Demand Forecasting LEARNING OBJECTIVES IEEM Understand commonly used forecasting techniques. 2. Learn to evaluate forecasts

Transcription

1 IEEM 57 Demand Forecasting LEARNING OBJECTIVES. Understand commonly used forecasting techniques. Learn to evaluate forecasts 3. Learn to choose appropriate forecasting techniques

2 CONTENTS Motivation Forecast Evaluation Qualitative Methods Causal Models Time-Series Models Summary PRODUCTION AND OPERATIONS MANAGEMENT 3 Product development Purchasing Manufacturing Distribution Demand fulfillment long term Product portifolio Supply networ design Partner selection Facility location and layout Distribution networ design medium term short term Derivative product development Adaptions Current product support Supply contract design Materials ordering Aggregate planning Demand forecasting is the starting point of all planning and control! Production control Operations scheduling Distribution planning Transport planning Demand forecasting Inventory management Fulfillment implementation

3 WAL-MART EXPERIENCE SITUATION Warner-Lambert Wal-Mart Store... Situation 996 Forecast errors of 60% 5% savings possible if forecast accuracy were improved (corresponding to $79 billion in US) No less than 0,000 SUs per store Store 500 Other suppliers WAL-MART EXPERIENCE SITUATION NOW 5 Collaborative forecasting and replenishment software installed Initial forecasts generated by Wal-Mart Forecasts refined by Warner-Lambert Inventory cost reduced by 70% Service levels improved from 96% to 99% System adapted by others 3

4 SOME CHARACTERISTICS OF FORECASTS 6 Forecasts are usually wrong; nowledge of the forecast error maes forecasts more meaningful Aggregate forecasts are more accurate than individual forecasts Short-term forecasts are more accurate than long-term forecasts Choosing appropriate aggregation levels, time horizons, and forecasting techniques is crucial CONTENTS 7 Motivation Forecast Evaluation Qualitative Methods Causal Models Time-Series Models Summary 4

5 TWO FORECASTS 8 Actual Forecast Forecast Sales Forecast quality Which forecast is better? How can we evaluate the forecasting performance? 7 6 Aug-0 Sep-0 Oct-0 Nov-0 Dec-0 FORECAST ERROR Actual Forecast 9 Sales 0 9 A t Forecast error ε t f t -A t ε ε 3 ε 4 ε 5 ε f t Time A t : Actual value in period t f t : Forecast for period t 5

6 MEASURES OF FORECAST ACCURACY 0 Mean absolute deviation T MAD εt T t Mean squared error T MSE εt T t Mean absolute percentage error T εt MAPE T A t t MEASURING FORECAST ACCURACY FORECAST t A t f t ε t ε t ε t ε t A t MAD MSE MAPE 6

7 MEASURING FORECAST ACCURACY FORECAST t A t f t ε t ε t ε t ε t A t MAD MSE MAPE EVALUATIONS OF FORECASTS 3 Forecast Forecast MAD 0.9 MAD.06 MSE.430 MSE.30 Evaluation Forecast has smaller MAPE 5.0% MAPE 5.4% Forecast has smaller 7

8 BIAS IN FORECASTS 4 Error ε t 4 Forecast Forecast t Biased: Persistent tendency for forecasts to be greater or smaller than the actual values (E(ε t ) > 0 or < 0) Unbiased: E(ε t ) 0 Forecast seems biased Forecast seems unbiased -4 BIAS IN FORECASTS - CONTINUED t Σ i ε i t Forecast Forecast An alternative test: judge bias by plotting t Σ ε i for t,, 3, i instead of plotting ε t Forecast seems biased Forecast seems unbiased 5-0 8

9 REASON FOR BIAS IN FORECASTS 6 If relevant elements are not considered in the forecast, the forecast can become biased. These elements can include: Linear trend or non-linear trend Seasonality Eternal factors, such as promotion and advertisement CONTENTS 7 Motivation Forecast Evaluation Qualitative Methods Causal Models Time-Series Models Summary 9

