Scalable No-Stockout Charging Scheduling for Battery Swapping Under Time-of-Use Prices

2026-07-26

AI Summary

This study addresses the challenges faced by battery swap stations under time-of-use electricity pricing, including the need to instantly supply fully charged batteries, satisfy hard no-stockout constraints, operate within limited charger capacity, and accommodate heterogeneous vehicle compatibility. To this end, we propose the first scalable charging scheduling framework that jointly accounts for hard no-stockout requirements, heterogeneous battery compatibility, and time-varying electricity prices. By formulating a battery-level mixed-integer linear programming model and deriving an equivalent reduced formulation to minimize binary variable count, we integrate a price-guided battery routing heuristic with rolling horizon optimization for real-time, efficient computation. Experiments demonstrate median solution times of 0.24–8 seconds for small-to-medium instances with only 7–8% cost premium, a posteriori optimality gaps bounded by 9–12% for large-scale cases, and approximately 50% lower charging costs compared to immediate-charging strategies over 1,002 real-world swaps across 30 days—while guaranteeing 100% service fulfillment.

Abstract

A battery-swapping station must provide every arriving vehicle with a charged battery while minimizing the time-of-use cost of recharging returned units. Coordinating heterogeneous compatibility, vehicle-specific return times, and finite charger capacity requires service-aware recharge decisions across the planning horizon. We formulate a per-battery mixed-integer linear program that captures these operational features under a hard no-stockout constraint and derive a provably equivalent reduced form with fewer explicit binary variables. In the synthetic scaling study, a price-guided battery-path heuristic returned a full-service schedule for every instance; regime-level median solve times ranged from 0.24 to 8.0 seconds. Its median cost premiums were 7-8% over certified reference costs at the Small and Medium scales, and its certified ex post optimality-gap upper bounds were 9-12% at the Large and xlarge scales. For each operational baseline, the certified reference schedules reduced charging-energy cost by 50-60% on instances that the baseline fully served and for which a certified reference was available. In a 30-day replay of 1,002 swaps recorded at a commercial station, the reduced-model and heuristic rolling controllers served every swap and reduced charging-energy cost by approximately 50% relative to immediate charging.

Problem

• battery swapping
• no-stockout constraint
• time-of-use pricing
• charging scheduling
• energy cost minimization

Innovation

• battery swapping
• time-of-use pricing
• no-stockout scheduling
• mixed-integer linear programming
• scalable heuristic