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In response to the challenges of global warming to sustainable development, electric vehicles (EVs) have become an important part of the supply chain. Numerous studies have focused on the electric vehicle routing problem with time windows (EVRPTW) to design an optimal routing plan for EVs and meet customers' demands within th e specified time windows. However, most studies have been conducted in deterministic situations and neglected the uncertain travel time in reality. Therefore, this study proposes a novel mean–standard-deviation-based EVRPTW model and describes uncertain travel time with the expected travel time, travel time variance, and reliable parameters. Besides, the proposed model considers the partial recharge policy and capacitated recharge stations in an uncertain environment, and proposes a time-discrete state-space-time-energy representation network to better simulate real-world situations. To effectively solve the proposed model, a new Lagrangian relaxation and extended alternating direction method of multipliers (LR–EADMM)-based decomposition algorithm is proposed. In the LR–EADMM, dynamic penalty parameters and subgradient method are employed to update the Lagrangian multipliers, strengthen the algorithmic convergence, and improve the quality of solutions. Furthermore, to validate the performance of the proposed algorithm, several comparison experiments are conducted with the Gurobi optimizer and two baseline algorithms. With reliable parameter 0, the experimental results show that the average upper bounds obtained by LR–EADMM is 0.78% greater than the best-known solutions. With reliable parameters 1 and 2, the average gap between lower and upper bounds obtained by LR–EADMM is 8.08% smaller than that obtained by baseline algorithm in solving small instances, and the average upper bounds obtained by LR–EADMM is, respectively, 3.01% and 5.71% better than those obtained by two baseline algorithms in solving large instances. [ABSTRACT FROM AUTHOR]

The aim of a Green Vehicle Routing Problem is to find an optimal route for alternative fuel vehicles to minimize the overall travelling distances while reducing energy consumption and CO2emissions. In this problem each vehicle handles a subset of customers/orders, leaving from and returning to the depot, with respect to maximum distance travelled, while minimizing energy consumptions. We proposed a time window‐based GVRP solution (GVRP‐TW) with exact routing approach. Wherein, each route serves a subset of customers/orders with minimum intermediate refuelling/recharges. To test our method, we conducted experiments using MATLAB software on a set of three reference problem specimens (C‐101, R‐101 and RC‐11). Our approach, evaluated on these benchmark problems, par exceeds in performance in relation to the existing VRP methods (like tabu search, variable neighbourhood search, and GRASP). Moreover, the proposed GVRP‐TW can be further optimized to solve other VRP problems with energy minimisations and less intermediate stops. [ABSTRACT FROM AUTHOR]

This document discusses the emergence of online-to-offline logistics services, such as attended home delivery, bike sharing, and ride-hailing, which have become integral to modern on-demand lifestyles. The management of these services requires considering the behavior of customers and drivers in decision-making processes. The document highlights a special issue of OR Spectrum that focuses on data-driven operations research methods for online-to-offline logistics, covering topics such as parcel delivery management, attended home delivery, same-day delivery, vehicle sharing systems, and airline revenue management. The papers in the special issue explore various approaches, including predictive and prescriptive analytics, clustering and forecasting, and simulation, to address the challenges of managing these services effectively. [Extracted from the article]

