Challenges in Large Scale Article Discounting Torsten Gellert Pricing Platform

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1. Challenges in Large Scale Article Discounting Torsten Gellert Pricing Platform GOR working group Real World Optimization, 2022-10-06

2. Fashion Champion of style Fashion > 1,800,000 articles > 6,500 brands Dedicated content creation by Zalando Content Solutions Beauty > 35,000 products Strategic partnership with Sephora

3. Large Scale Article Discounting

4. Pricing Goal: Provide proﬁt optimal discounts simplistic Pricing Idea: stock bought ahead of time → sell it for best proﬁt ● recommend best discount schedule per article ● for all articles in the shop ● for all countries we are serving ● with a certain frequency, e.g., weekly until season end (→ couple hundred millions of discounts) rationale: maximum proﬁt for entire assortment → maximum proﬁt per article Issue: Business targets (et.al.) combine single article optimization (discount rate in Italy 20%, discount rate Kids articles 10%) → profit maximization is a huge connected problem

5. Optimal Discounts with Targets ● Given some forecasts (demand, return rate, cost...), the stock ﬂow can be modeled as Mixed Integer Program per article → Optimal discount schedule computable easily per article over all countries (few seconds) ● Targets across articles modelled via Lagrangian Relaxation (decouples huge single problem in many small problems)

6. Optimal Discounts with Targets Target Steering Optimization ● consumes article data and forecasts ● runs iterations of the lagrangian relaxation ● heuristic generates prefered solution at the end ● reaches typical targets ● generates reports to for users Large-scale Price Optimization for an Online Fashion Retailer Initialize multipliers Lagrangian Relaxation Optimize 500k subproblems Stopping Criteria Build Solution (Primal Heuristic) Collect target violations Update multipliers

7. Optimal Discounts with Targets Success?: Yes ● hitting targets given by business partners ● provable gap and lower bound ● predictable and stable runtime and execution ● scalable towards an ever-growing assortment BUT….. Lots of hidden challenges and complications for this rather clean approach

8. Expectations And Requirements

9. “Pricing” Department Mission: Provide Engaging Discounts to our Customers Disclaimer: This reﬂects my point of view mostly Important Aspects for Optimization & Forecasting: ● black prices (original price) ○ ● ● setting original prices per country (e.g. different VAT) vouchers ○ for certain customers/markets on all or part of the assortment red prices (discounts) ○ ○ risk: ensuring to sell seasonal articles until the end of the season competitive and strategic: creating engaging offers ● specific marketing campaigns ○ e.g., special sales periods in selected countries

10. Resulting Requirements & Challenges Competitive Discounting match competitors` discounts strategically Sales Events support themed events selected countries Legal Requirements diﬀerent rules per country, i.e., share of articles at certain discount if advertised Seasonal and Non-Seasonal Articles some articles available all the time Brand Perception careful discounting for premium brands Guidance for Planning forecast impact of business goals Warehouse Capacities/Stock Availabilities slow down sales for warehouse capacities

11. Forecasting related Challenges

12. Forecasting Components - Demand or Sales Sales Forecast Demand Forecast Input: Input: single country-week discount Output: resulting demand discount schedule (all countries/weeks) Output: resulting sales ● less coupling between countries ● considering stock, returns, resupply,.. ● demand only observable if below stock ● matches observable data ● ● fewer parameter for optimization to keep track/work more possibilities/responsibilities for the optimization

13. Forecasting Components - Sales & Demand Uncertainty in Article Elasticity How far is the future reliable to predict? ● big spontaneous impact: weather ● also consumer’s willingness to spend money ● certain discounts rarely observed Possible approaches: ● (telescopic) time aggregation ● probabilistic forecasts → highly coupled to optimization

14. Forecasting Components - Sales & Demand Sizes and niche articles Which type of article has the most sizes?

15. Forecasting Components - Sales & Demand Sizes and niche articles Size Some articles have lots of sizes. (e.g., Jeans with 17 widths, each with several lengths →100 sizes) → Group sizes for forecasting purposes Niche Big share of assortment is sold rarely (long tail) → How to forecast when article is sold only every other week?

