The rapid growth of electric vehicles (EVs) is intensifying charging demand in space-constrained parking facilities, where fixed charging piles (FCPs) are often underutilized due to parking–charging coupling and stall blocking. This study develops a coordinated planning framework for a hybrid charging system that integrates FCPs and mobile charging robots (MCRs). Two optimization models—operator profit maximization and social welfare maximization—are formulated to jointly determine the capacity configuration (numbers of FCPs and MCRs) and the spatial layout of FCPs and MCR base stations, subject to a queueing-theory-based waiting-time constraint. A nested heuristic solution method combining particle swarm optimization (PSO) and K-means++ is designed for tractable computation. Numerical experiments on a representative parking facility demonstrate a clear complementarity between fixed and mobile chargers: FCPs serve baseload demand economically, while MCRs provide flexible capacity that reduces average waiting time and mitigates congestion. The results further quantify the divergence between private and social objectives; when robot costs are reduced, the social-welfare model deploys approximately 35% more robots than the profit-maximizing solution to reduce user time losses. By improving charger utilization, the proposed hybrid planning approach enhances resource efficiency and supports sustainable EV charging infrastructure in dense urban parking facilities.
Kong et al. (Sun,) studied this question.
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