In various sectors, such as retail, firms encounter customers with multiunit demand and often implement nonlinear pricing to accommodate this demand structure. While effective, this pricing strategy lacks the adaptability offered by dynamic pricing, a trend gaining significance in the retail landscape due to technological advancements. Neglecting multiunit demand in dynamic pricing, however, can result in suboptimal prices and revenue losses. In response, this paper introduces multiunit dynamic pricing which integrates the strengths of both nonlinear and dynamic pricing strategies. We formulate a stage-wise optimization problem, considering customer preferences for batches of a product through a model based on random willingness-to-pay. The willingness-to-pay is influenced by a combination of the customer's attraction to and consumption of the product—both private information. The firm, functioning as a monopoly, has the ability to price-discriminate between various order sizes by quoting nonlinear batch prices. Our investigation explores three cases of observable information: attraction to the product, consumption of the product, or both. Optimality conditions are derived for all cases, establishing a closed-form expressions for two of them. Additionally, we demonstrate the preservation of desirable monotonicity in time and capacity. Leveraging this monotonicity, we showcase the dynamics of the optimal pricing policy. A simulation study underscores the potential of our approach, highlighting the value of information in supporting strategic decisions, particularly regarding investments in customer profiling and segmentation. Furthermore, we illustrate how our solutions enable firms to make informed stocking and restocking decisions, providing practical insights for firms in multiunit dynamic pricing environments. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a last-mile delivery concept that is well suited for urban areas. By jointly optimizing the tour of a truck and a cargo bike, we ensure that each vehicle is used optimally. Here, we assume that the bike is restocked by meeting up with the truck so that no dedicated mini-hubs have to be constructed. We model different objective functions and analyze the different variants in comparison to the traveling salesperson problem as well as the capacitated vehicle routing problem. In an experimental evaluation, we compare MIP formulations for different problem variants and assess several heuristic approaches to solve large-scale instances. These results show that we can outperform the truck-only delivery in terms of completion time while reducing the distance driven by the truck. [ABSTRACT FROM AUTHOR]

To make the last mile of parcel delivery more efficient, service providers offer an increasing number of modes of delivery as alternatives to the traditional and often cost-intensive home delivery service. Parcel lockers and pickup stations can be utilized to reduce the number of stops and avoid costly detours. To design smart delivery networks, service providers must evaluate different business models. In this context, a multitrip vehicle routing problem with delivery options and location-dependent costs arises. We present a data-driven framework to evaluate alternative delivery strategies, formulate a corresponding model and solve the problem heuristically using adaptive large neighborhood search. By examining large, real-life instances from a major European parcel service, we determine the potential and benefits of different delivery options. Specifically, we show that delivery costs can be mitigated by consolidating orders in pickup stations and illustrate how pricing can be applied to steer customer demand toward profitable, eco-friendly products. [ABSTRACT FROM AUTHOR]

In humanitarian aid scenarios, the model of cumulative capacitated vehicle routing problem can be used in vehicle scheduling, aiming at delivering materials to recipients as quickly as possible, thus minimizing their wait time. Traditional approaches focus on this metric, but practical implementations must also consider factors such as driver labor intensity and the capacity for on-site decision-making. To evaluate driver workload, the operation times of relief vehicles are typically used, and multi-objective modeling is employed to facilitate on-site decision-making. This paper introduces a multi-objective cumulative capacitated vehicle routing problem considering operation time (MO-CCVRP-OT). Our model is bi-objective, aiming to minimize both the cumulative wait time of disaster-affected areas and the extra expenditures incurred by the excess operation time of rescue vehicles. Based on the traditional grey wolf optimizer algorithm, this paper proposes a dynamic grey wolf optimizer algorithm with floating 2-opt (DGWO-F2OPT), which combines real number encoding with an equal-division random key and ROV rules for decoding; in addition, a dynamic non-dominated solution set update strategy is introduced. To solve MO-CCVRP-OT efficiently and increase the algorithm's convergence speed, a multi-objective improved floating 2-opt (F2OPT) local search strategy is proposed. The utopia optimum solution of DGWO-F2OPT has an average value of two fitness values that is 6.22% lower than that of DGWO-2OPT. DGWO-F2OPT's average fitness value in the algorithm comparison trials is 16.49% less than that of NS-2OPT. In the model comparison studies, MO-CCVRP-OT is 18.72% closer to the utopian point in Euclidean distance than CVRP-OT. [ABSTRACT FROM AUTHOR]

