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In response to the challenges posed by economic globalisation and increasing customer demands, enterprises are compelled to adapt and refine their production models and operational objectives, which motivates this paper to address the integrated production scheduling and vehicle routing problem in the distributed manufacturing environment (IPSVRP-DME). The objective is to simultaneously minimise both total energy consumption and total earliness/tardiness. Initially, a mixed integer programming model is proposed to address small-scale problems using Gurobi. Considering the NP-hardness of the problem, a novel Self-adapted Gaussian Mutation-based Arithmetic Optimiser Algorithm (SGMAOA) is developed to handle medium-scale and large-scale instances. To address the complexity of decision-making, an innovative two-level encoding method that encompasses four decision dimensions is introduced. Additionally, an incremental repair strategy is devised to rectify infeasible solutions caused by unreasonable delivery batching, while a time relaxation strategy is proposed to further enhance service levels without compromising energy consumption. Comparative experiments are conducted to demonstrate the effectiveness of SGMAOA, which is benchmarked against five prominent metaheuristics. In addition, a specific example is applied for the discussion of managerial applications and to illustrate the practicality of the proposed model and solution method. [ABSTRACT FROM AUTHOR]

The rapid growth of pharmaceutical refrigerated logistics poses sustainability challenges, including elevated costs, energy consumption, and resource inefficiency. Collaborating multiple depots can enhance logistics efficiency when standalone distribution centres have limited transport resources, i.e. refrigerated vehicles. However, the sustainable benefits and performance across different strategies remain unexplored. This study fills this research gap by addressing a refrigerated pharmaceutical routing problem. While many collaborative strategies prioritise economic and environmental benefits, our approach highlights a vital social indicator: maintaining vehicle flow equilibrium at each depot during collaboration. This ensures the stability of transport resources for all stakeholders, promoting sustainable collaborative logistics. The problem is formulated as a multi-depot vehicle routing problem with time windows (MDVRPTW). Three collaborative strategies using Clustering VRP (CLUVRP) and improved Open VRP (OVRP) are proposed and compared. We develop two approaches to address traditional OVRP limitations in ensuring vehicle flow equilibrium at each depot. Our models consider perishable pharmaceuticals and time-dependent travel speeds. Three hybrid heuristics based on Simulated Annealing and Variable Neighborhood Search (SAVNS) are proposed and evaluated for efficacy. Computational experiments and a case study demonstrate distinct sustainable benefits across various strategies, offering valuable insights for decision-makers in the refrigerated logistics market. [ABSTRACT FROM AUTHOR]

E-commerce is a continuously growing sector significantly affected by sustainability issues during the last few years. To deal with economic, environmental and social sustainability aspects, e-commerce platforms consolidate orders to pick-up several requests from the same location, defining the so-called Few-to-Many Pick-up and Delivery Vehicle Routing Problem (F-M VRPPD). The proposed contribution addresses the optimisation of this problem by developing a multi-objective simulated annealing algorithm distinguished by four tailored Local Search (LS) operators specifically developed to increase the probability to identify feasible solutions and decrease the computational time. This algorithm is validated with several instances of a case study e-commerce platform based in an European mountain region. Firstly, the original LS operators are compared to benchmark literature ones to solve identical problems, reporting better performance in 84% of these instances. Furthermore, for the most relevant scenarios significant results are presented and discussed concerning the economic, environmental and social performance of the defined solutions according to the characteristics of the instances, as the routes height profile and the drivers' metabolic energy consumption. The tri-dimensional Pareto frontiers suggest how through a slight worsening in the economic objective function it is possible to improve the social one by up to 18.3% on average. [ABSTRACT FROM AUTHOR]

Along with the rapid growth of online purchasing, more and more e-retailers tend to adopt the front warehouse mode to improve the performance of customer service by locating multiple front warehouses with limited space and storage capacity closer to consumers. In this context, order splitting and distribution become increasingly crucial decisions that might impact the efficiency of order fulfillment. These two issues are investigated in the related works commonly as two independent problems, although they are inherently coupled with each other. This study established an integrated optimization model for order splitting and distribution routing for the front warehouse mode e-retailing. The model considers practical features, including order splitting constraints based on product type and quantity, finite inventory, heterogeneous vehicle routing constraints, and time windows. A branch-price-and-cut algorithm is proposed to solve the problem. Two logic-based Benders cuts are designed to deal with the infeasible distribution routes. The efficiency of the proposed algorithm is verified in an experimental study by considering CPLEX and two heuristic algorithms as benchmark methods. The dominance of our proposed algorithm is observed, especially for large-scale cases. The impacts of overlapping inventory levels, the combination of heterogeneous vehicles, and the width of time windows are also examined. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the non-unit demand capacitated minimum spanning tree problem with arc time windows and flow costs. The problem is a variant of the capacitated minimum spanning tree problem with arc time windows (CMSTP_ATW). We devise a mixed integer programming (MIP) formulation to model the problem and solve it using CPLEX. Furthermore, we propose three sets of inequalities, and we prove that they are valid. These valid inequalities tighten the model and lead to better lower bounds. To examine the quality of the solutions obtained, we convert the original data sets of Solomon (1987, "Algorithms for the Vehicle Routing and Scheduling Problem with Time Window Constraints." Operations Research 35 (2): 254–265. ) to approximate the non-unit demand CMSTP_ATW instances and provide results for the problems with 100 nodes. We execute extensive computational experiments, and the results show the positive effect of the inclusion of valid inequalities in the MIP. [ABSTRACT FROM AUTHOR]

This paper focuses on the combined maintenance and routing optimisation problem in a multi-period environment that consists of scheduling maintenance operations for a set of geographically distributed machines, subject to non-deterministic failures with a set of technicians that perform preventive maintenance and corrective operations. This study uses a two-step approach based on column generation. The first step consists of a maintenance model that determines the optimal time until the next preventive maintenance operation, and each machine's maintenance frequency while minimising the total expected maintenance costs. The second step involves a routing model that assigns and schedules maintenance operations for each technician over the planning horizon while minimising the routing and maintenance costs. We formulate the second step problem as a periodic vehicle routing problem and to solve it, we propose a column generation approach. The master problem is a set partitioning formulation that indicates which machines must be visited in the planning horizon. This decomposition has two auxiliary problems: the first one is an elementary shortest-path problem to find a feasible path for each period and the second one finds a set of visiting periods for each machine. Our approach balances the maintenance cost, routing cost, and failure probabilities. [ABSTRACT FROM AUTHOR]

