Search Results (144)

Combinatorial Route Optimization (CRO) problems, such as the Vehicle Routing Problem (VRP) or the Travelling Salesman Problem (TSP), are commonly seen in scheduling, logistics, and transportation. While current machine learning (ML) methods can overcome certain limitations of traditional approaches, including exact and heuristic algorithms, they typically require substantial computational resources, large training datasets, and carefully designed models, thereby limiting their scalability and practical deployment. In this paper, we develop a method to address such concerns in a data-efficient and near-training-free manner using foundation models. We select TSP, one of the most well-known combinatorial optimization problems, to solve in our experiments and employ the Tabular Prior-Data Fitted Network (TabPFN), one of the newly designed foundation models. Specifically, we develop a node-based formulation that converts TSP into a sequence of localized prediction tasks and constructs a complete route through in-context learning provided by TabPFN. The proposed method enables TabPFN, a model developed for regression and classification, to be applied to CRO problems with only one TSP sample for fine-tuning. We evaluate the proposed method across varying TSP instance sizes and demonstrate that our approach generalizes effectively without retraining, maintains competitive solution quality, and exhibits promising scalability. These findings suggest that CRO problems can be approached through foundation models, enabling scalability as well as generating rapidly deployable solutions with near-training-free adaptation. Full article

Last-mile delivery systems are under greater pressure to deliver cost-efficient, reliable, environmentally friendly, and resilient services amid operational challenges. Distance/cost is the usual optimization criterion for traditional vehicle routing methods, and factors related to disruptions, such as the delay frequency, delay severity, and delivery failure risk, are often treated separately or neglected. This study proposes a green-resilient last-mile delivery optimization framework that integrates operational costs, delivery delays, carbon emissions, and operational risk within a single multi-objective decision model. The proposed framework models the capacitated vehicle routing problem with time windows, accounting for vehicle capacity, service time commitments, fuel consumption, emission-level estimates, working hour limits, and lateness penalties and incorporating a disruption-based operational risk score. The risk score is based on the delay frequency, delay severity, and failure probability and can inform routing decisions based on efficiency and resilience. The framework is tested with a case study of urban last-mile delivery and compared with several benchmark scenarios: the current operational plan, a distance-based vehicle routing problem (VRP), a cost-based VRP, a green VRP, and a delay-aware vehicle routing problem with time windows (VRPTW). The results reveal balanced improvements in key performance indicators, in line with the proposed framework. It reduces the total distance by 35.11%, total operational cost by 34.01%, fuel consumption by 10.46%, CO₂ emissions by 9.34%, estimated late orders by 93.45%, and total delay minutes by 80.10%, and there are no working hour violations compared to the current case. Other sensitivity, weight, and ablation analyses illustrate the trade-offs among cost/service reliability/environmental goals and risk exposures. The results show that operational risk can be incorporated into the green last-mile routing problem to facilitate more comprehensive—and thus more robust and sustainable—delivery planning in the context of disruptions in urban environments. Full article

Despite the large amount of successful existing methods and frameworks for planning sets of multiple unmanned aerial systems (UASs), there is still a lack of coordination frameworks that are capable of coping with real-world operational conditions. This paper presents U-Plan, an integrated management framework for the coordination of multi-UAS missions. U-Plan is designed to plan, schedule, monitor, and replan a heterogeneous set of UASs to complete point of interest (PoI) visiting missions while ensuring that all the generated trajectories are safe, feasible, and compliant with the required PoIs’ arrival times, UAS kinematics and energy constraints, and the existing 3D no-fly zones (NFZs). U-Plan is designed as a practical tool for strongly dynamic missions and is built upon three core components: (1) an NFZ-aware route computation method that explicitly accounts for NFZs prior to vehicle routing problem (VRP) optimization, resulting in shorter NFZ-safe routes; (2) a trajectory smoothing module that ensures the generation of kinematically feasible trajectories for fixed-wing UASs; and (3) a mission supervision module for real-time monitoring and replanning in case of changes in the UAS, mission, wind speed, or airspace restrictions. To validate the proposed architecture, we conducted rigorous experiments utilizing the VECTOR-SIL autopilot and Visionair Ground Control Station to realistically replicate the behavior of certified fixed-wing autopilots under various weather conditions using the exact same hardware and flight control software that runs onboard the physical drones. The validation shows U-Plan’s capacity to efficiently satisfy complex mission requirements with strong scalability. Due to its high computational efficiency, U-Plan enables online mission replanning, allowing UAS fleets to seamlessly adapt to changes that are typical of real-world operational scenarios. Full article

