Grid-Aware Bi-Level Optimization for Truck–Drone Routing: Integrating Grid Feasibility and Shadow Pricing

Abstract

Electric trucks operating as mobile depots for delivery drones are promising for last-mile logistics, yet fleet electrification makes depot charging a critical issue governed by distribution-grid limits. Existing truck–drone routing formulations omit the electrical network, treating energy as exogenous, while grid-aware routing models overlook the combinatorial structure of mobile-depot drone synchronization. This paper introduces an energy-aware bi-level framework for the truck–drone routing problem that closes this gap. A distribution-grid leader solves slot-wise alternating current (AC) optimal power flow (OPF) under time-varying base loads and line deratings, returning a grid-feasible energy headroom and shadow prices. A logistics follower then co-optimizes truck routes, drone sorties, and ramp-constrained charging against this effective price, within a multi-objective cost structure. A damped fixed-point iteration couples the two levels, communicating grid scarcity through a single price signal without the logistics layer solving power-flow equations. On a Tokyo-inspired 100-customer instance with a stressed IEEE 33-bus feeder, the framework confines charging to slots with genuine headroom, reaching at most 81% loading and returning the fleet fully charged, whereas a grid-blind baseline reaches 109% loading. This comparison validates shadow pricing as an effective coordination mechanism.