Optimizing metro-integrated freight delivery under time-of-use electricity pricing and non-stationary shipment arrivals

Abstract

This study investigates a metro-integrated freight delivery optimization problem under time-of-use electricity pricing, where an entire planning horizon is divided into multiple rolling decision periods. Across these rolling decision periods, shipment arrivals may exhibit different distributions. In each decision period, trains operating along a metro corridor coordinate with external transport modes to deliver shipments. The resulting total energy cost includes both metro train energy cost and external transport energy cost, and is jointly affected by train timetables, speed profiles, shipment access-station choices, and train assignments. For this practical problem, a mixed-integer linear programming model is formulated to minimize the total energy cost by jointly optimizing these interdependent decisions. To improve computational efficiency, we design an online continual reinforcement learning (CRL)-guided algorithm to add cuts to the mixed-integer linear programming model, thereby reducing the solution space. Additionally, we adopt a progress-and-compress-based CRL framework to enable the agent to continually adapt to varying shipment arrival distributions across decision periods. Computational results show that the proposed algorithm obtains high-quality solutions more efficiently than both Gurobi and traditional reinforcement learning. Managerial insights further reveal that (i) minimizing energy cost is not always equivalent to minimizing total energy consumption under time-of-use electricity pricing, especially before the onset of higher electricity prices, and (ii) introducing a small shipment waiting-time penalty can promote just-in-time shipment transfers so as to reduce unnecessary storage pressure at stations.

Keywords

multi-mode logistics networks / metro-integrated freight delivery / TOU electricity pricing / continual reinforcement learning / energy optimal

RIGHTS & PERMISSIONS

Higher Education Press 2026

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