Background: The Vehicle Routing Problem (VRP) is foundational to logistics optimization, yet its alignment with the Triple Bottom Line (TBL) and UN Sustainable Development Goals (SDGs) remains fragmented. This study conducts a strategic bibliometric audit of 301 peer–reviewed publications (1992–2025) to quantify the evolutionary progression and thematic maturity of sustainable routing research. Methods: A four–stage scientometric framework was employed, utilizing Scopus–based data retrieval, longitudinal mapping, and Python 3.14–driven text mining to visualize keyword co–occurrence networks, author collaborations, and regional research clusters. Results: Findings reveal a pronounced “Sustainability Asymmetry,” where 51.5% of studies prioritize economic efficiency, while only 2.6% address the social pillar. Additionally, social sustainability remains an “isolated island” with minimal cross–citation to the research core. Geographic analysis identifies a heavy concentration in China, the USA, and Western Europe, uncovering a critical North–South—collaboration gap. Conclusions: The study proves that while environmental themes reached maturity between 2018 and 2022, social indicators exhibit a significant maturity lag. This quantified social deficit, centered on the neglect of SDG 3 and SDG 10, mandates a fundamental paradigm shift toward a geographically inclusive and socially conscious research agenda to ensure global logistical equity. Full article

This systematic literature review (SLR) synthesizes current research on integrating machine learning (ML) into robust optimization (RO) frameworks for solving Green Vehicle Routing Problems (Green-VRP) under uncertainty. The key contributions include utilizing the EmbedSLR 2.0 framework for objective screening, establishing a functional ML role taxonomy, and mapping uncertainty sets to computational tractability. Following PRISMA guidelines, searches across Scopus, Sage, and Dimensions identified 82 eligible studies validated through a three-point quality assessment scale. Bibliometric analysis indicates that the VRP has evolved into an interdisciplinary field that combines the power of rigorous RO with the integration capabilities of ML to achieve sustainability and resilience goals. Based on the results of the literature review, it was found that ML plays four crucial functional roles: as an end-to-end problem solver, a tool for predicting input parameters, a guide for search subroutines, and a mechanism for constructing more precise uncertainty sets. Various frameworks such as Adjustable Robust Optimization (ARO), Distributionally Robust Optimization (DRO), and Data-Driven Robust Optimization (DDRO) have been reported in various studies to offer improved cost efficiency and robustness compared to conventional static RO models by utilizing data more dynamically to reduce the level of conservatism. The integration of these environmental factors is carried out through emission and energy consumption parameters, which systematically give rise to operational trade-offs. This SLR has several limitations, including database and language limitations, the absence of cross-reference validation in EmbedSLR 2.0, and limitations in quality assessment. This publication is funded by the Universitas Padjadjaran through the LPDP on behalf of the Indonesian Ministry of Higher Education, Science and Technology and managed under the EQUITY Program (Contract No. 4303/B3/DT.03.08/2025 and 3927/UN6.RKT/HK.07.00/2025), as well as the Universitas Padjadjaran Research Grant under Research Grant for Graduate Students (Hibah Riset Melibatkan Mahasiswa Pascasarjana - RMMP) with contract number 5598/UN6.3.1/PT.00/2025. This systematic review was registered on the Open Science Framework (OSF) on 8 May 2026. Full article