This paper introduces an multi-compartment open vehicle routing problem with time window (MCOVRPTW) arising in fresh products distribution, which doesn't require the finished service vehicles return to the distribution center. There are three types of fresh products to be delivered by the multi-compartment vehicles, and the objective aims to find the vehicles scheduling scheme with the lowest cost. For this problem, we established a mathematical model in which the capacity constraint of each compartment and time window constraint must be satisfied. Then, we proposed a hybrid genetic algorithm with some local search-based operators, called GA-LS, to solve it. Each individual in initial population was generated by the nearest neighborhood method to obtain highquality initial population. When a child population was built, the local search procedure was executed on each individual in the child population to enhance its quality. Finally, we carried out some experiments to evaluate the effectiveness of the proposed algorithm. According to the results, the proposed algorithm can yield better solutions compared with existing approaches. Meanwhile, the proposed algorithm reveals good stability and convergence. [ABSTRACT FROM AUTHOR]

Medical Solid Wastes (MSWs) are major hazardous materials containing harmful biological or chemical compounds that present public and environmental health risks. The collection and transportation of waste are usually informed by optimized work‐balanced routing based on comprehensive spatial data in urban traffic networks, called a Vehicle Routing Problem (VRP). This may be unsuitable for MSWs as their special category means they impose additional complexity. The present article develops a planar graph‐based cluster‐routing approach for the optimal collection of MSWs informed by a Geospatial Information System (GIS). The problem is first formulated as a mixed integer linear program in road network spatial data, in the context of Tehran city. The work has two key aims: (i) to minimize the total routing cost of MSW collection and transfer to waste landfills; (ii) to balance workload across waste collectors. There are three main contributions of the proposed approach: (i) to simplify the large search space area by converting the road network to a planar graph based on graph theory, spatial parameters, and topological rules; (ii) to use a modified K‐means algorithm for clustering; (iii) to consider average traffic impacts in the clustering stage and momentary traffic in the route planning stage. A planar graph extraction procedure is applied to capture the network sketch (i.e., a directed graph) from the traffic roadway network. An iterative cluster‐first‐route‐second heuristic is employed to solve the proposed routing problem. This heuristic customizes a K‐means algorithm to determine the optimal number and size of clusters (i.e., routes). A Traveling Salesman Problem (TSP) algorithm is applied to regulate the optimal sequence of visits to medical centers. The experimental results show improvements in balancing collectors' workload (i.e., ~4 min reduction in the standard deviation of average travel time) with reductions in travel time (i.e., an average ~1 h for the entire fleet and ~4 min per route). These findings confirm that the proposed methodology can be considered as an approach for optimizing waste collection routes. [ABSTRACT FROM AUTHOR]

Many companies prefer to use third party logistics firms to deliver their goods and as such planning the return of the vehicles to the depot is not required. This is called open vehicle routing problem (OVRP). In literature, the OVRP is handled with minimum distance as objective function like vehicle routing problem. But in the real world, the objective function achieves minimum many costs like standard routing cost, stopping by cost and the deviation cost. The standard routes are previously defined under free market conditions by third party logistic firms. The deviation from the standard route is required to arrive cities which are not on the standard route. The stop by cost occurs on the delivery points. In this paper mentioned three costs are considered in the objective function while many papers consider only distance related costs in the literature. This paper proposes a new mathematical model for the OVRP. In the constraints, the last points of the routes are researched in detail. The standard route costs are determined by considering the last point of the route. Because of the NP-hard structure of the OVRP, the proposed mathematical model is solved with a hybrid metaheuristic called Civilized Genetic Algorithm (CGA). CGA is developed by hybridizing a modified genetic algorithm and a local search algorithm. The application of this study is implemented for the delivery routing of a combi boiler producer in Turkey. The third party logistic firms may use this proposed model and the solution approach for the real life applications. [ABSTRACT FROM AUTHOR]

