We consider dynamic assortment problems with reusable products, in which each arriving customer chooses a product within an offered assortment, uses the product for a random duration of time, and returns the product back to the firm to be used by other customers. The goal is to find a policy for deciding on the assortment to offer to each customer so that the total expected revenue over a finite selling horizon is maximized. The dynamic-programming formulation of this problem requires a high-dimensional state variable that keeps track of the on-hand product inventories, as well as the products that are currently in use. We present a tractable approach to compute a policy that is guaranteed to obtain at least 50% of the optimal total expected revenue. This policy is based on constructing linear approximations to the optimal value functions. When the usage duration is infinite or follows a negative binomial distribution, we also show how to efficiently perform rollout on a simple static policy. Performing rollout corresponds to using separable and nonlinear value function approximations. The resulting policy is also guaranteed to obtain at least 50% of the optimal total expected revenue. The special case of our model with infinite usage durations captures the case where the customers purchase the products outright without returning them at all. Under infinite usage durations, we give a variant of our rollout approach whose total expected revenue differs from the optimal by a factor that approaches 1 with rate cubic-root of Cmin, where Cmin is the smallest inventory of a product. We provide computational experiments based on simulated data for dynamic assortment management, as well as real parking transaction data for the city of Seattle. Our computational experiments demonstrate that the practical performance of our policies is substantially better than their performance guarantees and that performing rollout yields noticeable improvements.
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Performance Guarantees for Network Revenue Management with Flexible Products
Problem definition: We consider network revenue management problems with flexible products. We have a network of resources with limited capacities. To each customer arriving into the system, we offer an assortment of products. The customer chooses a product within the offered assortment or decides to leave without a purchase. The products are flexible in the sense that there are multiple possible combinations of resources that we can use to serve a customer with a purchase for a particular product. We refer to each such combination of resources as a route. The service provider chooses the route to serve a customer with a purchase for a particular product. Such flexible products occur, for example, when customers book at-home cleaning services but leave the timing of service to the company that provides the service. Our goal is to find a policy to decide which assortment of products to offer to each customer to maximize the total expected revenue, making sure that there are always feasible route assignments for the customers with purchased products. Methodology/results: We start by considering the case in which we make the route assignments at the end of the selling horizon. The dynamic programming formulation of the problem is significantly different from its analogue without flexible products as the state variable keeps track of the number of purchases for each product rather than the remaining capacity of each resource. Letting L be the maximum number of resources in a route, we give a policy that obtains at least [Formula: see text] fraction of the optimal total expected revenue. We extend our policy to the case in which we make the route assignments periodically over the selling horizon. Managerial implications: To our knowledge, the policy that we develop is the first with a performance guarantee under flexible products. Thus, our work constructs policies that can be implemented in practice under flexible products, also providing performance guarantees. Funding: The work of H. Topaloglu was partly funded by the National Science Foundation [Grant CMMI-1825406]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0583 .
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- Award ID(s):
- 1825406
- PAR ID:
- 10465498
- Date Published:
- Journal Name:
- Manufacturing & Service Operations Management
- ISSN:
- 1523-4614
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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