10 QUALITATIVE METHODS 8 Qualitative Methods Sales Force Estimate Eecutive Opinion Maret Research Application Used to generate forecasts if historical data are not available (e.g., introduction of new product) Used to modify forecasts generated by other approaches (e.g., considering information not included in quantitative methods) Delphi Method SALES FORCE ESTIMATE 9 Rationale Sales force is close to customer and has good information on future demands Approach Members of sales force periodically report their estimates. These estimates are then aggregated to generate the overall forecast Main advantages Sales force nows customer well Sales territories are typically divided by district/region. Sales forecasts can be broen down correspondingly 0

11 SALES FORCE ESTIMATE CONTINUED 0 Main drawbacs Bias of sales force - Might have incentives to overestimate sales or underestimate sales - Might naturally be optimistic or pessimistic Sales force does not always have all information necessary to generate forecast - Features of products launched in future - Preferences of customers in new maret segments Typical application Short-term and medium-term demand forecasting EXECUTIVE OPINION Rationale Upper-level management has best information on latest product developments and future product launches Approach Small group of upper-level managers collectively develop forecasts Main advantages Combine nowledge and epertise from various functional areas People who have best information on future developments generate the forecasts

12 EXECUTIVE OPINION CONTINUED Main drawbacs Epensive No individual responsibility for forecast quality Ris that few people dominate the group Typical applications Short-term and medium-term demand forecasting MARET RESEARCH 3 Rationale Ultimately, consumers drive demand Approach Determine consumer interests by creating and testing hypotheses through data-gathering surveys:. Design questionnaire. Select customer sample 3. Conduct survey (e.g., telephone, mail, or interview) 4. Analyze information and generate forecast

13 MARET RESEARCH CONTINUED 4 Main advantages Systematic and fact-based approach Ecellent accuracy for short-term forecasts Good accuracy for medium-term forecasts Main drawbacs Epensive Require considerable nowledge and sills Sometimes validity not guaranteed due to low response rates: For mailed questionnaires response rate often < 30% Typical application Short-term and medium-term demand forecasting DELPHI METHOD 5 Rationale Anonymous written responses encourage honesty and avoid that a group of eperts are dominated by only a few members Approach Coordinator sends initial questionnaire Each epert writes response (anonymous) Coordinator performs analysis Coordinator sends updated questionnaire No Consensus reached? Yes Coordinator summarizes forecast 3

14 DELPHI METHOD CONTINUED 6 Main advantages Generate consensus Can forecast long-term trend without availability of historical data Main drawbacs Slow process Eperts are not accountable for their responses Little evidence that reliable long-term forecasts can be generated with Delphi or other methods Typical application Long-term forecasting Technology forecasting LONG-TERM FORECASTS ARE OFTEN WRONG! 7 photographic telegraphy permits transmission of facsimile of any form or writing or illustration Jules Verne, 863 The telephone is a toy no one would want to use. Rutherford B. Hayes, 876 The phonograph is not of any commercial value. Thomas A. Edison, 880 The world maret for computers is 5. Thomas J. Watson, 948 There is no reason for any individual to have a computer in his home. en Olsen, 977 4

15 CONTENTS 8 Motivation Forecast Evaluation Qualitative Methods Causal Models Time-Series Models Summary CAUSAL MODELS 9 Causal Models Linear Regression Application Used to forecast the performance (demand, profit, etc.) of a business investment based on the observed data of eisting and similar business activities Non-linear Regression 5

16 LINEAR REGRESSION: A SIMPLE EXAMPLE 30 A company is going to open a new store with nearby population of 0 thousands. The company would lie to predict the daily demand. The company has collected data (i.e., nearby population and daily demand) of stores opened in other places. Population Demand ? Demand Population around the new store Population LINEAR REGRESSION: GENERAL SETTING 3 Have obtained data of eisting and similar business activities (y ;,,, m ) for,,, m: # predictive variables : # eisting activities demand population # competitors store-size Predicted variable Predictive variables Can obtain values of the predictive variables of the new business To predict the predicted variable of the new business 6

