An optimal stopping policy for car rental businesses with purchasing customers

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.

Optimal Real Estate Pricing and Offer Acceptance Strategy

“…Problems of optimal stopping have a long history and have been widely studied in both probability theory and operations research [1]. Recent papers have used optimal stopping theory to investigate various applications, such as selling an asset [2], selling an ex-rental car in a rental business [3], stopping testing in software test management [4], stopping the interaction between a seller and a buyer who bargain to determine the transfer price [5], and selecting a cell in 5G networks [6].…”

Integer programming models and linearizations for the traveling car renter problem

“…Researches in this area have been driven under the viewpoint of the car rental industry. For example, recent studies investigated vehicle reservation and assignment [11,14,16,17], profit management [13] and optimal selling policies [4].…”