FORECASTING EFFECTS OF PROMOTIONS WITH

CAUSAL METHODS IN GROCERY RETAILING

11/26/2015

1

Henri Nikula

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Agenda

1. Introduction and Motivation

2. Demand Forecasting and Data aggregation

3. Research Desing

4. Case Data

5. Results

6. Conclusions

RELEX provides comprehensive solutions for supply chain management and optimisation

– Forecasting and demand planning

– Store replenishment and inventory management

– Actionable analytics and reporting

3

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1. Introduction and Motivation

• Importance of promotions has grown

– Wider product assortments => promotions to attract customers

– Increased competition => have to do promotions as competitors do

• Sales impact of promotions can be very large

– These impacts need to be forecasted in order to maximize the availability and to minimize the spoilage and warehousing costs

• Current RELEX offering has module for forecasting promotions but it is based on a heuristic model

– Model does not take into account price changes or the effects of multiple different promotions

The goal of this thesis is to find more advanced causal methods to better forecast the effects of different promotional activites

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1. Introduction and Motivation

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1.1 Research questions

Question 1: How accurate forecast can be achieved with SCAN*PRO, Base Times Lift and Support vector regression models?

Question 2: Can we improve the forecasting accuracy of SCAN*PRO, Base Times Lift or Support vector regression models by changing the seasonal variables from weeks to months, adding the number of promotion days on a week as parameter or including a baseline forecasts into the models?

Question 3: Can we improve the forecasting accuracy using different levels of aggregation for training the forecasting models?

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2. Demand Forecasting

Forecasting Techniques

Qualitative Techniques

Based on the subjective

expectations and experiences of a

person

Quantitative Techniques

Time series based forecasts

Causal and Machine Learning

based forecasts

Figure 1: Qualitative and quantitative forecasting techniques

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2. Data aggregation

Figure 2: Three dimensional structure of demand data*

*H. Stadtler and C. Kilger, Supply chain management and advanced planning, Third Edit. 2000.

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3. Research design

• Comparison of different forecasting model – parameter – aggregation combinations

• Forecasts done on week level sales and compared with MPE and MAPE metrics

• Selected forecasting models:

– Baseline forecast with time series methods (BASE)

– Historical averages model (HIST)

– Base times lift model (LIFT)

– Multivariate regression model SCAN*PRO (LM)

– Support vector regression (SVR)

• Forecasts with BASE and HIST models were calculated in RELEX, others were done with R

1. Select test and

train data

2. Choose used

forecasts models

3. Choose additional

parameters

4. Select the

aggregation level

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3.1 Baseline (BASE) and Historical averages models (HIST)

• The baseline forecast is calculated for the normal sales with time series methods

– Idea is to forecast the normal sales without any promotions or events

– Really accurate for that purpose

• The Historical averages model searches for similar promotions in the past and uses the average sales uplift as the forecast for the promotion

– Searches from multiple different aggregation dimensions

– Proven to work in actual production environments

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3.2 SCAN*PRO model (LM)

m number of different types of promotions;

𝑇 number of weeks in a year;

K number of stores;

𝑆𝑘𝑗𝑡 unit sales of a product 𝑗 in store 𝑘, time 𝑡;

𝑝𝑘𝑗𝑡 unit price for product 𝑗 in store 𝑘, time 𝑡;

𝑝𝑘𝑗𝑡 median of the normal unit price for product 𝑗 in store 𝑘, time 𝑡;

𝐷𝑙𝑘𝑗𝑡 an indicator variable for different promotion types: 1 if product 𝑗 is promoted by

promotion type 𝑙 in store 𝑘, in time t; 0 otherwise;

𝑋𝑡 an indicator variable: 1 if observation is in time t;

𝑍𝑘 an indicator variable: 1 if observation is in store k;

𝛽𝑗 the price discount elasticity for product 𝑗;

𝛾𝑙𝑗 promotion type multipliers for product 𝑗 and promotion type 𝑙;

𝛿𝑗𝑡 week multiplier for product j and week t;

𝜆𝑘𝑗 store multiplier for product j and store k;

휀𝑘𝑗𝑡 disturbance term.