17 LINEAR REGRESSION: OBJECTIVE 3 Idea Find a linear function that represents the predicted variable y as a function of predictive variables,,, m and best fits the observed data Objective Find the coefficients b 0, b,, b m of the linear function y(,,, m ) b 0 + b + b + + b m m such that the sum of squared errors is minimized SSE [y(,,, m ) - y ] LINEAR REGRESSION: ANALYSIS SSE [ y(,,...,m ) y ] ( b0 + b + b bmm y ) T b A M A b y A b y where T ( A A) T b y The optimal value of T M Ab + y L L L T M m m m y b satisfies b0 y b y, b b, y M M y bm T ( A A) b A T y 33 7

18 8 34 LINEAR REGRESSION: EXPRESSIONS m m 0 m m m m m m m y y y y b b b b M M L M M M L L L 35 EXPRESSIONS FOR m When m (i.e., when there is only one predictive variable), the epression of b 0 and b can be written as 0 y y b y y b

19 EXAMPLE: m () 36 Observed data and analysis y y , , , , , , , , ,90 3,70,796 35,90 Coefficients,796, ,90 b 0, ,90 3,70 b, EXAMPLE: m () Demand y() b 0 + b Question: What demand would we epect from investing in a business with a nearby population 0 thousand? Answer: y(0) Population 9

20 EXAMPLE: m () 38 Observed data and analysis y y y 30 0, ,00 96,00 3,74, , , , ,400 7,359,800 5,65 39,578,0 0, ,464,00,464,00 3,080,00 8,89 74,049,90 9, ,664,00,664,00,758,00 9,043 69,39,0 3,70 7.0,54,400,54,400 5,366,400 7,86 96,34,490 3, ,0,00,0,00 0,740,800,44 6, , , ,400 6,66,00 3,377 36, , , ,600,68,400 5,44 7,37,90, ,664,00,664,00 5,88,300 9,907 94,34 480, ,400 30,400 5,84,800,57 34, , ,600 57,600,980, , , ,500 30,500 5,0,500,733 9,37 0,680 7, ,405,800,405,800 8,97,800 66,03 704,69 EXAMPLE: m () 39 Coefficients 0,680 0,680,405,800 7,830 8,97,800 7,830 b ,97,80 0 b 66,03,40,43, 500 b 704,69 y(, ) Question: What sales volume (i.e., y) would we epect from a store with one thousand customers per day (i.e., ) and a size of one thousand square meters ((i.e., )? Answer:,000 0,000 y y(, ) b 0 + b + b 0

21 NON-LINEAR REGRESSION 40 Idea Linear regression approaches can be often applied to non-linear regression with some modification. In this case, non-linear equations only need to be transformed to linear equations. Here we limit our consideration to some special forms of non-linear regression with one predictive variable. Non-linear equations Eponential y b 0 ep(b ) Power y b 0 ^b Logarithmic y b 0 + b ln() EXAMPLE: y() b 0 ep(b ) () 4 y b 0 ep(b ) (non-linear equation)

22 EXAMPLE: y() b 0 ep(b ) () 4 Observed data y y ln(y ) Figure in (, y) space - linear y y EXAMPLE: y() b 0 ep(b ) (3) 43 Coefficients in (, y) space b 0 0 Figure in (, y) space non-linear y b 0 y

23 COMMONLY USED TRANSFORMATIONS 44 Non-linear function Transformation Linear form Eponential y ln(y) y b 0 + b y b 0 ep(b ) b 0 ln(b 0 ) Power y b 0 ^b Logarithmic y b 0 + b ln() CONTENTS 45 Motivation Forecast Evaluation Qualitative Methods Causal Models Time-Series Models Summary 3

24 TIME-SERIES MODELS 46 Demand Constant Level Models Time Time-series Models Linear Trend Models Seasonality Models TIME-SERIES MODELS 47 Constant Level Models Naïve Forecast Time-series Models Linear Trend Models Moving Averages Eponential Smoothing Seasonality Models 4

25 NAÏVE FORECAST 48 Idea The forecasts for future periods equal the actual value of the demand that is just observed in the current period f t+τ A t τ,, t: current period τ: forecasting lag A t : demand observed in the current period t f t+τ :forecast for a future period t + τ Main characteristics Easy to prepare and easy to understand Benchmar for more advanced forecasting approaches Often low accuracy MOVING AVERAGES (MA) 49 Idea The forecasts for future periods equal the average value of demands of the previous m periods t ft+ τ + A,, i t m i τ m m: number of periods to average demands Main characteristics Puts equal weight on m most current observations Lags behind trend, if any trend eists Requires epertise in choosing the value of m 5