The global supply chain relies on road, land, and air transport, significantly contributing to greenhouse gas emissions. Various measures have been proposed to reduce these emissions, including energy taxes, environmentally friendly vehicles, and optimized transportation loads. Current optimization mainly considers fixed loads and vehicle types to reduce CO2 emissions. However, dynamic loads in distribution networks and their interactions with factors like distance and vehicle type have not been studied. The present work contributes by (a) extending a vehicle routing problem (VRP) database to include vehicle type and load size data; (b) developing a mathematical model for emissions based on traveled distance, vehicle type, and load size; (c) creating a multivariate database of the emissions considering optimal routing; and (d) analyzing the database to identify key factors influencing emissions. A factorial analysis determined that vehicle type, load size, and traveled distance are the main factors associated with CO2 emissions. By coding and rearranging the database considering three levels for each main factor, a 3k full factorial design was developed to analyze the interactions of these factors and their effect on CO2 emissions. The results of the analyses corroborate that optimizing vehicle utilization and minimizing routes, which depend on optimal load, distribution routes, and infrastructure planning, are recommended actions to reduce emissions. [ABSTRACT FROM AUTHOR]

The incessant consumption of goods and materials underscores the need to address the growing problem of waste generation and its profound impact on environmental sustainability. The problem of waste removal can be approached in different ways, whether it is the routing of vehicles, the work of drivers, the optimal distribution of waste bins, or other matters in the entire waste process. The aim of this study is to investigate the possibilities of optimizing waste collection processes in the region using a slightly modified Clark–Wright method. Optimal waste collection routes are defined with a focus on cost reduction and overall optimization of logistic chain processes. The established mathematical model for the capacitated vehicle routing problem includes the principles of sustainability and environmental friendliness. The results indicate that the largest messenger of all the newly proposed routes are the routes containing the surrounding settlements. Newly designed routes lead to significant reductions in fuel consumption and vehicle maintenance, which has a positive impact on financial and environmental resources. The conclusion indicates that by applying the Clark–Wright method, we have achieved a reduction in the number of routes of twenty fewer routes. This study provides regions with a detailed plan to improve waste management practices, contributing to a future of increased sustainability and environmental awareness. [ABSTRACT FROM AUTHOR]

The Vehicle Routing Problem (VRP) is a well-known discrete optimization problem that has an impact on theoretical and practical applications. In this paper, a freight distribution model that includes a charging system located at the depot, making it feasible for real world-implementation, is proposed. Two different solution methods are proposed and compared: a genetic algorithm (GA) and a population-based simulated annealing (PBSA) with the number of moves increasing during the iterations. Among the variety of algorithm used to solve the VRP, population-based search methods are the most useful, due to the ability to update the memory at each iteration. To demonstrate the practical aspects of the proposed solution a case study is solved using travel time on a real network to evaluate the potentiality for a real-world application. [ABSTRACT FROM AUTHOR]

We address two interrelated issues affecting the hinterland portion of the maritime container supply chain: reducing the movement of empty containers and reducing empty trips by trucks carrying these containers. In this paper, we show that empty container flow optimization can be implemented via a blockchain based on the proof‐of‐useful‐work concept where the proof of work requires the solution of an NP$\mathcal{NP}$‐hard optimization problem whose solution benefits the blockchain participants. Accordingly, we propose that anonymous miners compete to solve the container truck routing problem, which seeks to find the most efficient routes for trucks. We show that this problem is NP$\mathcal{NP}$‐hard. Miners must also solve the problem of optimally matching consignees and shippers, which will reduce transportation and storage costs for empty containers. In essence, the proposed framework turns blockchain into a massive optimization engine that directly benefits the hinterland container supply chain ecosystem. [ABSTRACT FROM AUTHOR]

Optimizing shared resources across multiple clients is a complex challenge in the production, logistics, and service sectors. This study addresses the underexplored area of forecasting service costs for non-cooperative clients, which is essential for sustainable business management. We propose a framework that merges Operations Research (OR) and Machine Learning (ML) to fill this gap. It begins by applying the OR model to historical instances, optimizing resource allocation, and determining equitable service cost allocations for each client. These allocations serve as training targets for ML models, which are trained using a combination of original and augmented client data, aiming to reliably project service costs and support competitive, sustainable pricing strategies. The framework's efficacy is demonstrated in a reverse logistics case study, benchmarked against two traditional cost estimation methods for new clients. Comparative analysis shows that our framework outperforms these methods in terms of predictive accuracy, highlighting its superior effectiveness. The integration of OR and ML offers a significant decision-support mechanism, improving sustainable business strategies across sectors. Our framework provides a scalable solution for cost forecasting and resource optimization, marking progress toward a circular, sustainable economy by accurately estimating costs and promoting efficient operations. [ABSTRACT FROM AUTHOR]

Last mile delivery is a significant component in the growth of e-commerce, especially in urban areas. The deliveries in dense cities cause several serious issues such as air/noise pollution and congestion. In this study, we compare the financial costs and CO2 emissions from different last mile delivery strategies of grocery bins in a scenario in Paris with four types of delivery vehicles (diesel/electric vans, cargo bikes, and autonomous delivery vehicles). We use costs associated with each vehicle type, location data with constraints for establishments in Paris, and delivery scenarios obtained by solving the vehicle routing problem for an overall cost comparison. We consider an economic analysis of the daily delivery to optimise the costs and estimate the CO2 emissions. The results highlight the competitiveness among last mile delivery and reflect the transition knowing the transport expenses since 2018: electric van costs become competitive with diesel ones, it concluded by some perspectives with cargo bikes and autonomous vehicles with their current limits. The strategies show a great impact on overall cost and emissions, which are vital in the development of sustainable urban last-mile delivery. [ABSTRACT FROM AUTHOR]

Many-objective optimization problem is one of the most important and widely faced optimization problems in the real world. To solve many-objective optimization problems (MaOPs), numerous multi-objective evolutionary algorithms (MOEAs) have been developed to find a good convergence and well-distributed Pareto front. However, with the increase of dimensions, the distribution of solutions obtained by MOEAs becomes more complex and tends to be orthogonal, which significantly reduces the effectiveness of the algorithms. In this paper, we propose an improved many-objective evolutionary algorithm (MaOEA-MSAR), which incorporates a multi-strategy selection mechanism into an existing MOEA, and develops an adaptive reproduction operation to produce promising offspring individuals. Firstly, the selection strategy based on the angle-penalized distance is used to improve the coverage of the solutions in the objective space. Then, the selection strategy based on convergence rate is employed to strengthen the balance between diversity and convergence. Finally, an adaptive reproduction operation is used to select different reproduction strategies for the gene-level global exploration or local exploitation. A series of experiments are carried out against seven state-of-the-art many-objective optimization algorithms. Experimental results on commonly used 31 benchmark test problems with up to 15 objectives and a multi-objective vehicle routing problem have demonstrated that MaOEA-MSAR is competitive in handling various kinds of MaOPs. [ABSTRACT FROM AUTHOR]