𝑆𝑘𝑗𝑡 =𝑝𝑘𝑗𝑡

𝑝𝑘𝑗𝑡

𝛽𝑟

𝑙=1

𝑚

𝛾𝑙𝑗

𝐷𝑙𝑘𝑗𝑡

𝑡=1

𝑇

𝛿𝑗𝑡𝑋𝑡

𝑘=1

𝐾

𝜆𝑘𝑗𝑍𝑘 𝑒𝜀𝑘𝑗𝑡

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3.3 Base times lift model (LIFT)

𝑆𝑘𝑗𝑡 = 𝐹𝑏𝑘𝑗𝑡𝑝𝑘𝑗𝑡

𝑝𝑘𝑗𝑡

𝛽𝑗

𝑙=1

𝑚

𝛾𝑙𝑗

𝐷𝑙𝑘𝑗𝑡

• The forecast for time periods with promotions is calculated by multiplying

the baseline forecast 𝐹𝑏𝑘𝑗𝑡 with the price elasticity multiplier 𝑝𝑘𝑗𝑡

𝑝𝑘𝑗𝑡

𝛽𝑗and

the different promotion type multipliers 𝛾𝑙𝑗

𝐷𝑙𝑘𝑗𝑡.

• Baseline forecast is the normal corrected forecast calculated in RELEX system

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3.4 Support vector regression model (SVR)

Figure 3. Architecture of the support vector regression machine*

*A. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput., vol. 14, pp. 199–222, 2004

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3.5 Aggregation levels and additional parameters

Figure 4. Amount of data used for estimation and training

on different levels of aggregation. Size of the rectangle

represents the amount of a data used in an abstract

situation.

• Additional parameters:• Baseline forecast as parameter• Number of promotion days in a

week• Months instead of weeks as

seasonal indicators

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4. Case data

Table 1. Number of products and product-locations in product categories

Group level 1 Number of sub

groups Number of products

Number of product-locations

Alcoholic Beverages 38 1 289 5 520

Beverages 29 812 3 627

Yogurts 35 495 2 012

Desserts 8 334 1 487

Cakes 28 692 2 841

Confectionary 52 1 890 7 458

Soft Drinks 26 1 047 4 455

Total 216 6 559 27 400

Table 1. Sales and promotional statistics for each product category

Group level 1

Average number of sales days

Percentage of sales days from total

Average number of promotional

sales days

Percentage of sales days on

promotion

Alcoholic Beverages

204 33 % 72 33 %

Beverages 258 33 % 51 20 %

Yogurts 472 66 % 305 63 %

Desserts 324 53 % 83 25 %

Cakes 190 40 % 35 32 %

Confectionary 219 40 % 40 22 %

Soft Drinks 335 43 % 111 32 %

Average 286 44 % 100 32 %

• Casa data from European grocery retailer• Sales and promotion data

between 01/11/2013-27/05/2015

• 5 stores and 6 product categories

• 10 different promotion types

• Test period:• Promotional weeks between

2014-09-1 – 2014-10-31

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5.1 Results: Basic models

Table 1. Forecasting accuracy measurements for different methods estimated on product

level measured from forecasts for 675 different product-locations.

MPE MAPE MAPE 50% Percentile

MAPE 90% Percentile

MAPE 99% Percentile

SVR nu radial -36 % 60 % 43 % 106 % 286 %

LIFT -2679 % 2743 % 53 % 142 % 1791 %

LM -370 % 413 % 47 % 286 % 7311 %

HIST -201 % 218 % 116 % 401 % 2058 %

BASE -305 % 312 % 126 % 466 % 1668 %

Model Accuracy measurements

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5.2 Results: Additional informationTable 1. Forecasting accuracy measurements for models with different modifications

estimated on product level. In the additional parameters columns 1 means that the

modification was used and 0 that it was not.

