Online Assortment Optimization with Reusable Resources

Abstract

We consider an online assortment optimization problem where we have n substitutable products with fixed reusable capacities c1,...,cn. In each period t, a user with some preferences (potentially adversarially chosen) arrives to the seller's platform who offers a subset of products St, from the set of available products. The user selects product j ∈ St with probability given by the preference model and uses it for a random number of periods, ˜ tj that is distributed i.i.d. according to some distribution that depends only on j generating a revenue rj(˜ tj) for the seller. The goal of the seller is to find a policy that maximizes the expected cumulative over a finite horizon T. Our main contribution in this paper is to show that a simple myopic policy (where we offer the myopically optimal assortment from the available products to each user) provides a good approximation for the problem. In particular, we show that the myopic policy is 1/2-competitive, i.e., the expected cumulative revenue of the myopic policy is at least 1/2 times the expected revenue of an optimal policy that has full information about the sequence of user preference models and the distribution of random usage times of all the products. In contrast, the myopic policy does not require any information about future arrivals or the distribution of random usage times. The analysis is based on a coupling argument that allows us to bound the expected revenue of the optimal algorithm in terms of the expected revenue of the myopic policy. We also consider the setting where usage time distributions can depend on the type of each user and show that in this more general case there is no online algorithm with a non-trivial competitive ratio guarantee. Finally, we perform numerical experiments to compare the robustness and performance of myopic policy with other natural policies.

Keywords: Online Algorithms, Assortment Optimization, Resource Allocation, Competitive Ratio