The idling of automobiles at street intersections can lead to pollutant accumulation which impacts the health of residents in street-facing buildings. Previous research focused on pollutant dispersion within street canyons and did not consider the coupling of indoor and outdoor pollutants. This paper employs the computational fluid dynamics (CFD) method to simulate the dispersion characteristics of vehicle emission pollutants in street canyons, primarily investigating the indoor and outdoor pollutant dispersion patterns under various window opening configurations (single-sided ventilation, corner ventilation, and different positions of the glass under corner ventilation). Additionally, the study considers the impacts of the aspect ratio and ambient wind speed. Studies have shown that corner ventilation is effective in reducing indoor pollutant levels. When the two window glass positions are far away from the center of the intersection, the average CO mass fraction in the single-sided ventilation room is reduced by 87.1%. The average indoor CO mass fraction on the leeward side decreases with the increasing wind speed and aspect ratio. At a wind speed of 8 m/s, the average indoor CO mass fraction on the leeward side decreases to 2.45 × 10−8. At an aspect ratio of 2, the indoor CO mass fraction on the leeward side decreases with increasing floors before stabilizing at approximately 4.77 × 10−9. This study suggests optimal window opening strategies to reduce indoor pollutant levels in street-facing buildings at street intersections, offering guidance to indoor residents on window ventilation practices. [ABSTRACT FROM AUTHOR]

Optimization algorithms have a wide range of applications in symmetry problems, such as graphs, networks, and pattern recognition. In this paper, a dynamic periodic multi-depot multi-trip vehicle routing model for scheduling test samples is constructed, which considers the differences in testing unit price and testing capacity of various agencies and introduces a cross-depot collaborative transport method. Both the cost and the testing time are minimized by determining the optimal sampling routes and testing agencies, subjecting to the constraints of vehicle capacity, number of vehicles, and delivery time. To solve the model, a knowledge-guided multi-objective shuffled frog leaping algorithm (KMOSFLA) is proposed. KMOSFLA adopts a convertible encoding mechanism to realize the diversified search in different search spaces. Three novel strategies are designed: the population initialization with historical information reuse, the leaping rule based on the greedy crossover and genetic recombination, and the objective-driven enhanced search. Systematic experimental studies are implemented. First, feasibility analyses of the model are carried out, where effectiveness of the cross-depot collaborative transport is validated and sensitivity analyses on two parameters (vehicle capacity and proportion of the third-party testing agencies) are performed. Then, the proposed algorithm KMOSFLA is compared with five state-of-the-art algorithms. Experimental results indicate that KMOSFLA can provide a set of non-dominated schedules with lower cost and shorter testing time in each scheduling period, which provides a reference for the dispatcher to make a final decision. [ABSTRACT FROM AUTHOR]

This paper studies the multi-trip vehicle routing problem with multiple time windows, which extends the multi-trip vehicle routing problem by deciding not only the sequence of customers that each vehicle serves but also the service time window of each customer. It also requires that the delivery service time is within the selected time windows and that the total demand of the customers served by the vehicle on each trip does not exceed the maximum carrying capacity. For solving the studied problem, we develop a mixed integer linear programming model with the objective of minimizing the total travel distance of vehicles and design a tailored iterative local search heuristic. Within the framework of the iterative local search, an improved Solomon greedy insertion algorithm suitable for multiple time windows and multi-trip scenarios is designed to generate the initial solution, and local search operators such as Or-opt and Relocate, as well as Random Exchange perturbation operations, are also developed. The experiment results demonstrate the effectiveness of the proposed model and algorithm and confirm that by providing customers with multiple time windows option, carriers can flexibly plan vehicle routes and select appropriate service time windows, thereby reducing the number of vehicles used and the total distance travelled and improve delivery success. [ABSTRACT FROM AUTHOR]