By analyzing the influence of stochastic perturbation matters on vehicle path optimization, a perturbation scheduling model for logistics and distribution with a carbon tax mechanism is established under the premise of time window variation and load capacity constraints. Herein, we propose an enhanced Genetic Algorithm (GA) based on a Gaussian matrix mutation (GMM) operator, which maintains the diversity of the population while speeding up the algorithm's convergence. The model builds a Gaussian probability matrix using the site positional order distribution characteristics implied in the original site data information, and applies the Gaussian probability matrix to individual gene mutations using a roulette-wheel-selection method; thus, the study guarantees the genetic diversity of the population while guiding it to evolve in the high-fitness direction. Finally, an experimental simulation is performed using data obtained from a commercial supermarket, thereby verifying the effectiveness of the proposed algorithm and comparing it with other algorithms. The results reveal that compared with the classical GA, the average convergence speed of the improved GA can be increased by 50–60% and the consumed algorithm time can be reduced by 48% while maintaining the difference in solution accuracy within 1%. [ABSTRACT FROM AUTHOR]

Quantum computing offers new heuristics for combinatorial problems. With small- and intermediate-scale quantum devices becoming available, it is possible to implement and test these heuristics on small-size problems. A candidate for such combinatorial problems is the heterogeneous vehicle routing problem (HVRP): the problem of finding the optimal set of routes, given a heterogeneous fleet of vehicles with varying loading capacities, to deliver goods to a given set of customers. In this work, we investigate the potential use of a quantum computer to find approximate solutions to the HVRP using the quantum approximate optimization algorithm (QAOA). For this purpose we formulate a mapping of the HVRP to an Ising Hamiltonian and simulate the algorithm on problem instances of up to 21 qubits. We show that the number of qubits needed for this mapping scales quadratically with the number of customers. We compare the performance of different classical optimizers in the QAOA for varying problem size of the HVRP, finding a trade-off between optimizer performance and runtime. [ABSTRACT FROM AUTHOR]

With the rapid advancement of drone technology, the efficient distribution of drones has garnered significant attention. Central to this discourse is the energy consumption of drones, a critical metric for assessing energy-efficient distribution strategies. Accordingly, this study delves into the energy consumption factors affecting drone distribution. A primary challenge in drone distribution lies in devising optimal, energy-efficient routes for drones. However, traditional routing algorithms, predominantly heuristic-based, exhibit certain limitations. These algorithms often rely on heuristic rules and expert knowledge, which can constrain their ability to escape local optima. Motivated by these shortcomings, we propose a novel multi-agent deep reinforcement learning algorithm that integrates a drone energy consumption model, namely EMADRL. The EMADRL algorithm first formulates the drone routing problem within a multi-agent reinforcement learning framework. It subsequently designs a strategy network model comprising multiple agent networks, tailored to address the node adjacency and masking complexities typical of multi-depot vehicle routing problem. Training utilizes strategy gradient algorithms and attention mechanisms. Furthermore, local and sampling search strategies are introduced to enhance solution quality. Extensive experimentation demonstrates that EMADRL consistently achieves high-quality solutions swiftly. A comparative analysis against contemporary algorithms reveals EMADRL's superior energy efficiency, with average energy savings of 5.96% and maximum savings reaching 12.45%. Thus, this approach offers a promising new avenue for optimizing energy consumption in last-mile distribution scenarios. [ABSTRACT FROM AUTHOR]

As telehealth utilization for ambulatory and home-based care skyrockets, there has been a paradigm shift to a decentralized and hybrid care delivery modality integrating both in-person and telehealth services provided at different layers of the care delivery network, i.e., central hospitals, satellite clinics, and patient homes. The operations of such care delivery systems need to take into consideration patients' mobility and care needs, and rely on multiple types of nurses who can support and facilitate telehealth (with hospital physicians) in clinics and patient homes. We formulate an optimization problem, aiming at operationalizing the proposed care delivery network. Decisions regarding the type of care delivered, the location of care delivered, and the scheduling of all kinds of nurses are determined jointly to minimize operating costs while simultaneously satisfying patients' care needs. We propose a bi-level approximation that exploits the structure of the hybrid telehealth system, and develop column generation-based heuristic algorithms to identify the joint decision rules for clinic selection, patient assignment, and visiting nurse routing problems. Numerical experiment results demonstrate our algorithm's capability to achieve high-quality solutions in reasonable computation time, and is capable of solving instances with large patient sizes and time windows. Our work supports the efficient and effective operation of the proposed hybrid telehealth systems to improve patient access to care. [ABSTRACT FROM AUTHOR]

Enhancing transportation is critical to urban development, particularly in rapidly growing regions like Sokoto State in Nigeria. The Vehicle Routing Problem (VRP) is a widely researched optimization problem that seeks to find the most efficient routes for a fleet of vehicles to service a set of customers or locations, minimizing travel costs and time. This paper explores how Vehicle Routing Problem (VRP) optimization can address transportation challenges in the Sokoto metropolis by designing efficient routes for vehicle fleets. The study incorporates extensive data collection, including geospatial data on road networks, traffic patterns, population density, analysis, VRP model creation, optimization, and key points of interest, to customize VRP solutions to the unique characteristics of Sokoto. Results indicate significant potential for VRP optimization to reduce travel distances, lower operational costs, and contribute to environmental sustainability. [ABSTRACT FROM AUTHOR]

The rapid growth of e-commerce has created new challenges in logistics optimization, particularly in terms of delivery route efficiency. This research develops a dynamic programming model to optimize delivery routes in the context of e-commerce in Indonesia. Using a modified Vehicle Routing Problem with Time Windows (VRPTW) approach, we implemented an algorithm that considers various factors such as distance, time, and cost. Simulations using synthetic datasets showed efficiency improvements of 18.7% in travel distance and 22.3% in delivery time compared to conventional methods. Field trials with an ecommerce partner resulted in a 21.5% reduction in travel distance and an increase in on-time delivery rate from 87% to 94%. Sensitivity analysis revealed that the algorithm's performance is most affected by demand fluctuations and changes in traffic conditions. Implementation challenges include integration with existing systems and consideration of workforce impact. This research opens avenues for further development in algorithm scalability, integration of sustainability factors, and adaptation to various geographical contexts, demonstrating significant potential for improving e-commerce logistics efficiency in the future. [ABSTRACT FROM AUTHOR]