The Multi-Destination Vehicle Routing Problem (MD-VRP) with a heterogeneous electric fleet is a critical challenge in optimizing commuter services for large-scale institutions and logistics operations. To address the complexities of electric fleet composition uncertainty and multi-center routing in “micro-city” campus environments, this paper establishes a robust multi-objective programming model. The model aims to simultaneously minimize three conflicting objectives, the total number of vehicles, total driving distance, and total electric energy consumption (kWh), under constraints of flow conservation and vehicle availability. Considering the nondeterministic polynomial-time hard (NP-hard) nature of the problem, a novel two-stage hybrid heuristic algorithm is proposed. In the first stage, a Modified Kruskal’s algorithm is employed to aggregate scattered stops into optimized clusters to reduce dimensionality. In the second stage, a State-Compressed Dynamic Programming (SC-DP) algorithm is applied to determine the optimal routing and electric vehicle type selection for each cluster. The methodology is validated using a case study of a large-scale campus network with 100 nodes. The optimization results identify an optimal fleet configuration of 41 campus electric commuter vehicles across three specific types (capacities of 45, 55, and 60), resulting in an annual total energy consumption of 5893.98 kWh. Compared with a global Ant Colony Optimization (ACO) baseline in this case study, the proposed framework reduces the required fleet size by 22.6% and annual energy consumption by 9.2%; however, this comparison should be interpreted as a preliminary case-study benchmark because the proposed method adopts a decomposition-based “Cluster-First, Route-Second” strategy. The results indicate that the approach achieves higher solution efficiency, offering an economically and environmentally friendly scheme for electric vehicle fleet operations. Full article

In many real-world logistics systems, two-echelon distribution structures and clustered customer demands often coexist. However, traditional Two-Echelon Vehicle Routing Problems (2E-VRPs) mainly focus on the coordination between depots, satellites, and customers, while usually ignoring clustered customer service requirements. To fill this research gap, this study investigates a novel variant of the 2E-VRP, called the 2E-VRP with Clustered Customers (2E-VRP-CC). In this problem, customers in the second echelon are partitioned into predefined clusters, and all customers within a cluster must be visited consecutively by the same vehicle. For the problem, a Mixed-Integer Linear Programming (MILP) model is first established, followed by the development of an Adaptive Large Neighborhood Search (ALNS) algorithm integrated with a local search method. To validate the effectiveness of the proposed algorithm, comparisons are conducted on instance sets adapted from the literature. For the traditional 2E-VRP, which is a special case of the 2E-VRP-CC, the proposed algorithm is compared with existing methods in the literature. For the proposed 2E-VRP-CC, it is compared with the CPLEX solver. Extensive computational experiments demonstrate that the proposed algorithm can achieve high-quality solutions within relatively short computing times, confirming its effectiveness and efficiency. In addition, sensitivity analysis shows that the number of customer clusters has a significant impact on transportation costs. The results indicate that moderately increasing the number of customer clusters can effectively reduce operational costs and provide practical decision support for customer clustering design and two-echelon logistics planning. Full article

This paper investigates a novel variant of the two-echelon vehicle routing problem (2E-VRP) within the context of modern e-commerce logistics. The model integrates time windows, occasional trucks, occasional drivers, heterogeneous regular vehicles, and two increasingly relevant types of intermediate facilities: transshipment nodes and parcel lockers. Goods are transported from a first-echelon depot to intermediate facilities via occasional trucks and heterogeneous regular trucks, then delivered to customers through occasional drivers and heterogeneous regular riders at the second echelon, or retrieved by customers from designated parcel lockers. Given significant disparities in service scope, vehicle attributes, delivery rules, and cost structures between the two echelons, the crowdsourcing model for the first echelon is redesigned, and new intermediate facilities are incorporated to expand application scenarios and further enhance the operational advantages of the crowdsourcing mode. The objective aims to minimize transportation costs and minimize customer dissatisfaction costs. This study constructed a two-echelon vehicle routing optimization model under the crowdsourcing mode with time windows and intermediate facilities and developed an improved multi-objective sparrow algorithm (IMOSSA) to solve it. Algorithm comparisons and extensive case studies validate the algorithm’s effectiveness and superiority. Scenario analysis investigates the impact of crowdsourced vehicles on routing decisions, experimentally demonstrates the crowdsourcing model’s advantages, and derives practical managerial insights. Full article

