Optimal Selection with Balanced Market Share: Static and Dynamic Assortment Optimization
New algorithm solves revenue optimization while limiting sales disparity between products by a factor α.
A team of researchers from Cornell Tech and other institutions has published a significant paper on arXiv titled 'Optimal Selection with Balanced Market Share: Static and Dynamic Assortment Optimization.' The work addresses a critical flaw in traditional online retail algorithms: optimizing purely for revenue can create unhealthy market dynamics, like a 'long tail' of unsold products or a single product dominating sales. The authors introduce a novel 'market share balancing constraint' that limits the disparity in expected sales between any two offered products to a factor of α, a parameter set by the seller.
In the static setting—where a seller selects a fixed assortment—the researchers show that this fairness-constrained optimization problem can be solved in polynomial time. The optimal solution has a clear structure: a product is included only if its revenue and customer preference weight exceed specific thresholds. They also extend this to cases with additional business constraints (like shelf space), proving that a β-approximation oracle for the base problem yields a β-approximation for the fair version.
For the dynamic setting, where products have finite inventory (like flash sales), the team designed a policy that is asymptotically optimal. This means its performance gap vanishes as starting inventories grow large, all while respecting both stock limits and the fairness constraint in expectation. This provides a practical tool for platforms needing to manage real-time inventory without letting a few hot items cannibalize all demand.
- Introduces a market share balancing constraint (parameter α) to limit sales disparity between products in assortment optimization.
- Proves the static fairness-constrained problem under the Multinomial Logit (MNL) model is solvable in polynomial time.
- Designs an asymptotically optimal dynamic policy for settings with finite inventory, with performance converging to optimal as stock grows.
Why It Matters
Enables retailers and platforms to maximize revenue while promoting product diversity and preventing market concentration, leading to healthier ecosystems.