The logistics demands of industries represented by e-commerce have experienced explosive growth in recent years. Vehicle path-planning plays a crucial role in optimization systems for logistics and distribution. A path-planning scheme suitable for an actual scenario is the key to reducing costs and improving service efficiency in logistics industries. In complex application scenarios, however, it is difficult for conventional heuristic algorithms to ensure the quality of solutions for vehicle routing problems. This study proposes a joint approach based on the genetic algorithm and graph convolutional network for solving the capacitated vehicle routing problem with multiple distribution centers. First, we use the heuristic method to modularize the complex environment and encode each module based on the constraint conditions. Next, the graph convolutional network is adopted for feature embedding for the graph representation of the vehicle routing problem, and multiple decoders are used to increase the diversity of the solution space. Meanwhile, the REINFORCE algorithm with a baseline is employed to train the model, ensuring quick returns of high-quality solutions. Moreover, the fitness function is calculated based on the solution to each module, and the genetic algorithm is employed to seek the optimal solution on a global scale. Finally, the effectiveness of the proposed framework is validated through experiments at different scales and comparisons with other algorithms. The experimental results show that, compared to the single decoder GCN-based solving method, the method proposed in this paper improves the solving success rate to 100% across 15 generated instances. The average path length obtained is only 11% of the optimal solution produced by the GCN-based multi-decoder method. [ABSTRACT FROM AUTHOR]

The allocation of tasks among multiple Autonomous Underwater Vehicles (AUVs) with energy constraints in underwater environments presents an NP-complete problem with far-reaching consequences for marine exploration, environmental monitoring, and underwater construction. This paper critically examines the contemporary methodologies and technologies in the task allocation for multiple AUVs, with a particular focus on strategies that optimize navigation time with energy consumption constraints. By conceptualizing the multiple AUVs task allocation issue as a Capacitated Vehicle Routing Problem (CVRP) and addressing it using the SCIP solver, this study seeks to identify effective task allocation strategies that enhance the operational efficiency and minimize the mission duration in energy-restricted underwater settings. The findings of this research provide valuable insights into efficient task allocation under energy constraints, providing useful theoretical implications and practical guidance for optimizing task planning and energy management in multiple AUVs systems. These contributions are demonstrated through the improved solution quality and computational efficiency. [ABSTRACT FROM AUTHOR]

The multi‐compartment vehicle routing problem is an extension of the vehicle routing problem and consists of designing a set of routes to perform the collection or delivery of different product types from customers with minimal costs. The product types are incompatible with each other and must be transported separately in multiple compartments. In practice, several uncertainties such as uncertainty in demands can arise, where the exact demand of customers is not known at the time of planning. To deal with these uncertainties, decision‐makers have to rely on robust solutions. A solution is considered robust when it can resist perturbations in every possible demand scenario as much as possible. In the day to day business of most logistic companies, historical data about each customer can be stored and used to make intelligent decisions regarding the expected demands. In this article, we propose an adaptive large neighborhood search for solving the robust multi‐compartment vehicle routing problem under demand uncertainty and present a robust solution approach for the problem in practical settings by employing machine learning. We show that by using our approach, the solutions obtained have lower recourse costs and have a lower gap between expected and actual costs, which is a favorable outcome to have in practice. [ABSTRACT FROM AUTHOR]

In vehicle routing problems (VRP), the optimal allocation of transportation by considering factors such as route hardness, driver experience and vehicle worn-out has a significant effect on costs reduction and approaching realworld conditions. In this paper, a novel fuzzy mixed integer non-linear mathematical model to address the two-echelon allocation-routing problem under uncertainty is proposed by applying route and fleet conditions. The cost of allocating drivers to diverse vehicles is computed at the first echelon of the problem, considering factors such as vehicle type, vehicle wear-out, and driver experience. Additionally, different routes are defused with varying levels of hardness. The goal of the second echelon of the model is to improve reliability by defining the reliability of routes within each section. To solve the model, the Torabi and Hessini (TH), the Selimi and Ozkarahan (SO) methods, and a newly proposed approach (PIA) were utilized to transform the multiobjective model into a single-objective one. Numerical tests and performance indicators were used to validate the effectiveness of both the multi-objective mathematical model and the proposed solution method. The validation computation results indicate that the proposed solution approach outperforms both the TH and SO approaches. [ABSTRACT FROM AUTHOR]

Last mile delivery is an important and growing part of the supply chain that has a sizeable negative environmental impact. This paper considers more sustainable approaches to home-delivery that are pragmatic for many non-rural environments. We address the two-echelon, multi-trip, capacitated vehicle routing problem with home-delivery and optional self-pickup services using different combinations of drones, trucks, and electric-assisted bikes (i.e. e-bikes). In the proposed approach, parcels are transported from a depot to parcel lockers by either drones or trucks and are then delivered to customer locations by either e-bikes or trucks. The four approaches range from the most sustainable (drones then e-bikes) to partly green (drone then truck or truck then e-bike) to finally the traditional (truck then truck). We formulate a mathematical model that determines the vehicle routes to minimize the total cost, which consists of vehicle operational cost and operator wages. The four types of delivery networks are assessed and compared for both costs and emissions. Experimental results suggest that with a modest increase in total cost (as little as 13%), emission reductions of up to 92%, on average, can be achieved when using the greenest delivery strategy of drones and e-bikes. The other delivery options have varying tradeoffs between costs and environmental impact. The percentage of self-pickup customers is an influencing factor to consider when choosing the delivery strategy that best meets the organization's budget and environmental goals, especially when using e-bikes in the second echelon. [ABSTRACT FROM AUTHOR]

Bandung and Lembang are cities that are chosen by tourists as their destinations. Even though these cities are located side-by-side, each city has different characteristics. Bandung has many hotels and culinary spots, meanwhile, Lembang has many scenery spots. Tourists usually have limited time to visit all the destinations on holiday, which makes them choose several destinations. This paper proposes a tourism itinerary recommendation system based on the calculation of the most optimal route between destinations using the vehicle routing problem with time windows (VRPTW). Later, the optimal route is defined using the shortest path algorithm (Dijkstra). Data for the algorithm came from the collaboration between the several road information and criteria weights that are determined using the analytics hierarchy process (AHP). According to the simulation, the criteria weights are 6.9%, 62.7%, 18.6%, and 11.9% for route length, traffic condition, travel time, and weather condition, respectively. Moreover, the optimal number of tourism itinerary plans is 4 destinations. As the usage of computational resources, it takes 31.8% and 61.9% of CPU and memory usage. The time processing increases exponentially as the increment of the number of requested stops. The output of this research is expected to be a solution to the tourist itinerary plan. [ABSTRACT FROM AUTHOR]

Last-mile delivery systems are one of the numerous industrial applications of uncrewed aircraft systems (UAS). This study analyzes UAS-based package delivery systems in the context of the integrated operations of crewed and uncrewed aircraft. It introduces a multi-trip, time-dependent vehicle routing problem aimed at optimizing UAS delivery routes within integrated operations. By conducting numerical simulations of helicopters (crewed aircraft) and UAS missions sharing the same airspace, the optimal UAS routes for resolving potential conflicts in the shared airspace can be effectively determined without any adverse impact on helicopter operations. Knowing the helicopter mission times in advance enables the efficient planning of UAS missions. The results of this study provide valuable insights regarding the implementation of integrated crewed and uncrewed aircraft operations. [ABSTRACT FROM AUTHOR]

