Aug 2026· Engineering, Technology & Applied Science Research· 0 citations· 29 references
Abstract
The Two-Echelon Vehicle Routing Problem with Drones (2E VRP-D) model can initiate flights from the truck, complete several deliveries to different customer locations, and then rendezvous with the truck again. In addition to economic benefits, logistics providers must consider the environmental impacts of the order-fulfillment process. A novel multi-objective optimization framework is established in this study to simultaneously minimize the total time required for truck travel while also reducing total carbon emissions. Due to restrictions in payload capacity and battery energy limits, drones need to work alongside trucks to deliver services effectively. A dynamic energy consumption model is applied for the drone, where energy use changes based on the loading rate, enabling a more realistic representation of actual operations. This complex problem is addressed using the Non-Dominated Sorting Genetic Algorithm (NSGA-II) with two approaches: the Giant Chromosome (GC) and K-means methods. Routing plans for both trucks and drones are then constructed using a novel heuristic algorithm. Overall, the K-means method delivers better average objective values, reflecting enhanced exploitation performance. Conversely, the GC method produces a higher Hypervolume (HV), indicating superior convergence and coverage of the Pareto front, supported by a lower spacing value, while K-means achieves a slightly better spread. These outcomes contribute to improving logistics operations and informing government policy decisions.
Truck–multi-drone collaborative delivery can reduce last-mile costs, but fleet sizing and routing are often optimized separately, making it difficult to match resources with demand under a delivery-period constraint. This study addresses the scenario of collaborative delivery involving multiple trucks and multiple drones by constructing a two-stage optimization framework that integrates fleet sizing and route planning. In the first stage, queueing models and continuous approximation are employed to determine the initial configuration of trucks and drones based on demand intensity and delivery cycle constraints. The second stage introduces continuous drone delivery and cross-vehicle retrieval to enhance the flexibility of truck–drone collaboration; while optimizing collaborative routes, the framework adjusts the allocation of trucks and drones—adding or reducing resources based on route feasibility and equipment utilization—thereby achieving the joint optimization of transport capacity and collaborative routes with the objective of minimizing total system costs. A node–resource–flow-separated three-chain encoding and an adaptive large neighborhood search–simulated annealing algorithm are designed to solve the model. Multi-scale numerical experiments show that, compared with four simplified fleet-sizing strategies, the proposed framework achieves average cost savings of 15.4–15.5% for medium- and large-scale instances. The results reveal an economic saturation point of the delivery period that shifts with node scale and a non-monotonic relationship between fleet size and coordination efficiency. The framework supports demand-driven fleet configuration and provides operational guidance for cost-effective truck–drone last-mile delivery.
The increasing demand for urban last-mile delivery services has intensified the need for routing approaches that simultaneously address operational efficiency and environmental sustainability. This study introduces the Green Multi-Courier Delivery Routing Problem (GMCDRP), a heterogeneous routing and assignment problem involving pedestrian couriers, electric bicycles, and motorized vehicles under capacity, distance, and service-time constraints. To solve the problem, a state-aware constructive heuristic named Emission-Minimizing Green Routing (EMGRO) is proposed. Unlike conventional metaheuristics that evaluate emissions after route generation, EMGRO integrates emission awareness directly into the assignment process by considering the real-time operational state of each courier and prioritizing the lowest-emission feasible alternative. The proposed method is evaluated using 20 large-scale scenarios derived from the real road network of Adana, Türkiye, each containing up to 1000 delivery requests. Its performance is compared with Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO) approaches. Experimental results demonstrate that EMGRO achieves the lowest average emission per delivered package (0.512 g CO2/package), outperforming ACO, PSO, and GA by 47.9%, 44.1%, and 41.9%, respectively, while maintaining identical delivery coverage. Furthermore, EMGRO generates solutions within seconds, providing substantial computational advantages over population-based metaheuristics. The findings indicate that embedding environmental considerations directly into the decision-making process can significantly improve both sustainability and computational efficiency in heterogeneous urban delivery systems.
Urban freight systems in megacities must simultaneously address carbon reduction targets and emergency preparedness requirements. This study develops a systems-oriented optimization framework for truck-drone collaborative delivery that integrates both objectives. Using Chengdu as a case study, we propose a dual-mode routing model that explicitly incorporates carbon costs as a carbon tax into the objective function. The model is solved using an Adaptive Large Neighborhood Search algorithm enhanced with Q-learning (ALNS-RL), featuring carbon-sensitive destruction and battery-constrained repair operators. We calibrate the model using Chengdu’s emission inventory across nine transport modes (2020–2025) and simulate it under carbon tax scenarios of 80, 150, and 300 CNY/ton. Results show that the drone usage ratio increases from 10.3% to 25.0% as the carbon tax rises, with a marginal incentive threshold near 150 CNY/ton. Under emergency mode, drone usage increases by 20%, while total cost and carbon emissions decrease by 4.3% and 4.2%, respectively. Overall, the proposed method reduces total cost by 31.0% and carbon emissions by 29.2% relative to a pure truck baseline. This study provides a practical decision-support framework for designing low-carbon and resilient urban logistics systems in megacities.
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.
Heictor A. O. Costa, F. V. Von Zuben· Algorithms· 0 citations
With the rapid growth of e-commerce logistics demand, transportation networks have become increasingly complex, making multi-modal transport a critical strategy for improving efficiency and reducing costs. We propose a cargo routing model grounded in arc-flow optimization to address the problem of multi-modal freight route planning and scheduling optimization. The objective function integrates weighted sums of transportation cost and time, while multiple constraints,including vehicle capacity limits, flow balance, transfer consistency, and path structure requirements, are incorporated to ensure practical feasibility. To enhance computational efficiency, nonlinear transfer logic constraints are linearized using the McCormick method. A case study is conducted on an integrated freight network comprising rail, road, and air transport modes across the Yangtze River Delta and surrounding major cities, using the 2023 "Singles’ Day" e-commerce peak season as the simulation scenario. Numerical results demonstrate that, compared with single-mode transport, the proposed multi-modal approach significantly reduces both transportation cost and time, improves resource utilization, enhances network flexibility and reliability, and effectively supports regional freight coordination and decision-making. The model exhibits strong adaptability and scalability, offering theoretical and methodological support for logistics operators in complex logistics environments.
Jun-Zhe Chen, Jie Wen· 2026 12th International Conf...· 0 citations
This study focuses on an Electric Vehicle (EV) cold chain logistics location-routing problem with charging-stations that aims at optimizing the location of depots, the delivery routing of EVs, the time planning for visiting all customers and the location of charging-stations. To tackle this problem, a multi-objective optimization model is established to minimize cold chain logistics cost, and at the same time maximize cold chain logistics network efficiency. An integrated algorithm that combines an Improved Artificial Fish Swarm Algorithm (IAFSA) and a Label-based Charging-station Optimization Algorithm (LCOA) is used to solve the proposed model. Extensive computational experiments are conducted to demonstrate the applicability of the proposed model, and show the efficiency of the developed algorithm. Moreover, the effects of battery driving range and traveling speed on the results are explored through the sensitivity analysis that provides decision supports for logistics enterprises to operate an EV cold chain logistics network.
First published online 31 July 2026
Yi Liu· Transport· 0 citations
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