The rapid increase in carbon emissions from the logistics transportation industry has underscored the urgent need for low-carbon logistics solutions. Electric logistics vehicles (ELVs) are increasingly being considered as replacements for traditional fuel-powered vehicles to reduce emissions in urban logistics. However, ELVs are typically limited by their battery capacity and load constraints. Additionally, effective scheduling of charging and the management of transportation duration are critical factors that must be addressed. This paper addresses low energy consumption scheduling (LECS) problem, which aims to minimize the total energy consumption of heterogeneous ELVs with varying load and battery capacities, considering the availability of multiple charging stations (CSs). Given that the complexity of LECS problem, this study proposes a heterogeneous attention model based on encoder-decoder architecture (HAMEDA) approach, which employs a heterogeneous graph attention network and introduces a novel decoding procedure to enhance solution quality and learning efficiency during the encoding and decoding phases. Trained via deep reinforcement learning (DRL) in an unsupervised manner, HAMEDA is adept at autonomously deriving optimal transportation routes for each ELV from specific cases presented. Comprehensive simulations have verified that HAMEDA can diminish overall energy utilization by no less than 1.64% compared with other traditional heuristic or learning-based algorithms. Additionally, HAMEDA excels in maintaining an advantageous equilibrium between execution speed and the quality of solutions, rendering it exceptionally apt for expansive tasks that necessitate swift decision-making processes.