Integrating Valet Charging with Mobile Discharging Services: A Strengthened Integer L-Shaped Method

Valet charging is an emerging business model in which a platform recruits couriers to assist electric vehicle (EV) owners with recharging their vehicles. Although the service provides a convenient charging solution, especially for those without residential chargers, its adoption has been limited because of affordability concerns. To address this challenge, we propose integrating valet charging with mobile discharging services. Under the integrated model, customers can receive discounted prices by allowing their EVs to participate in discharging tasks. The success of this integration hinges on incentivizing customers to extend their vehicle return deadlines despite uncertainty about their willingness to delay. We model the incentive design problem as a two-stage stochastic program. In the first stage, the platform designs a deadline-differentiated price menu, offering multiple return time options, each with an associated price. In the second stage, customers select the return deadline that maximizes their utility, after which the platform assigns EVs to discharging jobs and schedules charging operations. This problem is challenging given its nonlinearity and mixed-integer recourse. To tackle the problem, we first devise an exact linear reformulation that preserves decomposability without any loss of optimality. We then adapt the integer L-shaped method to this reformulation, constructing strengthened optimality cuts that encode the intrinsic interdependence between first and second stage decisions. These cuts are proven to dominate those used in the standard integer L-shaped method. Additionally, we develop a model reduction technique that projects the problem onto a smaller decision space independent of the sample size, thereby facilitating the use of a larger scenario set within the sample average approximation framework. Experimental results show that our proposed method significantly outperforms commercial solvers and the integer L-shaped method in its standard form, achieving enhanced efficiency and scalability. Furthermore, the findings underscore the mutual benefits of the integrated service: the platform increases its revenue and customers enjoy reduced valet charging costs. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0912 .