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ZEOS Inventory Optimisation System

ZEOS Inventory Optimisation System is the umbrella name this wiki gives to Zalando ZEOS's AI-driven replenishment recommendation product — a two-pipeline system that produces probabilistic 12-week demand forecasts for 5 million SKUs and feeds them into a Monte Carlo + black-box-optimiser inventory engine that recommends what to stock, when to replenish, and where in a multi-echelon warehouse network. Exposed to Zalando B2B partners through the partner portal with both daily batch and real-time interactive endpoints.

ZEOS is Zalando's B2B logistics & e-commerce service (zeos.eu); the inventory-optimisation system documented here is one of the AI-driven tools ZEOS offers partners alongside fulfillment, logistics, and storefront services.

Role

Two-stage replenishment decision pipeline:

  1. Demand Forecaster — weekly pipeline producing probabilistic 12-week forecasts per (article_id, merchant_id, week) over 3 years of sliding-window history, 5M SKUs, end-to-end under 2 hours.

  2. Replenishment Recommender — daily batch + real-time online optimiser consuming the forecast + per-SKU inventory state, pricing, cost factors, lead times; uses Monte Carlo simulation + gradient-free black-box optimisation.

Cost optimisation objective (from the post)

$$Min\ Costs(\theta) = C_{storage}(\theta) + C_{lost\ sales}(\theta) + C_{overstock}(\theta) + C_{operations}(\theta) + C_{inbound}(\theta)$$

Find replenishment decisions θ* that:

  • Reduce stockouts to avoid lost-sales cost.
  • Limit inventory in warehouses to reduce stock-holding cost.
  • Balance long-term overstock cost vs short-term lost-sales cost.
  • Satisfy operational constraints (lead times, desired review frequency).
  • Capture the stochastic nature of demand / lead times via Monte Carlo simulation.

Platform substrate

Both constituent pipelines are implemented on zFlow, Zalando's internal ML platform. zFlow:

Delivery to partners

Partners interact via the Zalando B2B partner portal, which renders:

  • Holistic inventory-health metrics and KPIs.
  • Daily batch replenishment reports covering all of the partner's articles.
  • Interactive / online optimisation — partners can mutate inventory settings and re-score their catalog on the fly. See concepts/partner-portal-interactive-planning.

Canonical disclosure (2025-06-29)

See sources/2025-06-29-zalando-building-a-dynamic-inventory-optimisation-system-a-deep-dive for the full architectural disclosure. Key quote on the two-pipeline framing:

"We break the inventory optimisation problem into two isolated but connected building blocks: Demand Forecast and Inventory Optimisation."

Key quote on scale:

"Our weekly forecasting pipeline processes 3 years of historical data for 5 million SKUs (size and colour) using a sliding window approach, and takes less than 2 hours."

Positioning on the wiki

  • This is a deep-dive into one workload inside Zalando's ML Platform, as opposed to sources/2022-04-18-zalando-zalandos-machine-learning-platform which is the platform-overview post, or which was the first publicly-named zFlow workload (Payments risk-scoring, online endpoint).
  • Architectural distinguishing feature vs axis 10 and axis 11: hybrid online + offline delivery of the same algorithm against the same features, with an explicit parity invariant between the two.

Seen in

  • sources/2025-06-29-zalando-building-a-dynamic-inventory-optimisation-system-a-deep-dive — canonical architecture disclosure. Full two-pipeline architecture, numbers, cost objective, model choice, online-vs-offline delivery split, drift-monitoring architecture.

  • sources/2026-01-14-zalando-paper-announcement-replenishment-optimization-extended-rsq — canonical algorithm disclosure (Nature Scientific Reports paper announcement). Where the 2025-06 post disclosed the platform shape, this post discloses the algorithm shape:

  • Extended (R, s, Q) policy — classical (R, s, Q) extended with kick-start quantity Q₀ at time t₀ + lifecycle cutoff t_limit; parameter vector θ = (t₀, Q₀, s, Q).
  • DES — 12-week horizon per run with intra-week ordered events (inbound/2 → fulfilment → inbound/2 → reorder check → cost accrual); Gamma-distributed lead times sampled per run.
  • P75 cost objective — optimise 75th percentile of cost distribution, not mean; explicit tail-risk protection.
  • Counterfactual stockout demand — unfulfilled demand during stockouts sampled from the probabilistic forecast distribution rather than zeroed.
  • Five-pillar cost decomposition — holding + inbound + outbound + returns + lost_sales (lost_sales adjusted by return rate).
  • Quantile LightGBM forecasts — demand forecaster produces quantile distributions directly, not point forecasts post-processed into intervals.
  • Computational backtest — Oct 2023–Sep 2024 × ~2M articles × ~800 merchants vs human replenishment baselines: +22.11% GMV, +21.95% Gross Margin, +33.63% availability (to 86.40%), +23.63% fill rate (to 91.14%); 70–80% of merchants positive uplift. Theoretical-100%-adoption caveat.
  • Baseline comparison — Extended (R, s, Q) beats Tuned (s, S), Periodic base-stock, Myopic Newsvendor under identical data + simulation settings.
  • Forecast × Objective ablation — probabilistic forecast is the first-order lever (+15.74pp GMV); percentile objective is the second-order stability lever (+3.09pp GMV). Both needed.
  • Canonical pairing canonicalised as patterns/probabilistic-forecast-plus-percentile-objective and patterns/des-plus-gradient-free-optimiser-under-uncertainty.
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