Blind and Near-Optimal Dynamic Assortment Optimization with Reusable Resources

Abstract

Dynamic assortment optimization with reusable resources arises in applications in cloud computing, healthcare, and hospitality, where customers rent resources for random durations before returning them. Even when system parameters are fully known, resource reusability creates complex dependencies between current decisions and future availability. These challenges become more pronounced when arrival and return rates are unknown possibly due to non-stationarity or high estimation costs. Classical approaches rely on precise estimates of demand and usage patterns. In contrast, we propose a simple, blind, state-dependent policy requiring no information about arrival or return rates; it relies only on observable system states and known resource attributes (expected revenues and choice probabilities). The policy uses an exponential penalty mechanism to dynamically balance resource utilization and guide assortment decisions. Despite operating in a parameter-agnostic environment, the policy achieves strong theoretical guarantees: an absolute revenue loss of O(√ n) in general and an O(1) loss in both overloaded and fully under-loaded regimes, where n denotes the total number of resources. These performance bounds match the best-known results under comparable assumptions, demonstrating that near-optimal performance is possible without estimating demand or usage patterns. Numerical experiments confirm the theoretical guarantees and illustrate the robustness of the policy across a range of operating conditions.

Keywords: dynamic assortment optimization, reusable resources, blind policies, revenue management