Designing Surprise Bags for Surplus Foods

Problem definition: Surplus-food marketplaces, such as Too Good To Go, enable retailers to monetize leftover inventory and reduce food waste by selling discounted “surprise bags.” Participating stores, however, face complex operational challenges. They must jointly set a reservation price and the number of bags made available before daily demand and end-of-day surplus are realized, while customers’ ex-post experiences affect future demand through the platform’s rating system. Moreover, although evenly distributing surplus across bags is intuitive and operationally convenient, it remains unclear whether bag-value differentiation can improve consumer experience and profitability. Methodology/results: We study these questions through an infinite-horizon two-stage stochastic dynamic program. In each period, the store first sets a reservation price per bag and the number of bags available and then, after observing accepted reservations and surplus, allocates surplus food across surprise bags, potentially supplementing from regular inventory. We show that this infinite-dimensional allocation problem can be reduced to a scalar choice of average bag value. Specifically, the optimal allocation is characterized by the upper concave envelope of the consumer utility function and requires at most two bag types. Building on this structural reduction, we develop linear value-function and deterministic fluid approximations that provide explicit performance guarantees and transparent implementation rules. The linear value-function approximation captures most of the dynamic-program profit improvement and produces the lowest average modeled total waste across the main grid, while the deterministic fluid approximation yields transparent steady-state comparative statics. Managerial implications: Price and the reservation cap are not interchangeable: price shifts latent requests and customer net utility, whereas the cap truncates high-request realizations before surplus is known. This division of control provides a basis for platform decision-support tools that balance retailer profit with food recovery.