Characterizing retail demand with promotional effects for model - PowerPoint PPT Presentation

Characterizing retail demand with promotional effects for model selection Patrícia Ramos, José Oliveira, Robert Fildes, Shaohui Ma INESC TEC, Lancaster Centre for Forecasting, Jiangsu University of Science and Technology

Outline • Motivation • Retail sales dataset • Demand forecasting models • Experimental design • Forecasting results • Clustering analysis results • Conclusions ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 2

Retail business • Increasing product variety with decreasing life cycles makes sales at the SKU level in a particular store difficult to forecast as – times series for these items tend to be short and often intermittent – there are often thousands of different SKUs • Retailers are increasing their marketing activities such as promotions • Demand is usually substantially higher during promotions leading to potential stock-outs due to inaccurate forecasts • An automated and reliable multivariate forecasting system is required ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 3

Key questions Forecasts needed on a weekly or daily basis • Which forecasting models perform best on weekly data with promotional information? The issue: selecting a best model for sub-sets of SKUs • Can we identify a best model for groups of time series with common “features”? • Which “features” are relevant in the choice of the model? • How does this compare with ‘individual selection’? ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 4

Outline • Motivation • Retail sales dataset • Demand forecasting models • Experimental design • Forecasting results • Clustering analysis results • Conclusions ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 5

Pingo Doce Retailer The largest food distribution • group in Portugal 409 stores • Around 130M SKUs • ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 6

The dataset Promotional activity of some • Daily SKU information between Jan 2012 categories of fast moving goods and Apr 2015 (1211 days/173 weeks) MEAN Units sold CATEGORY PERCENTAGE – OF WEEKS Price – FRESH FISH AQUACULTURE 49.42 • Selection of SKUs from the 6 main areas WILD FRESH FISH 45.86 TOMATO 33.81 (93% of daily sales total volume) FRESH PORK MEAT 24.43 Perishables, grocery, beverage, cleaning – PEPPER 23.41 products and personal products LETTUCE 19.37 LIQUID YOGURT 16.19 • Selection of a store with the largest BEER WITH ALCOHOL 12.43 dimension FRESH VEGETABLES 10.12 BAKED BREAD 8.09 Fast moving goods (SKUs with sales on • FROZEN COD 7.23 100% of the weeks) CONFECTIONERY 6.64 PASTEURIZED CREAM 5.37 Data sample • PASTRY GOODS 4.78 988 SKUs – EGGS 3.85 – 203 categories PAPER NAPKINS 2.89 AIR FRESHENER 1.73 – Intense promotional activity NATURAL FLOWERS 0.52 – Seasonal and non-seasonal ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 7

Outline • Motivation • Retail sales dataset • Demand forecasting models • Experimental design • Forecasting results • Clustering analysis results • Conclusions ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 8

Forecasting models Univariate models (4) • – ETS 1 – TBATS 2 – ARIMA 2 – SNaïve Multivariate models (7) • – LASSO 3 • Regressors (1+50) – log(Sales): t-1 – Price: t, t-1 – Relative discount*: t, t-1 – Promotion days in the week: t, t-1 – Last week of the month: t, t-1 – 13 Calendar events: some with t+1, t, some with t-1 *relative discount = (regular price - price with discount)/regular price 1- smooth R package, 2- forecast R package, 3- glmnet R package ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 9

Forecasting models • Multivariate models (cont.) – TBATS & LASSO 2,3 • Three stages – 1º Fit a TBATS model and forecast – 2º Apply LASSO to the residuals with the regressors and forecast – 3º Add both forecasts – TBATSX 2,3 • Three stages – 1º Fit a TBATS model and extract the components – 2º Apply LASSO with the TBATS components and the regressors as exogenous variables – 3º Forecast 2- forecast R package , 3- glmnet R package ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 10