The vehicle routing problem with time windows (VRPTW) remains a formidable challenge, due to the intricate constraints of vehicle capacity and time windows. As a result, an algorithm tailored for this problem must demonstrate robust search capabilities and profound exploration abilities. Traditional methods often struggle to balance global search capabilities with computational efficiency, thus limiting their practical applicability. To address these limitations, this paper introduces a novel hybrid algorithm known as large neighborhood search with modified rat swarm optimization (LNS-MRSO). Modified rat swarm optimization (MRSO) is inspired by the foraging behavior of rat swarms and simulates the search process for optimization problems. Meanwhile, large neighborhood search (LNS) generates potential new solutions by removing and reinserting operators, incorporating a mechanism to embrace suboptimal solutions and strengthening the algorithm's prowess in global optimization. Initial solutions are greedily generated, and five operators are devised to mimic the position updates of the rat swarm, providing rich population feedback to LNS and further enhancing algorithm performance. To validate the effectiveness of LNS-MRSO, experiments were conducted using the Solomon VRPTW benchmark test set. The results unequivocally demonstrate that LNS-MRSO achieves optimal solutions for all 39 test instances, particularly excelling on the R2 and RC2 datasets with percentage deviations improved by 5.1% and 8.8%, respectively, when compared to the best-known solutions (BKSs). Furthermore, when compared to state-of-the-art algorithms, LNS-MRSO exhibits remarkable advantages in addressing VRPTW problems with high loading capacities and lenient time windows. Additionally, applying LNS-MRSO to an unmanned concrete-mixing station further validates its practical utility and scalability. [ABSTRACT FROM AUTHOR]

This editorial paper reviews the articles published in a special issue devoted to the application of active particle methods applied to the study of the collective dynamics of large systems of interacting entities in science and society. The applications presented in this special issue focus on the study of financial markets, cell dynamics in the context of cancer modeling, vehicle and crowd vehicle and crowd dynamics, and classical problems in the kinetic theory of active particles and swarm theory. A critical analysis is proposed to look forward to research. Perspectives with emphasis on the interaction of multiple social dynamics. [ABSTRACT FROM AUTHOR]

A cooperative is a business entity with the primary objective of providing benefits, services, and goods to its members, who both own and exercise democratic control over it. In the context of a cooperative, a fleet typically consists of vehicles owned by self-concerned individually rational owners who prioritize their own efficiency and the fairness of the system. This fairness refers to how their individual gain aligns with the gain of others. In this paper, we focus on the routing of such cooperative fleets. Considering only the fleet's efficiency in terms of minimising its overall cost, the studied problem corresponds to the multiple Traveling Salesman Problem (mTSP). However, our interest lies in finding both efficient and fair solutions, so we propose two new variants of this problem that integrate and maximise the fleet's egalitarian and elitist social welfare. Additionally, to enhance the balance between fleet efficiency and fairness, we propose the systematic elitist and systematic egalitarian social welfare optimisation algorithm. Through simulation results, we observe a wide diversity of routes depending on the approach considered. Therefore, a cooperative may choose a model that best balances its fleet's efficiency and fairness based on its specific requirements. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Cumulative Capacitated Vehicle Routing Problem (CCVRP), which is used to model many real-world applications, especially in the area of supplying humanitarian aid after a natural disaster. Interestingly, in this study, Unmanned Aerial Vehicles (UAVs) so-called drones are used to assist the trucks in delivering parcels to customers. Each of them travels to different locations to perform specified tasks and meet periodically with the vehicle from which it takes off to swap its battery. In this paper, a mathematical model is formulated which is then tested with small-sized problems using CPLEX software. Due to the difficulty of solving large instances to optimality, we propose a heuristic algorithm based on a well-established type of cluster-first, route-second approach. Then, it is enhanced by some proposed properties. Hereafter, we develop a minimum spanning tree based-lower bound. Finally, extensive computational experiments are carried out by using instances from the literature. They show the good performance of the proposed heuristic algorithm to solve large instances in a very competitive running time. [ABSTRACT FROM AUTHOR]

