Last year, Zalando hosted the 106th meeting of the Gesellschaft für Operations Research e.V. (Germany Society of Operations Research) working group on Practice of Mathematical Optimization. The workshop took place October 6-7, 2022 at the Zalando Headquarters in Berlin.

Applied Methods from Mathematical Optimization and Machine Learning

Techniques from the field of mathematical optimization on the one hand and from machine learning on the other hand have been crucial components in delivering solutions to customers in the e-commerce industry. Serving over 50 million customers and delivering a quarter billion orders last year, Zalando, is one of the largest online retail stores in Europe. Operating at such a large scale gives rise to a plethora of technical problems within these two fields that our applied scientists tackle across various teams. Thus, Zalando was uniquely positioned to host this workshop at the confluence of these two scientific fields, titled "Applied Methods from Mathematical Optimization and Machine Learning in E-commerce". The workshop included a number of talks by representatives from industry and academia from all over Germany. The presentations included applications ranging from forecasting to network design, pricing, logistics, scheduling, and vehicle routing, among others. See the full program of the workshop for more details.

The event took place in hybrid mode with streaming available for virtual attendees and presenters. The majority participants, i.e. around sixty, attended the event in person. They took advantage of the various networking opportunities during coffee breaks, the conference dinner and a tour of the historic east-side gallery, the largest remaining section of the Berlin wall, right across from the workshop venue at Zalando headquarters in Berlin.

Applied Scientists from Zalando presented two different use-cases at the confluence of optimization and ML in the workshop. The pricing team gave a talk about challenges in large scale article discounting, while the logistics team made a presentation about stock distribution and its challenges.

Pricing

The pricing team is responsible for the science behind offering attractive prices to customers. Their talk about Challenges in Large Scale Article Discounting gave a glimpse in the multitude of challenges that are connected to discounting for the entirety of Zalando's assortment.

Even with a proven machinery that manages to recommend millions of discounts under given business targets, many pitfalls have to be circumvented. We discussed the following complications and mentioned potential treatments.

Forecasting Challenges

The demand for niche articles, typically with just few sales per month, is hard to predict accurately. Moreover, articles with many sizes, e.g. jeans with many length and width combinations, can behave like multiple separate articles: different customers consider purely their own size, which creates a demand only on certain sizes. On top, some costs like shipping and returns are a mixed calculation based on the collection of articles handled together.

Optimization Challenges

An optimization model has to respect the business setup in its decisions. Several constraints were created so that the model has to follow business decisions, e.g. the model has to sell to customers in a sales period even if it would be more profitable to keep items now for sales in the future. Without them, it could be proposed to take an article offline for a certain period or prefer to sell stronger in countries where shipment costs are lower. On a technical side, some optimization problems can be infeasible through incompatible business targets and require adjustment recommendations.

Processes and Measuring

Further consideration stem from the connected processes around pricing. Matching competitors' prices, incorporating sales events and warehouse capacities are crucial in order to recommend profitable discounts. Ultimately, the impact has to be measured via A/B testing. When it comes to pricing, we have to carefully set it up to rule out customer discrimination by different prices and to enable gathering valuable insights.

Logistics

The logistics team delivered a talk titled Mathematical Optimization Meets Machine Learning to Optimize Stock Distribution. Zalando operates a network of interconnected warehouses and return centers serving its customer base across Europe. In order to best serve our customers we need to make our stock available to our customers where and when they desire it. This requires listening to our customers' demands and distribute stock across our network and within each facility accordingly. In this talk, we outlined the challenges at the core of this stock distribution problem and dived deep into some technical aspects.

Demand Forecasting

We model demand prediction as a time series forecasting problem at the individual article level for each of the markets we are active in for any given day. We produce probabilistic forecasts for each such problem using a deep recurrent neural network. Challenges abound in demand forecasting for the fashion industry where articles have fast turnover due to seasonality, the fast moving nature of fashion, and the diversity of trends in our vast customer base. This probabilistic demand forecast is used as input to solve two major optimization problems: (i) Item Network Distribution Problem: how best to distribute our stock across our facilities, and (ii) In-warehouse Item Relocation Problem: how best to position our articles within each facility.

Item Network Distribution

In the item network distribution problem, items are moved between warehouses: We need to ensure that for each country, the warehouses serving that country have the article assortment and stock quantities that best fulfill the country's expected demand. Our objectives are to maximize sales and minimize delivery times and costs. We discussed the algorithm currently used to make distribution decisions and presented some results.

In-warehouse Item Relocation

The in-warehouse item relocation problem is defined at the warehouse level. A warehouse contains various storage areas with different capacities and speed for collecting one item. Given a constant stream of incoming and outgoing items, we can relocate items between storage areas to achieve a distribution that is optimal for the demand reduced to a warehouse. We presented a formalization of the problem and prospective approaches to solve it.

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