Relocating idle assets is a core operational challenge in the transportation industry, particularly for shared mobility services such as ride-hailing, car-sharing, and bike-sharing. The productivity and profitability of these services depend on effectively aligning the spatial and temporal distribution of available assets with fluctuating demand. This often requires routinely repositioning idle assets to anticipated high-demand areas—or “hot spots.” Although relocation is costly and non-revenue-generating in itself, it is essential for mitigating persistent supply–demand imbalances. Efficient relocation strategies are therefore critical to enhancing both user experience and operational performance.
The central challenge of relocation lies in the inherent uncertainty of demand. In ride-hailing and car-sharing markets, for example, passenger arrivals at specific locations vary not only by hour of the day but also from day to day. Such variability is only partially predictable, as travel patterns are often influenced by irregular events such as weather or accidents. To cope with this uncertainty, relocation strategies must be designed to be robust, protecting the service against extreme outcomes. Our study is motivated by the formulation and solution of such a robust relocation problem.
While the basic formulation of the problem is straightforward, solving it efficiently is not. We address this challenge with a novel insight inspired by the well-known “bucket effect.” Specifically, given a fixed relocation routing policy, once a zone is saturated with supply—meaning its demand is fully met at steady state—shifting additional demand elsewhere cannot increase overall profit. This insight, first conceived by Ruijie Li, the lead author and a long-term collaborator who visited my lab, provided the foundation for our approach.
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Abstract: Relocating idle vehicles is a key challenge in autonomous shared mobility systems. This paper develops a robust optimization framework for steady-state relocation under uncertain demand, extending the fluid queuing network model of Braverman et al. [2019] to account for coupled uncertainty-where zone-level demand variations are bounded both locally and by a global budget. Although such uncertainty typically makes robust optimization intractable, we uncover a structural property, which we call the bucket effect: once a zone is saturated with supply (i.e., its demand is fully met) at steady state, shifting demand elsewhere cannot increase overall profit. This insight allows us to reformulate the robust relocation problem as a tractable linear program. Using New York City taxi data, we demonstrate the model’s practical value. The robust relocation strategy delivers higher profit and service availability than no-relocation baselines, while also providing greater stability under demand fluctuations. Importantly, these gains are achieved with sparse relocation patterns, indicating that targeted repositioning-guided by the bucket effect-can yield substantial benefits with modest operational effort.