This article presents a novel contribution to the Periodic Vehicle Routing Problem (PVRP) by introducing two new problem formulations which differ in the usage of the crucial flow variable. The formulations are tailored to meet the specific demands of the vending machine industry in Medellín, Colombia, and require considering a PVRP with time windows, a heterogeneous fleet, and multiple depots. This scenario, tailored to address real-world complexity and computational challenges, brings to light an exponential surge in integer variables as customer numbers increase. The research presents an analysis of PVRPs that include the four mentioned attributes, compares their similarities, and delves into their nuances. From the analysis it is derived that the variant of the PVRP presented has not been considered previously, taking into account not only these attributes, but also the restrictions involved. Empirical experiments are conducted to examine the intricate interplay between the two proposed formulations, highlighting their impact on the performance of the GUROBI solver. The study provides valuable insights into problem-specific adaptations and algorithmic approaches, emphasizing the significance of the proposed formulations in addressing multifaceted PVRPs. In essence, this research positions the introduction of these two formulations as a pioneering step, offering a new paradigm for approaching the PVRP. [ABSTRACT FROM AUTHOR]

With the increasing penetration of renewable energy sources (RES), a battery energy storage (BES) Train supply system with flexibility and high cost-effectiveness is urgently needed. In this context, the mobile battery energy storage (BES) Train, as an efficient media of wind energy transfer to the load center with a time–space network (TSN), is proposed to assist the system operations. A real-time operation strategy for this TSN is proposed considering the vehicle routing problem (VRP) of BES Train. To achieve this goal, stochastic scheduling of BES Trains integrated with network constraints along wind power uncertainty is addressed in this work. Autoregressive integrated moving average (ARIMA) models generate power scenarios. Also, consider uncertainties related to wind power and standard deviation to optimize the placement of charging/discharging BES Train station. The uncertain parameter connected to wind power for scenario generations is observed. The proposed mixed-integer linear programming (MILP) to solve the model efficiently is based on tackling the strong coupling between integer and continuous variables. Using GAMS software, the proposed model is simulated on the IEEE six-bus systems, and case studies examine the capability of the suggested approach based on operational, flexibility, and reliability criteria. [ABSTRACT FROM AUTHOR]

This paper introduces a novel bi-objective routing model based on Artificial Intelligence of Things (AIoT) principles. Our model not only aims to minimize vehicle transportation costs and prevent time window violations but also endeavors to mitigate environmental pollutants. This study addresses the complex challenge of optimizing routes for heterogeneous vehicle fleets usingAIoT technology. Analyzing the bi-objective model using AI tools (MOSCA and NSGA II), we unveil a fascinating trade-off: as energy consumption decreases, system costs increase. Employing robust optimization techniques, we validate the model's performance under pessimistic conditions characterized by rising uncertainty rates. Notably, heightened uncertainty correlates with increased objective function values. Through a series of diverse test cases, we observe that MOSCA demonstrates superior efficiency, notably outperforming in NP, MD, and T indices. Our findings offer valuable insights for practitioners, policymakers, and researchers in the domains of transportation optimization, AIoT, and environmental sustainability. [ABSTRACT FROM AUTHOR]

This paper aims to discuss the concept of modeling and simulation for addressing transportation challenges in Malaysia's agriculture industry, focusing on the capabilities of distribution centers (DC) and collection centers (CC). To identify the optimal solution for the single-period vehicle routing problem (SP-VRP), we developed an optimization model that accurately represents the real-world problem, accompanied by a transportation problem simulation. The challenge involves determining the collection quantities, times, and routes to the CCs within the SP-VRP system. Consequently, we constructed a linear mixed-integer program to solve the SP-VRP. A comprehensive analysis of a sample problem demonstrates how our proposed approach is integrated. The results indicate that vehicle capacity is optimized efficiently, with an average capacity utilization of 100% across all tours and solving optimal routes allows for an evaluation of how well the model achieves this objective, as well as how different routes affect logistics performance. [ABSTRACT FROM AUTHOR]

This study addresses the Vehicle Routing Problem with Time Windows (VRPTW) in the context of ice distribution by introducing a novel mathematical model that incorporates practical constraints essential for real-world applications. These constraints include customer retention strategies and quality preservation methods, which are important for maintaining customer satisfaction and product integrity. The objective is to minimize the total costs, including fuel expenses, standard and bonus driver wages, missed delivery penalties, and costs related to a quality preservation strategy. Given the NP-hard nature of this problem, this study proposes a hierarchical cluster-first-route-second approach and a Differential Evolution (DE) algorithm to solve large-scale problems. The effectiveness of these methods was examined and compared through test cases involving various problem sizes using real-world data from an ice distribution company in Thailand. The results show that the hierarchical cluster-first-route-second approach is more effective for the practical problem. Using capacitated K-means clustering, this hierarchical approach groups customers, enabling the solution of manageable subproblems through Mixed-Integer Linear Programming (MILP). The proposed method not only provides cost-effective and scalable solutions, but also outperforms traditional methods in terms of computation time and feasibility for large-scale applications. This study offers significant theoretical contributions by extending VRPTW models and providing practical implications for optimizing distribution strategies in competitive market environments, leading to substantial cost reductions and enhanced operational efficiency. [ABSTRACT FROM AUTHOR]

The data management system of health cloud authentication plays an important role in the optimization of logistics vehicle routing. It can not only help logistics vehicles choose the best distribution path, but also save time and cost and improve economic efficiency. At present, logistics has not yet formed a complete service system. High distribution costs and low distribution efficiency limit the development of the entire logistics. The reduction of logistics costs and the improvement of distribution efficiency have become the top priorities of the society. The optimization of the distribution route is the key to cost saving and distribution logistics. It is particularly important to study and optimize the distribution route, because the distribution route affects the logistics transportation efficiency and the loss cost during transportation. Therefore, this paper adjusted the scheduling system of logistics vehicles through a distributed intelligent system, and optimized the path of logistics vehicles according to the improved genetic algorithm, thereby reducing the transportation cost of logistics and improving the efficiency of logistics distribution. This article first explains the definition, classification, and main components of the delivery vehicle routing problem. Then, using cloud authentication path optimization, a distributed intelligent system is constructed. Finally, an improved ant colony algorithm is used to analyze and study the distance constraints of vehicles. By improving the ant colony algorithm, it can be seen that the optimized path pheromone concentration and the optimized sub-function have gradually increased with time. The mean pheromone concentration was 40 %, and the seventh day was 15 % higher than the first. The mean value of the optimized subfunction was 0.34 %, and the seventh day was 20 % higher than the first. The distribution cost and distribution efficiency of the optimized logistics vehicle distribution path were much higher than those of the traditional logistics distribution path. Moreover, the distribution cost of the logistics distribution path was 9 % lower than the traditional one, and the distribution efficiency was 13 % higher. The average smoothness of the optimized logistics path is about 90 %, and the seventh day is 11 % higher than the first day. The average fitness of the optimized logistics path is 88 %, and the seventh day is 14 % higher than the first day. In a word, the data management system can uniformly schedule logistics vehicles and improve the efficiency of distribution. [ABSTRACT FROM AUTHOR]

