An optimal stopping policy for car rental businesses with purchasing customers

Belleh Fontem ()
Additional contact information
Belleh Fontem: University of Mary Washington

Annals of Operations Research, 2022, vol. 317, issue 1, No 5, 47-76

Abstract: Abstract We analyze decisions for a car rental firm using a common pool of cars to serve both rental, and purchasing customers. The rental customers arrive successively, and rent out cars for random durations while effectuating random incremental mileages on them. This stochastic rental behavior makes the decision of when to sell a rental car quite a crucial one for the firm because it involves a certain amount of risk. On one hand, selling a car when its mileage is low proactively avoids a huge decline in the car’s residual market value (even though it could also cause the firm to forfeit income from future rental customers who intend to rent that car for long durations while driving it sparingly). On the other hand, delaying selling is equally risky because the sample of early rental customers whom that car serves may only successively keep the car for short durations while significantly adding to its mileage. Such opportunistic customers would therefore have the effect of drastically diminishing the car’s market value without providing sufficient rental income to compensate. We use optimal stopping theory to derive the firm’s optimal selling policy algorithm which unfortunately comes with a practical implementation challenge. To address this issue, we propose three heuristic selling policies, one of which is based on the restart-in formulation introduced by Katehakis and Veinott (Math Oper Res 12(2):262–268, 1987). Numerical experiments using real and artificial parameter settings (1) reveal conditions under which the proposed heuristic policies outperform the firm’s current (suboptimal) policy, and (2) demonstrate how all four suboptimal policies compare to the optimal policy.

Keywords: Optimal stopping; Joint renting and vending; Applications of stochastic models; Sequential decision making (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10479-016-2240-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:317:y:2022:i:1:d:10.1007_s10479-016-2240-2

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-016-2240-2

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().