Forecasting models • Multivariate models (cont.) – ETSX 1 • Regressors included as Principal Components – ARIMA Fourier 2 • Seasonality handled with Fourier terms – ARIMAX 2 • Regressors included as Principal Components – ARIMAX Fourier 2 • Seasonality handled with Fourier terms • Regressors included as Principal Components 1- smooth R package, 2- forecast R package ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 11

Outline • Motivation • Retail sales dataset • Demand forecasting models • Experimental design • Forecasting results • Clustering analysis results • Conclusions ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 12

Experimental design • Data (173 weeks) split into – training set (121 weeks) – test set (52 weeks ~30%) • Annual seasonality (frequency = 52) • Rolling forecast origin with 1-step ahead • Fit a model using the first training set • Re-estimate the parameters of the fitted model at each forecast origin and use it to forecast • Error measures – MAPE, MdAPE – MRMAE, MdRMAE, GMRMAE, MRRMSE, MdRRMSE, GMRRMSE (SNaïve holdout forecasts used as benchmark) – MASE, MdASE (scaled by SNaïve forecasts of the in-sample) ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 13

Outline • Motivation • Retail sales dataset • Demand forecasting models • Experimental design • Forecasting results • Clustering analysis results • Conclusions ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 14

Main Results Method Avg Rank MAPE MdAPE GMRMAE GMRRMSE MASE MdASE TBATSX 1.50 36.92 20.62 0.59 0.60 0.67 0.44 TBATS & LASSO 2.83 36.44 21.47 0.61 0.62 0.69 0.45 ARIMAX Fourier 3.17 35.58 21.61 0.61 0.63 0.69 0.45 ETSX 3.33 38.26 21.59 0.61 0.62 0.69 0.45 ARIMAX 4.17 35.77 21.80 0.62 0.63 0.70 0.45 ARIMA Fourier 6.25 38.32 22.25 0.66 0.69 0.76 0.47 TBATS 7.25 39.06 22.74 0.67 0.70 0.76 0.47 ARIMA 7.83 39.83 22.68 0.67 0.71 0.78 0.47 ETS 9.08 45.44 23.43 0.69 0.70 0.80 0.49 LASSO 9.58 40.74 22.77 0.73 0.71 0.88 0.61 SNAIVE 11.00 68.90 34.17 1.00 1.00 1.10 0.71 Univariate models perform worse than correspondent multivariate • models TBATSX is the best model based on the average rank • • Seasonality handled with Fourier terms is preferred for ARIMA • LASSO has a relatively poor performance indicating that the dynamics of the series is essential and difficult to integrate in an ADL model All models perform better than the benchmark • ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 15

Outline • Motivation • Retail sales dataset • Demand forecasting models • Experimental design • Forecasting results • Clustering analysis results • Conclusions ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 16

Characteristics/features for time series • ACF1 : first order autocorrelation of Rt obtained from STL decomposition: Yt = St + Tt + Rt • Strength of trend based on STL: Yt = St + Tt + Rt 1-[Var(Rt)/Var(Yt-St)] • Entropy : spectral entropy from ForeCA package A low value of entropy suggests a time series easier to forecast • Relative promotion activity: No. weeks with promotion/Total no. of weeks • Optimal Box-Cox transformation of Yt: lambda Extract 2 principal components to summarize the data ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 17

Features space of fast moving goods Principal component analysis ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 18

Features space of fast moving goods ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 19

Method selection - based on ‘best’ performing methods • ETS • ETSX • TBATS • TBATSX • TBATS & LASSO • LASSO • ARIMA • ARIMA Fourier • ARIMAX • ARIMAX Fourier • SNaïve ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 20

Classification based on clustering Algorithm 1. Identify the best model for each SKU from the 7 selected methods based on RMAE 2. Specify the number of clusters 3. Assign a cluster to each SKU in the features space using K-Means Clustering 4. Identify the most frequent best method in each cluster 5. Assign to each SKU in the cluster the most frequent best method of its cluster ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 21

Classification based on clustering ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection 22