Uncertainty in travel and service times poses significant challenges for vehicle routing in logistics systems. This paper proposes a stochastic model predictive control (SMPC) strategy to manage a Vehicle Routing Problem with time windows (VRPTW) under stochastic service times with correlation across customers. The approach combines a dynamic optimization model with single and joint chance constraints and a forecasting tool for updating travel plans as new information becomes available. A deterministic reformulation of the stochastic constraints is developed so that the problem can be solved via mixed-integer programming. The aim of this paper is to demonstrate that the SMPC strategy can maintain a high level of time-window reliability (meeting customer time windows with high probability) at a reasonable cost by re-optimizing routes over a moving horizon. In numerical case studies, the SMPC approach achieves the desired reliability levels while incurring only modest increases in total cost, and it flexibly adjusts the cost–risk tradeoff by switching between single and joint chance constraints. These results illustrate the potential of the proposed method for real-time distribution routing under uncertainty and highlight the novel contribution of integrating chance-constrained optimization with Model Predictive Control in a VRPTW context. Full article

The Vehicle Routing Problems with Time Windows (VRPTW) has remained a classic and continuously studied problem since its introduction. With the rapid growth of cold chain product distribution demands, VRP research has become increasingly important for guiding real-world scheduling decisions. However, most studies focus on further subdividing new scenarios and constraints, often overlooking fundamental real-world applications. This includes the impact of unknown road conditions on costs, rough cost modeling, and poor algorithm adaptability to high-dimensional cold chain constraints. To address these three issues, this paper proposes the Spatio-temporal dependency and road network distribution-based traffic forecasting model (STD-RND) to provide region-level traffic scheduling information. The model also constructs cost functions to quantify cargo spoilage, refrigeration, and carbon emissions. Finally, we introduce an Improved Hippo Optimization with Traffic Forecasting (IHTF) that incorporates traffic prediction to enhance the solution quality of the VRPTW in cold chain scenarios. To strengthen optimization performance and prevent premature convergence to local optima, we integrate several enhanced strategies, including chaotic mapping, dynamic Cauchy mutation, and an escape mechanism. Through a series of experiments on the Solomon dataset and simulation datasets based on real road networks, we demonstrate that the proposed algorithm shows consistent superiority and effectiveness. Full article

Urban freight and service operations represent a critical challenge for cities, contributing to greenhouse gas emissions, congestion, and competition for curb space. In addition to parcel deliveries, many service trips combine transport with installation, maintenance, or packaging recovery, generating long vehicle dwell times and inefficient use of public space. This paper investigates alternative operational scenarios for such activities, evaluating technological and organizational options that can reduce their environmental and spatial impacts. The study compares a diesel LCV baseline with four zero-emission configurations: battery electric LCVs; battery electric LCVs integrated with micro-hubs and cargo e-bikes; hydrogen fuel cell LCVs for long-range operations, and hydrogen fuel cell LCVs combined with cargo e-bikes via micro-hubs. The methodological framework is based on a vehicle routing problem (VRP) formulation supported by empirical data from Rome. It integrates indicators of energy use, carbon emissions, and curb-side occupation, and it includes the spatial representation of routes on urban and inter-urban maps to highlight operational differences across the five scenarios. Results indicate that zero-emission vehicles can eliminate tailpipe emissions, while logistics reorganization through decoupling improves the use of public space and enables the recovery of packaging materials. Battery solutions appear best suited to short and medium distances, whereas hydrogen is advantageous for longer routes. Overall, the study shows that combining technological and organizational measures provides a robust pathway toward sustainable logistics and more efficient service operations in metropolitan contexts. Full article

Background: Agricultural logistics in arid, geographically dispersed areas require complex trade-offs among efficiency, equity, and robustness under uncertainty. Standard multi-objective vehicle routing problem (VRP) formulations, which primarily focus on cost or environmental parameters, do not explicitly account for social equity or transparency in decision-making. However, existing work seldom combines the objective of social equity as an endogenous optimization objective with robustness and interpretability within a unified mathematical framework. Methods: In this paper, we present a systems engineering decision-support framework informed by a multi-objective mixed-integer linear programming formulation for agricultural logistics planning. Economic, environmental, operational, and social equity goals are combined through ε-constraint to create trade-offs that can be interpreted at the policy level. We assess robustness against demand and travel-time uncertainty using the Bertsimas–Sim framework. A staged activation strategy separates conceptual model completeness from numerical implementation, and sensitivity analyses are conducted by perturbing vital operational parameters. Results: An illustrative situation in Northern Chile shows that this framework produces stable decision regimes and clear trade-offs in practice. The results show that meaningful improvements in workload balance and service equity can be achieved with negligible changes in operational efficiency. As we have learned in sensitivity experiments, assignment structures and qualitative trade-off patterns are robust under realistic parameter variations, and structural changes occur only beyond known threshold regimes. Conclusions: The major contribution of this work is the formulation of a systems engineering framework that extends traditional multi-objective VRP formulations and integrates social equity, robustness, and decision transparency as core design principles. Instead of focusing only on numerical optimization performance, the framework encourages auditable planning decisions in the face of uncertainty. The numerical analysis results are for a proof-of-concept scale only; however, the framework can be extended to larger agricultural networks using decomposition and/or hybrid solutions. Full article

