Experiments with product mixes reduce revenue loss risks in retail
The Value of Experiments in Assortment Optimization
Data Structures and Algorithms
Summary
Picking which products to sell in a store is hard when customer preferences are unknown. The researchers study how retailers can test out one or a few fixed product groups to learn preferences and improve sales. They show that even a single experiment with one product assortment can greatly reduce potential revenue loss. The work also explains when testing multiple assortments helps so much that the retailer nearly eliminates this loss. Their findings help decide how much experimenting is worth when changing products is costly or difficult.
What this means in practice
- •For retail merchandisers: Optimize product selections when testing only a few fixed assortments to reduce potential sales losses under unknown customer tastes.
- •For ecommerce platform teams: Design limited product experiments that improve assortment recommendations while minimizing disruptions from frequent product changes.
A theory result. No direct application yet.
Authors
Mohammadreza Ahmadnejadsaein, Amine Bennouna, Omar El Housni
Abstract
Retailers can learn customer preferences by experimenting with different assortments. However, the cost of each experiment and the operational burden of repeatedly changing product offerings can make extensive experimentation impractical. We study how much a retailer can improve its final assortment decision using customer observations from one (or a very small number of) fixed experimental assortments. We consider the multinomial logit model, where product revenues are known but customer preferences are unknown. In this setting, we jointly design the experimental assortment and the rule for selecting a final assortment from observed customer choices to minimize worst-case regret: the expected revenue loss of the final assortment relative to an optimal assortment under the true preferences, maximized over possible customer preferences. We first characterize exactly the minimax regret and an optimal assortment when no experimentation is possible. We then show, surprisingly, that offering a single experimental assortment to just one customer can already substantially reduce regret, depending on how the products' revenues compare. We derive the exact minimax regret and an optimal experimental policy in this setting. When a single fixed experimental assortment is offered to many customers, we give a geometric characterization of the limiting minimax regret and construct an asymptotically optimal policy. Depending on product revenues, this single experiment can yield no improvement over no experimentation or nearly complete regret reduction. Finally, we extend our analysis to multiple experimental assortments chosen in advance, characterizing the limiting minimax regret, constructing asymptotically optimal policies, and identifying which collections of assortments allow worst-case regret to vanish as the number of customer observations grows.