The design of fault-tolerant production and delivery systems is one of the priority areas in modern operations research. The traditional approach to modeling such systems is based on the use of stochastic models that describe the choice of a possible scenario of actions in the event of problems in a production or transportation network. Along with a number of advantages, this approach has a known drawback. The occurrence of problems of an unknown nature that can jeopardize the performance of the entire simulated system significantly complicates its use. This paper introduces the minimax problem of constructing fault-tolerant production plans (reliable production process design problem, RPPDP), the purpose of which is to ensure the uninterrupted operation of a distributed production system with minimal guaranteed cost. It is shown that the RPPDP is NP-hard in the strong sense and remains intractable under quite specific conditions. To find exact and approximate solutions with accuracy guarantees for this problem, branch-and-bound methods are developed based on the proposed compact model of the mixed integer linear program (MILP) and novel heuristic of adaptive search in large neighborhoods (adaptive large neighborhood search, ALNS) as part of extensions of the well-known Gurobi MIP solver. The high performance and complementarity of the proposed algorithms is confirmed by the results of numerical experiments carried out on a public library of benchmarking instances developed by the authors based on instances from the PCGTSPLIB library. [ABSTRACT FROM AUTHOR]

Snow and ice route removal activities play an essential role in travelers' safety and roadways' reliability. They often require the deployment of a large number of snowplow trucks on a vast maintenance area and involve a set of vehicle routing problems with multiple objectives and constraints. Many transportation agencies have limited resources and budgets for snow and ice route removal activities during winter maintenance operations. The objective of this paper is to propose a constraint-based snowplow optimization model to accommodate vehicle routing problems and justify the optimized fleet size for achieving the maximum level of service in snow and ice route removal. The proposed snowplow optimization model was developed using the geographic information system (GIS) base maps created by using ArcGIS Pro (version 2.7). After the model was tested and verified by experts in the Kansas Department of Transportation, it was applied to the snow and ice route removal activities in a district in Kansas as an illustrative example. The optimization results showed that the level of service could be increased up to 81% with an average route removal efficiency of 86% and the total travel time required to treat all snow routes in the selected district can be reduced by approximately 29 h for one treating iteration. The proposed model contributed to the winter operation maintenance body of knowledge by providing an efficient approach to snow and ice route removal activities. The findings of this study also may assist transportation agencies in optimizing their snow route removal practice in winter maintenance operations. This study developed a snowplow route optimization model using a geographic information system (GIS)-based software platform to enhance the efficiency of snow removal of Departments of Transportation of states in their winter maintenance. The model outcomes provided a detailed set of optimized snowplow route maps with time-related parameters (e.g., total travel time, plowing time, and deadhead time), snowplow route efficiency, and percentage of level of service (LOS) satisfaction of snow removal. Then, transportation agencies can utilize the optimized routing networks to monitor their resources spent on snow and ice control activities and increase the LOS in their maintenance operations. The results of this study enable transportation agencies to effectively justify the fleet size required at each service area and efficiently allocate limited resources to maintain all roadways in an economic, safety, and reliability manner. This study also facilitates the automation of snowplow optimization processes using GIS to provide satisfactory services during snow and ice events. The proposed model can serve as a tool to assist the agencies in directing any future facility locations and capacities for their winter maintenance. [ABSTRACT FROM AUTHOR]

The hybrid genetic search (HGS) metaheuristic has produced outstanding results for several variants of the vehicle routing problem. A recent implementation of HGS specialized to the capacitated vehicle routing problem (CVRP) is a state‐of‐the‐art method for this variant. This paper proposes an improved HGS for the CVRP obtained by incorporating a new solution generation method into its (re‐)initialization process to guide the search more efficiently and effectively. The solution generation method introduced in this work combines an approach based on frequent patterns extracted from good solutions by a data mining process and a randomized version of the Clarke and Wright savings heuristic. As observed in our experimental comparison, the proposed method significantly outperforms the original algorithm regarding the final gap to the best known solutions and the primal integral. [ABSTRACT FROM AUTHOR]