We studied a variant of the vehicle routing problem (VRP) arising in last-mile distribution, called the multi-depot two-echelon vehicle routing problem with delivery options (MDTEVRP-DO). The MDTEVRP-DO involves two decision levels: (i) designing routes for a fleet of vehicles located in multiple depots to transport customer demands to a set of satellites and (ii) routing a fleet of vehicles from the satellites to serve the final customers. Nowadays, a relevant feature of the problem characterizing delivery services is that customers can collect their packages at pickup stations near their homes or workplaces. We designed an effectively simulated annealing (SA) heuristic for the problem. The new algorithm was extensively tested on benchmark instances from the literature, and its results were compared with those of start-of-the-art algorithms. The results show that the proposed SA obtains 30 out of the 36 best solutions for the MDTEVRP-DO benchmark instances. Moreover, its computation performance is superior to state-of-the-art algorithms for the MDTEVRP-DO. [ABSTRACT FROM AUTHOR]

In this work, we introduce a generalisation of the Vehicle Routing Problem for a specific application in the monitoring of a Water Distribution Network (WDN). In this problem, multiple technicians must visit a sequence of nodes in the WDN and perform a series of tests to check the quality of water. Some special nodes (i.e., wells) require technicians to first collect a key from a key centre. The key must then be returned to the same key centre after the test has been performed, thus introducing precedence constraints and multiple visits in the routes. To solve the problem, a Mixed Integer Linear Programming model and an Iterated Local Search have been implemented. The efficiency of the proposed methods is demonstrated by means of extensive computational tests on randomly created and real-world instances. [ABSTRACT FROM AUTHOR]

This study presents a bi-objective optimization model for the Green Vehicle-Routing Problem in cold chain logistics, with a focus on symmetric distance matrices, aiming to minimize total costs, including carbon emissions, while maximizing customer satisfaction. To address this complex challenge, we developed a Stage-Specific Multi-Objective Five-Element Cycle Optimization algorithm (MOFECO-SS), which dynamically adjusts optimization strategies across different stages of the process, thereby enhancing overall efficiency. Extensive comparative analyses with existing algorithms demonstrate that MOFECO-SS consistently outperforms in solving the multi-objective optimization model, particularly in reducing total costs and carbon emissions while maintaining high levels of customer satisfaction. The symmetric nature of the distance matrix further aids in achieving balanced and optimized route planning. The results highlight that MOFECO-SS offers decision-makers flexible route planning options that balance cost efficiency with environmental sustainability, ultimately improving the effectiveness of cold chain logistics operations. [ABSTRACT FROM AUTHOR]

Public transportation system is one of the most effective ways to conserve energy and reduce carbon emissions. However, the traditional public transportation system does not provide customized service and cannot guarantee the arrival time to destination. To address these issues, we formulate the minimum shared bus scheduling problem to minimize the number of shared buses such that all orders can be completed under constraints of deadlines and capacity of shared bus. We propose the approximation algorithms, S‐MBSA for the shared bus with strong endurance and E‐MBSA for the large‐scale order scenario, to solve the minimum shared bus scheduling problem. We further formulate the constrained maximum revenue shared bus scheduling problem to maximize the revenue under the limited number of shared buses, and propose an approximation algorithm, CMRBSA, to find the shared bus route schedules. Through the extensive simulations, we demonstrate the significant superiority of S‐MBSA and E‐MBSA in terms of number of shared buses. Furthermore, CMRBSA outperforms the benchmark algorithms significantly in terms of revenue. [ABSTRACT FROM AUTHOR]

The challenge of optimizing the distribution path for location logistics in the cold chain warehousing of fresh agricultural products presents a significant research avenue in managing the logistics of agricultural products. The goal of this issue is to identify the optimal location and distribution path for warehouse centers to optimize various objectives. When deciding on the optimal location for a warehousing center, various elements like market needs, supply chain infrastructure, transport expenses, and delivery period are typically taken into account. Regarding the routes for delivery, efficient routes aim to address issues like shortening the overall driving distance, shortened travel time, and preventing traffic jams. Targeting the complex issue of optimizing the distribution path for fresh agricultural products in cold chain warehousing locations, a blend of this optimization challenge was formulated, considering factors like the maximum travel distance for new energy trucks, the load capacity of the vehicle, and the timeframe. The Location-Route Problem with Time Windows (LRPTWs) Mathematical Model thoroughly fine-tunes three key goals. These include minimizing the overall cost of distribution, reducing carbon emissions, and mitigating the depletion of fresh agricultural goods. This study introduces a complex swarm intelligence optimization algorithm (MODRL-SIA), rooted in deep reinforcement learning, as a solution to this issue. Acting as the decision-maker, the agent processes environmental conditions and chooses the optimal course of action in the pool to alter the environment and achieve environmental benefits. The MODRL-SIA algorithm merges a trained agent with a swarm intelligence algorithm, substituting the initial algorithm for decision-making processes, thereby enhancing its optimization efficiency and precision. Create a test scenario that mirrors the real situation and perform tests using the comparative algorithm. The experimental findings indicate that the suggested MODRL-SIA algorithm outperforms other algorithms in every computational instance, further confirming its efficacy in lowering overall distribution expenses, carbon emissions, and the depletion of fresh produce in the supply chain of fresh agricultural products. [ABSTRACT FROM AUTHOR]

The placement of electric vehicle charging stations (EVCS) and battery swapping stations (BSS) is crucial to meet demand while minimizing their impact on the power system network. This article addresses the placement and scheduling of EVCS and BSS within a radial distribution network (RDN) overlaid with a road network. Electric Vehicle Routing Problem (EVRP) and Traffic Assignment Problem (TAP) is introduced to reduce EV energy consumption during trips to EVCS and BSS. A Bi-layer optimization approach is used, with the outer layer minimizing energy loss by allocating EVCS and BSS optimally, and the inner layer optimizing scheduling considering associated costs. Uncertainties related to EV is considered on a real-time trip basis and modelled using 2m-Point estimation method. The problem is solved using Differential Evolution (DE) and Prairie Dog Optimization (PDO) techniques. PDO results in a 9.6% reduction in total energy losses and a 22.5% decrease in total associated costs by optimally placing EVCS at 69, 25,114 and BSS at 19, 84,113 of the RDN compared to DE. Inclusion of 2-m PEM uncertainty increases total energy loss by 8.76% but decreases total associated costs by 6.97% compared to real-time uncertainty cases, enhancing the realism of the results. [ABSTRACT FROM AUTHOR]