In the context of sustainable logistics planning, carbon emission costs have become a critical factor influencing distribution decisions. Meanwhile, the time-dependent characteristics of urban road networks and simultaneous pickup–delivery operations present significant challenges to vehicle routing problems (VRPs). This study addresses a time-dependent vehicle routing problem with simultaneous pickup–delivery and time windows (TDVRPSPDTW). Fuel consumption and carbon emission costs are quantified using a comprehensive emission model, while time-dependent network conditions, simultaneous pickup–delivery demands, and time window constraints are integrated into a unified modeling framework. To solve this NP-hard problem, an improved ant colony optimization (IACO) algorithm is developed by incorporating adaptive large neighborhood search to enhance solution diversity and convergence efficiency. Computational experiments are conducted using internationally recognized VRPSPDTW benchmark datasets and newly constructed TDVRPSPDTW instances, together with sensitivity analyses under varying traffic conditions, time window flexibility, and delivery strategies. The results indicate that the proposed IACO effectively addresses the TDVRPSPDTW. Comparing ant colony optimization with local search (ACO-LS), the IACO achieves a maximum reduction of 11.78% in total distribution cost. Furthermore, relative to the conventional separate pickup–delivery strategy, the simultaneous pickup–delivery mode reduces total distribution cost and carbon emission cost by 49.96% and 53.48%, respectively. Full article

This paper introduces a novel, integrated optimization framework for sustainable multi-site logistics planning, which simultaneously addresses production, inventory, and distribution decisions. The proposed hybrid methodology combines a Genetic Algorithm (GA) with Linear Programming (LP) to minimize total logistics costs while proactively integrating environmental impact assessment. The model determines optimal production schedules across multiple facilities, manages inventory levels, and solves the Vehicle Routing Problem (VRP) for distribution. A key innovation is the incorporation of a CO₂ emission forecasting module directly into the optimization loop, allowing the algorithm to anticipate and mitigate the environmental consequences of logistics decisions during the planning phase, rather than performing a post-hoc evaluation. The framework was implemented in Python 3.13.4, utilizing the PuLP library for LP components and custom-developed GA routines. Its performance was validated through a numerical case study and a series of sensitivity analyses, which investigated the effects of fluctuating demand and key cost parameters. The results demonstrate that the inclusion of emission forecasting enables the identification of solutions that achieve a superior balance between economic and environmental objectives, leading to significant reductions in both total costs and predicted CO₂ emissions. This work provides practitioners with a scalable and practical decision-support tool for designing more sustainable and resilient multi-echelon supply chains. Full article

Background: The vehicle routing problem (VRP) is of great importance in the Industry 4.0 era because enabling technologies such as the internet of things (IoT), artificial intelligence (AI), big data, and geographic information systems (GISs) allows for real-time solutions to versions of the problem, adapting to changing conditions such as traffic or fluctuating demand. Methods: In this paper, we model and optimize a classic multi-link distribution network topology, including randomness in travel times, vehicle availability times, and product demands, using a hybrid approach of nested linear stochastic programming and Monte Carlo simulation under a time-window scheme. The proposed solution is compared with cutting-edge metaheuristics such as Ant Colony Optimization (ACO), Tabu Search (TS), and Simulated Annealing (SA). Results: The results suggest that the proposed method is computationally efficient and scalable to large models, although convergence and accuracy are strongly influenced by the probability distributions used. Conclusions: The developed proposal constitutes a viable alternative for solving real-world, large-scale modeling cases for transportation management in the supply chain. Full article