technology and Economics uzonyi-kecskes@mvt.bme.hu

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? 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

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 Most frequently used methods: Moving average Simple exponential smoothing

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

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: 1 200 2 250 3 176 4 189 5 224 6 236 7 214

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: Forecasts for the following periods:

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:

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

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

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: 1 200 2 250 3 176 4 189 5 224 6 236 7 214

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:

Example

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:

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

Trend examples in real life

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

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

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.

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

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:

Example Further steps:

Example

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.