Dynamic Inventory Repositioning in On-Demand Rental Networks

73 Pages Posted: 30 Mar 2017 Last revised: 28 Oct 2019

See all articles by Saif Benjaafar

Saif Benjaafar

University of Minnesota - Minneapolis - Industrial & System Engineering

Daniel Jiang

University of Pittsburgh

Xiang Li

University of Minnesota - Minneapolis - Industrial & System Engineering

Xiaobo Li

National University of Singapore

Date Written: December 18, 2018

Abstract

We consider a rental service with a fixed number of rental units distributed across multiple locations. The units are accessed by customers without prior reservation and on an on-demand basis. Customers can decide on how long to keep a unit and where to return it. Because of the randomness in demand and in returns, there is a need to periodically reposition inventory away from some locations and into others. In deciding on how much inventory to reposition and where, the system manager balances potential lost sales with repositioning costs. Although the problem is increasingly common in applications involving on-demand rental services, not much is known about the nature of the optimal policy for systems with a general network structure or about effective approaches to solving the problem. In this paper, first, we show that the optimal policy in each period can be described in terms of a well-specified region over the state space. Within this region, it is optimal not to reposition any inventory, while, outside the region, it is optimal to reposition but only such that the system moves to a new state that is on the boundary of the no-repositioning region. We also provide a simple check for when a state is in the no-repositioning region. Second, we leverage the features of the optimal policy, along with properties of the optimal cost function, to propose a provably convergent approximate dynamic programming algorithm to tackle problems with a large number of dimensions.

Keywords: rental networks; inventory repositioning; optimal policies, approximate dynamic programming algorithms, stochastic dual dynamic programming

Suggested Citation

Benjaafar, Saif and Jiang, Daniel and Li, Xiang and Li, Xiaobo, Dynamic Inventory Repositioning in On-Demand Rental Networks (December 18, 2018). Available at SSRN: https://ssrn.com/abstract=2942921 or http://dx.doi.org/10.2139/ssrn.2942921

Saif Benjaafar

University of Minnesota - Minneapolis - Industrial & System Engineering ( email )

111 Church Street S.E.
Minneapolis, MN 55455
United States

Daniel Jiang

University of Pittsburgh ( email )

135 N Bellefield Ave
Pittsburgh, PA 15260
United States

Xiang Li

University of Minnesota - Minneapolis - Industrial & System Engineering ( email )

111 Church Street S.E.
Minneapolis, MN 55455
United States

Xiaobo Li (Contact Author)

National University of Singapore ( email )

10 Kent Ridge Crescent
Singapore, 115260
Singapore

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