The wild horse optimizer (WHO) is a novel metaheuristic algorithm, which has been successfully applied to solving continuous engineering problems. Considering the characteristics of the wild horse optimizer, a discrete version of the algorithm, named discrete wild horse optimizer (DWHO), is proposed to solve the capacitated vehicle routing problem (CVRP). By incorporating three local search strategies-swap operation, reverse operation, and insertion operation-along with the introduction of the largest-order-value (LOV) decoding technique, the precision and quality of the solutions have been enhanced. Experimental results conducted on 44 benchmark instances indicate that, in most test cases, the solving capability of discrete wild horse optimizer surpasses that of basic wild horse optimizer (BWHO), hybrid firefly algorithm, dynamic space reduction ant colony optimization (DSRACO), and discrete artificial ecosystem-based optimization (DAEO). The discrete wild horse optimizer provides a novel approach for solving the capacitated vehicle routing problem and also offers a new perspective for addressing other discrete problems. [ABSTRACT FROM AUTHOR]

The emergence of electric vehicles in distribution and logistics activities has brought significant benefits due to their unique characteristics, such as energy-efficient and lower carbon emissions. In the perspective of vehicle routing problem, electric vehicles pose challenging constraints regarding the limited battery capacity, and thus their traveling ranges, and the availability of charging stations. In this paper, we propose a model of the fleet electric vehicle routing problem (EVRP) with soft time windows, where a mixed integer linear programming framework is implemented in model formulation. The objective of mathematical programming is to minimize the total operational cost, which consists of a fixed cost, a traveling cost, a battery charging cost, and probably a penalty cost due to time window violation. We implement our model in two simple cases, namely homogeneous and heterogeneous fleets EVRPs, characterized by loading and battery capacities. Each case consists of one depot, five customers, two electric vehicles, and two charging stations. Optimal routes are obtained using the well-known branch-and-bound method under Lingo 17.0. It is found that the existence of charging stations may affect the routes selection and the implementation of soft time windows rather than hard time windows has been proven to increase the feasibility of routing problem. [ABSTRACT FROM AUTHOR]

In the realm of supply chain logistics, the Multi-Depot Multi-Supplier Vehicle Routing Problem (MDMSVRP) poses a significant challenge in optimizing the transportation process to minimize costs and enhance operational efficiency. This problem involves determining the most cost-effective routes for a fleet of vehicles to deliver goods from multiple suppliers to multiple depots, considering various constraints and non-linear relationships. The routing problem (RP) is a critical element of many logistics systems that involve the routing and scheduling of vehicles from a depot to a set of customer nodes. One of the most studied versions of the RP is the Vehicle Routing Problem with Time Windows (VRPTW), in which each customer must be visited at certain time intervals, called time windows. In this paper, it is considered that there are multiple depots (supply centers) and multiple suppliers, along with a fleet of vehicles. The goal is to efficiently plan routes for these vehicles to deliver goods from the suppliers to various customers while considering relaxed time windows. This research is intended to establish a new relaxation scheme that relaxes the time window constraints in order to lead to feasible and good solutions. In addition, this study develops a discrete optimization model as an alternative model for the time-dependent VRPTW involving multi-suppliers. This research also develops a metaheuristic algorithm with an initial solution that is determined through time window relaxation. [ABSTRACT FROM AUTHOR]

Researchers have been investigating solutions to the Vehicle Routing Problem (VRP) as a practical means of tackling the rising transportation costs in businesses. The goal is to develop innovative methods that minimize shipping expenses and maximize profits. The transportation of Hazardous Materials (HazMat) is particularly complex and has attracted significant attention from scholars. When designing logistics networks for HazMat, factors such as time window constraints, uncertainties, vehicle capacity, and mileage capacity in sub-tours need to be considered to minimize overall transportation and pollution costs. This study presents a mathematical model for vehicle routing of HazMat from economic, route sensitivity, and uncertainty perspectives. An optimization approach using a hybrid Genetic and Simulated Annealing (SA) algorithm is then applied to solve the problem. The study includes numerous numerical examples and sensitivity analyses to demonstrate the model's efficacy. The results indicate that an increase in the route sensitivity coefficient leads to an increase in the objective function. Additionally, the effect of demand on the objective function generally increases, although there are instances where it decreases. [ABSTRACT FROM AUTHOR]

Providing first aid and other supplies (e.g., epi‐pens, medical supplies, dry food, water) during and after a disaster is always challenging. The complexity of these operations increases when the transportation, power, and communications networks fail, leaving people stranded and unable to communicate their locations and needs. The advent of emerging technologies like uncrewed autonomous vehicles can help humanitarian logistics providers reach otherwise stranded populations after transportation network failures. However, due to the failures in telecommunication infrastructure, demand for emergency aid can become uncertain. To address the challenges of delivering emergency aid to trapped populations with failing infrastructure networks, we propose a novel robust computational framework for a two‐echelon vehicle routing problem that uses uncrewed autonomous vehicles (UAVs), or drones, for the deliveries. We formulate the problem as a two‐stage robust optimization model to handle demand uncertainty. Then, we propose a column‐and‐constraint generation approach for worst‐case demand scenario generation for a given set of truck and UAV routes. Moreover, we develop a decomposition scheme inspired by the column generation approach to generate UAV routes for a set of demand scenarios heuristically. Finally, we combine the decomposition scheme within the column‐and‐constraint generation approach to determine robust routes for both trucks (first echelon vehicles) and UAVs (second echelon vehicles), the time that affected communities are served, and the quantities of aid materials delivered. To validate our proposed algorithms, we use a simulated dataset that aims to recreate emergency aid requests in different areas of Puerto Rico after Hurricane Maria in 2017. [ABSTRACT FROM AUTHOR]

This study focuses on the delivery routing problem faced by a transport company located in Phuket, Thailand. The goal of this study is to find a daily optimum route in order to minimize the total transportation cost, which comprises fixed costs associated with vehicle rental and variable costs calculated based on factors of travel distance, fuel prices, and fuel consumption. The complexity of this problem is compounded by the fact that customer demand often exceeds a vehicle capacity, in terms of weight and volume. In addition, delivery must be made within specific time windows. To tackle this issue, the delivery routing problem is classified as a multi-trip capacitated vehicle routing problem with time window (MTCVRPTW). Since the problem is NP-hard, an application of metaheuristic is more practical to determine the delivery routing of the company within a reasonable computing time. In this study, Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithm are applied to solve MTCVRPTW. The numerical results show that DE provides better solution quality compared to those obtained from PSO and company current practices. [ABSTRACT FROM AUTHOR]