26 EXPONENTIAL SMOOTHING (ES) 50 Idea The forecasts for future periods equal the eponentially weighted average of demands of previous periods F t αa t + ( α)f t- f t+τ F t τ,, F t : level estimate made at the end of period t α: smoothing parameter, 0 α Main characteristics More sensitive to recent observations if α is larger Lags behind trend, if any trend eists Requires epertise in choosing the value of α 5 EXPONENTIAL SMOOTHING: WHY EXPONENTIAL The forecast equation can be re-written as: F t αa t + ( α)f t- The new level estimate is the weighted average of most recent observation and previous level estimate" F t- αa t- + ( α)f t- F t- αa t- + ( α)f t-3 Repetitive substitution yields F t αa t + α( α)a t- + α ( α)a t "Declining set of weights is put on all previous observations" 6

27 WEIGHTS IN EXPONENTIAL SMOOTHING 5 Weights 0.0 Where the name "Eponential Smoothing" Comes from α current 0.00 t-8 t-7 t-6 t-5 t-4 t-3 t- t- t EXAMPLE 53 One-step forecast τ period Actual Naïve MA MA ES ES m m3 α0. α

28 COMPARING NAÏVE FORECAST, MA, AND ES 54 Assumptions Demand in period t is generated by a level value µ plus a noise e t e t is normally distributed with mean 0 and variance σ e t is independently distributed over periods One-step forecast τ Forecast errors Naïve Forecast Moving averages Eponential smoothing Forecasts f t+ A t ft i m + t t m + A i f + α(- α) A t i 0 t i i Forecast errors ε NF t+ A t A t+ t ε MA t+ t m ε t+ ES A i m i A + t+ i α( - α) A t i A i 0 t+ FORECAST ERROR OF MA 55 Mean MA t t E[ εt ] E A A E A i t m i t i t m i t m m mµ - µ 0 m [ ] E[ A ] Variance MA t t Var[ εt ] Var A A Var i t m i t i t m i t m m m + mσ + σ σ m m [ A ] + Var[ A ] 8

29 PROPERTIES OF FORECAST ERROR OF MA 56 Distribution of forecast error MA m + ε t+ ~ N0, σ m Property The variance of forecasting error m + σ m gets smaller when m gets large Why would not we always choose a very large value for m? Because we do not fully believe the assumption of stationary demands, i.e., that µ will not change over time FORECAST ERROR OF ES 57 Mean E[ ε ES t+ ] E i 0 i 0 i 0 Variance Var[ ε ES t+ ] Var i 0 α (-α) i i [ α(-α) A t-i A t+ ] α (-α) Var[ A t-i] + Var[ A t+ ] i 0 i α(-α) µ - µ 0 i i [ α(-α) A t-i A t+ ] α(-α) E[ A t-i] E[ A t+ ] i σ + σ -α σ i 0 9

30 PROPERTIES OF FORECAST ERROR OF ES 58 Distribution of forecast error ES ε t+ ~ N0, σ - α Property The variance of forecasting error α - σ gets smaller when α gets small Why would not we always choose a very small value for α? Because we do not fully believe the assumption of stationary demands, i.e., that µ will not change over time and we would sometimes prefer to give recent observations more weight than older observations TIME-SERIES MODELS 59 Constant Level Models Double Eponential Smoothing (Holt) Time-series Models Linear Trend Models Regression Analysis Seasonality Models 30

31 DOUBLE EXPONENTIAL SMOOTHING (DES) 60 Idea The forecasts for future periods contain both the level estimate and the trend estimate based on the demands of previous periods F t αa t + ( α)(f t- + T t- ) T t β(f t -F t- ) + ( β)t t- f t+τ F t + τt t τ,, F t : level estimate made at the end of period t T t : trend estimate made at the end of period t α: smoothing parameter for the level estimate, 0 α β: smoothing parameter for the trend estimate, 0 β Main characteristics More sensitive to recent observations if α and β are larger Captures trend Requires epertise in choosing the values of α and β INTERPRETATION OF PARAMETERS 6 f t+τ F t + τt t F t αa t + ( α)(f t- + T t- ) A t F t T t Weighted average of just observed demand and one-step forecast made in the previous period F t- +T t- T t- T t β(f t -F t- ) + ( β)t t- F t- t- t t+ Weighted average of current estimate of slope and pervious estimate of slope Current period 3

