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

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

2

• Motivation
• Retail sales dataset
• Demand forecasting models
• Experimental design
• Forecasting results
• Clustering analysis results
• Conclusions

Outline

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

3

• 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

Retail business

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

4

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’?

Key questions

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

5

• Motivation
• Retail sales dataset
• Demand forecasting models
• Experimental design
• Forecasting results
• Clustering analysis results
• Conclusions

Outline

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

6

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

7 CATEGORY MEAN PERCENTAGE OF WEEKS FRESH FISH AQUACULTURE 49.42 WILD FRESH FISH 45.86 TOMATO 33.81 FRESH PORK MEAT 24.43 PEPPER 23.41 LETTUCE 19.37 LIQUID YOGURT 16.19 BEER WITH ALCOHOL 12.43 FRESH VEGETABLES 10.12 BAKED BREAD 8.09 FROZEN COD 7.23 CONFECTIONERY 6.64 PASTEURIZED CREAM 5.37 PASTRY GOODS 4.78 EGGS 3.85 PAPER NAPKINS 2.89 AIR FRESHENER 1.73 NATURAL FLOWERS 0.52

The dataset

• Daily SKU information between Jan 2012

and Apr 2015 (1211 days/173 weeks)

– Units sold – Price

• Selection of SKUs from the 6 main areas

(93% of daily sales total volume)

– Perishables, grocery, beverage, cleaning products and personal products

• Selection of a store with the largest

dimension

• Fast moving goods (SKUs with sales on

100% of the weeks)

• Data sample

– 988 SKUs – 203 categories – Intense promotional activity – Seasonal and non-seasonal Promotional activity of some categories of fast moving goods

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

8

• Motivation
• Retail sales dataset
• Demand forecasting models
• Experimental design
• Forecasting results
• Clustering analysis results
• Conclusions

Outline

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

9

• Univariate models (4)

– ETS1 – TBATS2 – ARIMA2 – SNaïve

• Multivariate models (7)

– LASSO3

• 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

Forecasting models

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

10

• Multivariate models (cont.)

– TBATS & LASSO2,3

• Three stages

– 1º Fit a TBATS model and forecast – 2º Apply LASSO to the residuals with the regressors and forecast – 3º Add both forecasts

– TBATSX2,3

• 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

Forecasting models

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

11

• Multivariate models (cont.)

– ETSX1

• Regressors included as Principal Components

– ARIMA Fourier2

• Seasonality handled with Fourier terms

– ARIMAX2

• Regressors included as Principal Components

– ARIMAX Fourier2

• Seasonality handled with Fourier terms
• Regressors included as Principal Components

1- smooth R package, 2- forecast R package

Forecasting models

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

12

• Motivation
• Retail sales dataset
• Demand forecasting models
• Experimental design
• Forecasting results
• Clustering analysis results
• Conclusions

Outline

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

13

• 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)

Experimental design

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

14

• Motivation
• Retail sales dataset
• Demand forecasting models
• Experimental design
• Forecasting results
• Clustering analysis results
• Conclusions

Outline

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

15

• 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

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

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

16

• Motivation
• Retail sales dataset
• Demand forecasting models
• Experimental design
• Forecasting results
• Clustering analysis results
• Conclusions

Outline

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

17

• 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

Characteristics/features for time series

Extract 2 principal components to summarize the data

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

18

Features space of fast moving goods

Principal component analysis

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

19

Features space of fast moving goods

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

20

• ETS
• ETSX
• TBATS
• TBATSX
• TBATS & LASSO
• LASSO
• ARIMA
• ARIMA Fourier
• ARIMAX
• ARIMAX Fourier
• SNaïve

Method selection

• based on ‘best’ performing methods

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

21

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

Classification based on clustering

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

22

Classification based on clustering

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

23

GMRMAE vs the number of clusters

• Aggregate selection is effective: the classification procedure improves

GMRMAE after 101 clusters!

• The optimum is obviously obtained with 988 clusters (no. of SKUs)
• The classification procedure improves GMRMAE’s benchmark in about 11%
• Individual selection has potential to improve
• Need to identify method for cluster ex ante (rather than as here, ex post)

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

24

Using the classification to identify a model for a time series

Procedure: Given a fast moving SKU, compute its PCs and select its model by identifying the cluster whose centroid is closest

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

25

• Multivariate models integrating the series patterns give

the best forecasts for retail data with promotions

• Improvement in relative accuracy of TBATSX achievable is

41% (measured by RMAE)

• Moving from univariate methods to ‘best’ multivariate

method improves accuracy by 11% (measured by RMAE)

• Classification based on clustering give good insights for a

model identification procedure

• The classification procedure for method selection can

improve forecasts when compared with the best performing method for the population

Conclusions

ISF 2017, 25-28 June Characterizing retail demand with promotional effects for model selection

26

Thank you for your attention! Question?