Background: Milkrun-based material supply plays an important role in the automotive industry, as it is a material supply concept where high efficiency can be achieved. When implementing milkrun-based material supply, the milkrun supply of the production plant often has to be integrated with an existing warehouse material handling system, which frequently leads to a less efficient solution. Methods: In this paper, the author investigates the impact of a hub-based milkrun supply, where the collection processes in the component's warehouse and the distribution processes in the assembly plant are connected to a hub, which is responsible for the sequencing of component demands. After a systematic literature review, the paper introduces a novel mathematical model, which makes it possible to describe the conventional milkrun-based solutions, the hub-based milkrun solutions, and to compare them in terms of the length of transportation routes, transportation time, total service time, and virtual emission points of view. Results: The scenario analysis demonstrates that the hub-based solution can lead to an efficiency improvement of about 13% in total service time, 23% savings in transportation time, and 45% savings in transportation time in the component's warehouse. Conclusions: The article's findings suggest that implementing a hub-based milkrun system in automotive material supply can significantly enhance efficiency. The described approach could lead to more streamlined operations in production plants by optimizing the integration of milkrun systems. [ABSTRACT FROM AUTHOR]

Background: This research aims to solve a home healthcare vehicle routing problem (HHCVRP) model that considers the social aspect of sustainability and will be implemented in smart cities. In addition to the dynamism and uncertainty caused by variations in the patient's condition, the proposed model considers parameters and variables that enhance its practicability, such as assuming different levels of patient importance (priority). Methods: The model was solved using a metaheuristic algorithm approach via the Ant Colony Optimization algorithm and the Non-Dominated Sorting technique due to the ability of such a combination to work out with dynamic models with uncertainties and multi-objectives. Results: This study proposes a novel mathematical model by integrating body sensors on patients to keep updating their conditions and prioritizing critical conditions in service. The sensitivity analysis demonstrates that using a heart rate sensor improves service quality and patient satisfaction without affecting the energy consumed. In addition, quality costs are increased if the importance levels of patients increase. Conclusions: The suggested model can assist healthcare practitioners in tracking patients' health conditions to improve the quality of service and manage workload effectively. A trade-off between patient satisfaction and service provider satisfaction should be maintained. [ABSTRACT FROM AUTHOR]

Vehicle routing problem (VRP) is a classic NP-hard optimization problem. It is generally accepted that an optimized routing scheme can cause huge difference in the cost in all stages of transportation. Consequently, the VRP has evoked interest among the researchers of the field. Usually, a metaheuristic or an evolutionary algorithm is used for the solution of a VRP variant. In the last years, a number of swarm intelligence algorithms have been used for the solution of the problem. Initially, the two most classic swarm intelligence algorithms, the Ant Colony Optimization and the Particle Swarm Optimization, were used for the solution of this kind of problems. However, in the last years, more and more researchers solved the problem using a different swarm intelligence algorithm. In this paper, we focused in the presentation and analysis of the swarm intelligence algorithms that have been used for the solution of the problem. We give the advantages and disadvantages of each method, we focus in those ones that produced the best results in difficult VRPs and we present directions for the future of this kind of algorithms for the solution of a VRP variant. [ABSTRACT FROM AUTHOR]

Approximation of the optimal tour length in a Euclidean traveling salesman problem (TSP) has been studied by many researchers. In a previous study, we used the standard deviation in random tour lengths to approximate the optimal tour length in both Euclidean and non‐Euclidean TSPs and we obtained good estimates. In this paper, we show that the strong power‐law relationship between the standard deviation in random feasible solution values and the optimal solution value also holds for other Euclidean and near‐Euclidean combinatorial optimization problems like the minimum spanning tree (MST) and maximum weight matching (MWM) problems. We then enhance the estimation ability of the model by considering a second predictor: the mean in random feasible solution values. Experimental results show that by using the mean, standard deviation, and randomization, we can accurately predict the optimal solution values for the TSP, MST, MWM, and the capacitated vehicle routing problem (VRP). [ABSTRACT FROM AUTHOR]

The split delivery vehicle routing problem (SDVRP) is a relaxed variant of the capacitated vehicle routing problem (CVRP) where the restriction that each customer is visited precisely once is removed. Compared with CVRP, the SDVRP allows a reduction in the total cost of the routes traveled by vehicles. The exact methods to solve the SDVRP are computationally expensive. Moreover, the complexity and difficult implementation of the state-of-the-art heuristic approaches hinder their application in real-life scenarios of the SDVRP. In this paper, we propose an easily understandable and effective approach to solve the SDVPR based on an a priori adaptive splitting algorithm (AASA) that improves the existing state of the art on a priori split strategy in terms of both solution accuracy and time complexity. In this approach, the demand of the customers is split into smaller demand values using a splitting rule in advance. Consequently, the original SDVRP instance is converted to a CVRP instance which is solved using an existing CVRP solver. While the proposed a priori splitting rule in the literature is fixed for all customers regardless of their demand and location, we suggest an adaptive splitting rule that takes into account the distance of the customers to the depot and their demand values. Our experiments show that AASA can generate solutions comparable to the state of the art, but much faster. [ABSTRACT FROM AUTHOR]

In this paper, we study the pickup and delivery problem with time windows and multiple compartments (PDPTWMC). The PDPTWMC generalizes the pickup and delivery problem with time windows to vehicles with multiple compartments. In particular, we consider three compartment-related attributes: (1) compartment capacity flexibility that allows the capacities of the compartments to be fixed or flexible, (2) item-to-compartment flexibility that specifies which items are compatible with which compartments, and (3) item-to-item compatibility that considers that incompatible items cannot be simultaneously in the same compartment. To solve the PDPTWMC, we propose an exact branch-price-and-cut algorithm in which the pricing problem is solved by means of a unified bidirectional labeling algorithm. The labeling algorithm can tackle all possible combinations of the studied compartment-related attributes of the PDPTWMC. Furthermore, we implement several acceleration techniques that allow to, among others, reduce the symmetry in the label extensions with empty compartments, the symmetry in the dominance between compartments with similar attributes, and the complexity of the algorithm with fixed compartment capacity. Finally, we introduce benchmark instances for the PDPTWMC and conduct an extensive computational campaign to test the limits of our algorithm and to derive relevant managerial insights in order to highlight the applicability of considering the studied compartment-related attributes. Funding: This work was supported by Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant 439.18.459] and the Natural Sciences and Engineering Research Council of Canada [Grant 2017-06106]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0252. [ABSTRACT FROM AUTHOR]