32 EXAMPLE 6 α 0., β 0. period Actual F t T t One-step Two-step Three-step τ τ τ Level and trend estimates made at the end of period 8,,3-step forecasts made at the end of period 8 REGRESSION ANALYSIS 63 Causal approach Time-series approach Demand Demand Population Time 3

33 LINEAR TIME-SERIES REGRESSION 64 Idea The optimal values of b 0 and b that best fits the demands of the previous periods are b0 A t+ - ( + )b b A + ( ) : number of periods to fit demands t+ A t+ Thus the forecasts are f t+τ b 0 + b ( + τ) τ,, Main characteristics Requires epertise in choosing the value of EXAMPLE 65 4 period Actual b 0 b One-step Two-step Three-step τ τ τ Estimates of parameters b 0,b made at the end of period 8,,3-step forecasts made at the end of period 8 33

34 TIME-SERIES MODELS 66 Constant Level Models Time-series Models Linear Trend Models Triple Eponential Smoothing (Winters) Seasonality Models Regression Analysis (not covered in class) SEASONALITY IN TOY INDUSTRY 67 Percentage of annual demand 40% Quarter one Quarter two Quarter three Quarter four 30% 0% 0% 0%

35 TRIPLE EXPONENTIAL SMOOTHING (TES) 68 Assumptions Each season (e.g., a year) contains N periods (e.g., 4 quarters or months) A seasonal factor c t represents how much demand in period t is above/below overall average The underlying model is A t (b 0 + b t)c t, c t c t+n, c + c + + c N N demand de-seasonalized part (linear trend) seasonal factor Eample: N 4, c 0.65, c 0.75, c 3.3, and c 4.3 TRIPLE EXPONENTIAL SMOOTHING (TES) Idea The forecasts for future periods contain the de-seasonalized level estimate, the de-seasonalized trend estimate, and seasonal-factor estimate based on the demands of previous periods F t αa t /c t-n + ( α)(f t- + T t- ) T t β(f t -F t- ) + ( β)t t- c t γa t /F t + ( γ)c t-n f t+τ (F t + τt t ) c t+τ-n τ,,, N 69 F t : de-seasonalized level estimate made at the end of period t T t : de-seasonalized trend estimate made at the end of period t c t : seasonal-factor estimate made for period t α: smoothing parameter for the level estimate, 0 α β: smoothing parameter for the trend estimate, 0 β γ: smoothing parameter for the seasonal-factor estimate, 0 γ Main characteristics More sensitive to recent observations if α, β, and γ are larger Captures both trend and seasonality Requires epertise in choosing the values of α, β, and γ 35

36 INITIALIZATION PROCEDURE 70. Select season (i.e., N periods) of data for initialization. For period N (the last period of the first season), set F N (A + A + + A N )/N T N 0 c i A i /F N 3. Start forecasting for period N+ EXAMPLE: INITIALIZATION 7 Quarter Sales Level Trend Season-fac One-step estimate estimate estimate forecast t A t F t T t c t Q Q Q Q Q

37 EXAMPLE: RESULT 7 Quarter Sales Level Trend Season-fac One-step estimate estimate estimate forecast t A t F t T t c t Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q CONTENTS 73 Motivation Forecast Evaluation Qualitative Methods Causal Models Time-Series Models Summary 37

38 SUMMARY 74 Demand planning/forecasting is the starting point of all planning The performance of forecasting approach can be evaluated based on various metrics -MAD -MSE - MAPE Various forecasting approaches eist. Which one is appropriate depends on the situation. The approaches covered in class can be classified as - Qualitative methods, - Causal models, or - Time-series models ANNOUNCEMENTS 75 For the topic of Demand Forecasting, read Section