Model MO

NT

HS

NB

R O

F P

RO

MO

DA

YS

BA

SELI

NE

MP

E

MA

PE

MA

PE

50

% P

erc

enti

le

MA

PE

90

% P

erc

enti

le

MA

PE

99

% P

erc

enti

le

LM 0 0 0 -370 % 413 % 47 % 286 % 7311 %

LM 1 0 0 -277 % 317 % 44 % 186 % 3798 %

LM 0 1 0 -816 % 859 % 47 % 324 % 10879 %

LM 0 0 1 -683 % 724 % 46 % 343 % 14358 %

LIFT 0 0 0 -2679 % 2743 % 53 % 142 % 1791 %

LIFT 1 0 0 -40 % 105 % 51 % 123 % 1187 %

LIFT 0 1 0 -331 % 397 % 53 % 137 % 4877 %

SVR nu radial 0 0 0 -36 % 60 % 43 % 106 % 286 %

SVR nu radial 1 0 0 -22 % 51 % 38 % 100 % 265 %

SVR nu radial 0 1 0 -31 % 55 % 40 % 103 % 263 %

SVR nu radial 0 0 1 -36 % 58 % 42 % 106 % 293 %

Model Additional

parameters Accuracy measurements

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5.3 Results: Effects of aggregation levelTable 1. Forecasting accuracy measurements for models estimated on different aggregation

levels.

Model Aggregation level M

PE

MA

PE

MA

PE

50

% P

erc

enti

le

MA

PE

90

% P

erc

enti

le

MA

PE

99

% P

erc

enti

le

LIFT GROUP 1 -1 % 55 % 40 % 73 % 342 % LIFT GROUP 2 -2607 % 2676 % 48 % 91 % 528 % LIFT PRODUCT -2679 % 2743 % 53 % 142 % 1791 % LIFT PL -12037 % 12094 % 46 % 131 % 5807 % LM GROUP 1 -27 % 65 % 40 % 119 % 546 % LM GROUP 2 -69 % 108 % 45 % 161 % 1209 % LM PRODUCT -370 % 413 % 47 % 286 % 7311 % LM PL -20990 % 21034 % 48 % 374 % 45276 % SVR nu radial GROUP 1 -14 % 64 % 42 % 109 % 518 % SVR nu radial GROUP 2 -19 % 55 % 42 % 104 % 254 % SVR nu radial PRODUCT -36 % 60 % 43 % 106 % 286 % SVR nu radial PL -45 % 65 % 48 % 124 % 357 %

Model and aggregation level Accuracy measurements

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5.4 Results: Best models

Table 1. Forecasting accuracy measurements for best parameter-aggregation level

combinations for each model type ordered by the MAPE metric

Mo

del

Agg

rega

tio

n le

vel

MO

NT

HS

NB

R O

F P

RO

MO

DA

YS

BA

SELI

NE

MP

E

MA

PE

MA

PE

50

% P

erc

enti

le

MA

PE

90

% P

erc

enti

le

MA

PE

99

% P

erc

enti

le

SVR nu radial GROUP 2 1 1 1 -11 % 46 % 36 % 72 % 225 %

LM GROUP 1 1 1 1 -22 % 51 % 38 % 89 % 325 %

LIFT GROUP 1 0 1 0 3 % 53 % 40 % 70 % 332 %

HIST - 0 0 0 -201 % 218 % 116 % 401 % 2058 %

BASE - 0 0 0 -305 % 312 % 126 % 466 % 1668 %

Model and aggregation level

Additional information

Accuracy measurements

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5.4 Results: Best models

Figure 1. Density of MAPE values amongst the 675 product-locations for the best

parameter-aggregation level combinations for each model type. The dotted lines represent

the median of the MAPE values and the color of the line indicates the model.

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6. Conclusions

Finding 1: Forecasting accuracy can be improved for majority of the product-locations by using causal methods compared to the time series and Historical Average model.

Finding 2: Forecasting accuracy of the tested causal methods can be improved with the tested additional information, adding months and the baseline forecasts both improve the forecasting accuracy.

Finding 3: Aggregation level has a significant impact on the overall forecasting performance on all of the tested models. Higher aggregation levels give better forecasts.

Finding 4: Combining the selection of aggregation level and the model modifications further improves the forecasting accuracy with all the tested methods.

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Questions?