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.

Evaluating Forecasts There are almost always errors in forecasts Random effects, noises Inappropriate forecasting methods Analysis of the size of forecasting errors the validity of forecasting models

Forecast Error Difference between the forecasted value for a period and the actual demand for the same period Covers only one period Does not give information about the acceptability of the forecasting method

Mean Error The average error during a term of n periods Positive and negative errors cancel each other Measures bias: If ME is positive, the forecast is over-estimated If ME is negative, the forecast is under-estimated

Absolute Error Measures Measures of forecasts accuracy during n periods Mean absolute error Mean squared error Positive and negative errors cannot cancel each other Do not give information about the relative size of error

Mean Absolute Percentage Error Arithmetical average of percentage error of n periods Gives information about the average, relative size of the absolute error observed during several periods

Example A hotel makes the following forecasts for rooms needed for a month and compares these with actual bookings. Period Demand Forecast 1 100 110 2 130 169 3 150 135 4 140 168 5 121

Example First determine the forecast error in each period Period Demand Forecast Error 1 100 110   2 130 169 39 3 150 135 -15 4 140 168 28 5 121 11

Example Determine the presented error measures after period 5 (t=5, T=4)

Example

Validity of Forecasting Method Analyzing the validity of the forecasting method used Signs that forecast is inappropriate will be inappropriate in the immediate future Tracking signal will be used Monitoring the size of tracking signal values the tendency of tracking signal values

Tracking Signal Moving sum of forecast error in period t Mean absolute error in period t Tracking signal in period t

Monitoring the Tracking Signal Monitoring size Monitoring tendency Tracking signal diagram Typical patterns: Small-scale, random alternating near to zero Increasing trend Decreasing trend

Example We have the following forecast and demand data. Evaluate the validity of forecast model. Period Demand Forecast 1 100 110 2 126 130 3 124 120 4 129 125 5 135 115

Example Determine the value of tracking signal in each period Period Dt Ft et MSFEt |et| MAEt TSt 1 100 110   2 126 130 4 3 124 120 -4 129 125 -1 5 135 115 -20 -24 20 8 -3

Example Draw the tracking signal diagram Evaluate the validity of forecasting method applied Only few data were available Does not step out of control borders Decreasing trend, systematic undervaluation There is a negative trend instead of constant demand, there is a constant demand instead of positive trend, etc.

Potential questions in the exam Name subjective forecasting methods In which life cycle period are subjective/objective methods used? Name the similarities/differences between moving average and exponential smoothing. Name differences between forecasts made by simple exponential smoothing(moving average) with a small and a large α (N) value? Name three different forecasting errors

Potential exercises in the exam Give forecast using moving average Give forecast using exponential smoothing Give forecast using Holt model Compare two methods Determine the values of forecasting errors Determine and explain the values of tracking signal You can find examples for these in the presentation!