16. Forecasting Components - Expected Costs ● ● Shipping and Handling ● discounts are set per article, shipping is done with entire order ● mixed calculation of costs ● articles might or might not be in the same warehouse (cost depends on customer’s order and warehouse allocation) Return Rates and Return Costs ● returns are possible up to 14 weeks after purchase → observed very late ● returns are not always in re-sellable (in shop) condition (estimated share) Mixed calculations that aren’t perfect

17. Forecasting Components - Expected Costs Cannibalization and Halo Eﬀect ● demand/sales interdependent between articles ● High discount on similar article → less demand (e.g., similar sweater) ● High discount on a complementing article → higher demand (matching shorts & t-shirt) Also: Recommendations play a big role, can work as price anchor Residual Values ● How to deal with stock that cannot be sold? What is its value? ● Past observations might be incorrect for this seasons article

18. Optimization related Challenges

19. Optimization Problems and Components Model Behavior & Reality sales are modelled as variables, bound by stock & demand (depending on discount) Balanced Sales demand proﬁt/sale 20 30€ 15 25€ 10 28€ What could clash with reality if model “decides” sales?

20. Optimization Problems and Components Model Behavior & Reality sales are modelled as variables, bound by stock & demand (depending on discount) Balanced Sales demand profit/sale 20 30€ 15 25€ 10 28€ Model ● pushes sales to most lucrative countries ● refuse to sell if it is unproﬁtable Example: stock = 25 items → sales: CH: 20 (100% demand), DE: 0 (0%), FR: 5 (50%) Reality: No country preference, orders fulfilled as they occur Simple Constraint: Same ratio of demand fulfilled per time

21. Optimization Problems and Components Model Behavior & Reality sales are modelled as variables, bound by stock & demand (depending on discount) Stock Hedging min. discount Keep stock to sell later with less discount → optimization could choose against fulfilling demand ● ● fighting against sales periods potentially exploiting demand forecasts time Reality: Articles are not taken offline Binary constraint: either demand fulfilled or stock depleted

22. Optimization Problems and Components Infeasible Targets Business Targets can be incompatible Lagrangian Relaxation: best upper bound is -∞ 10% discount ?% ?% ?% 5% discount ?% ?% ?% ● How to detect upfront? 15% discount ?% ?% ?% ● What is smallest change to make it feasible? → Theoretical hard questions s id r po s e ho S K nt nt u u o o isc sc sc i i d d d % % % 5 0 5 2 3 nt u o S different types of targets hard to judge (GMV, average discount, stock levels,...) ts Approaches (all with lots of eﬀort) ● provide guidance to planners ● adjusts targets automatically ● provide reasonable fallback solution

23. Optimization Problems and Components Long Term Proﬁt Optimization Business has quarterly, monthly, weekly, …. targets Optimization looks ahead at the end of a season Target Horizon 30% 28% Optimization Horizon 23% 15% 10% 12% 9% 10% avg. discount weeks Targets aﬀect optimization in nearest future → optimizer’s believes it can be compensated later Adjusted targets can harm this plan Approaches: Hierarchical model, include long term targets as well

24. Optimization Problems and Components AB Testing “Easy”: diﬀerent web page layout, checkout, recommendations, sortings, ... A Complications: ● compare B ● AB Tests possible but tricky to setup and analyze How to setup an AB test? ○ diﬀerent prices per customer → forbidden price discrimination ○ diﬀerent prices per country → countries already show diﬀerent behavior ○ diﬀerent prices per article granting ■ same general behavior ■ robust against cross eﬀects, e.g., cannibalization ■ keep for some time to observe long term eﬀects How to measure long term proﬁts of two diﬀerent discount strategies?

25. Conclusion Attention to Detail in Modelling setup optimization and forecast models carefully mathematically perfect solution pointless if missing details Measure Real Impact analysis can be complicated but crucial starting point to spot issues or celebrate successes Stay in Contact with Users learn how and why they use or avoid your product misusage or desired feature can lead to better products

26. Thank you