As a method of reducing costs and enhancing service quality, companies integrate production and distribution scheduling to improve performance. Thirty-two articles published between 2017 and 2022 are classified based on a review methodology as a continuation of a literature review of the integrated production and distribution scheduling problems at the operational level that was published in 2016. The characteristics of mathematical models and the solution algorithms used are discussed in order to identify gaps and determine future research directions. Through the review, it was found that some real-life characteristics still need further study. Future research may need to consider uncertainty, stochastic elements and evaluating different heuristics and metaheuristics in different production environments. Finally, additional research is necessary to determine under what conditions integration is most effective. [ABSTRACT FROM AUTHOR]

Background: This publication presents a review, multiple criteria optimization models, and a practical example pertaining to the integration of automated smart locker systems, capillary distribution networks, crowdshipping, last-mile delivery and supply chain management. This publication addresses challenges in logistics and transportation, aiming to enhance efficiency, reduce costs and improve customer satisfaction. This study integrates automated smart locker systems, capillary distribution networks, crowdshipping, last-mile delivery and supply chain management. Methods: A review of the existing literature synthesizes key concepts, such as facility location problems, vehicle routing problems and the mathematical programming approach, to optimize supply chain operations. Conceptual optimization models are formulated to solve the complex decision-making process involved in last-mile delivery, considering multiple objectives, including cost minimization, delivery time optimization, service level minimization, capacity optimization, vehicle minimization and resource utilization. Results: The multiple criteria approaches combine the vehicle routing problem and facility location problem, demonstrating the practical applicability of the proposed methodology in a real-world case study within a logistics company. Conclusions: The execution of multi-criteria models optimizes automated smart locker deployment, capillary distribution design, crowdshipping and last-mile delivery strategies, showcasing its effectiveness in the logistics sector. [ABSTRACT FROM AUTHOR]

The increasing power demand growth and extreme weather conditions push utilities to search for a more sustainable and resilient power distribution infrastructure. Dispatchable distributed generators (DGs) can contribute to achieving the goals. This paper reveals a general framework for allocating dispatchable DGs with their suitable location, capacity, and type in the test distribution networks to bring sustainability and resilient planning synergy. A multiobjective optimization approach has been presented to minimize payback year (PBY) for DGs, enhance the network's operational efficiency, and promote system resiliency by satisfying various operating constraints. The proposed planning model is structured to give the best possible solution in compliance with changes in seasonal peak demands. The efficacy of the proposed scheme has been tested on a 28-bus Indian distribution system and an IEEE 33-bus test system, and results concerning the number of customers served, and priority customers restored are presented. [ABSTRACT FROM AUTHOR]

Given the swift expansion of fresh e-commerce, the front warehouse mode can respond quickly and ensure the quality of fresh products. However, the complexity of the supply chain structure under front warehouse mode poses a challenge in reducing logistics costs and improving distribution efficiency while meeting consumers' immediate delivery demands. Therefore, this paper studies the vehicle routing problem of two-echelon fresh e-commerce under front warehouse mode. Considering trans-shipment time constraints between the two echelons and the characteristics of terminal distribution, this paper initially models the vehicle routing problem for front warehouses as a two-echelon multi-trip capacitated vehicle routing problem with time windows. A mixed-integer linear programming model is subsequently established. To solve the model, a hybrid genetic algorithm integrated with neighborhood search is developed. Matrix coding is employed to merge vehicle selection and route assignment decisions. Simultaneously, neighborhood search is applied to enhance the search capability of algorithms, thereby improving the quality of solutions. Furthermore, the effectiveness and efficiency of the model and algorithm are verified through experiments of varying scales. Finally, comparative strategies and sensitivity analysis highlight the advantages of multi-trip strategies and provide insights into the optimal vehicle capacity limit. [ABSTRACT FROM AUTHOR]

The process of transferring money from the treasury to the branches and returning it at specific and limited periods is one of the applications of the Vehicle Routing Problem (VRP). Many parameters affect it, but choosing the right route is the key parameter so that the money delivery process is carried out in a specific period with the least risk. In the present paper, new relationships are defined in the form of three concepts in order to minimize route risk. These concepts are: 1) the vehicle does not travel long routes in the first three movements, 2) a branch is not served at the same hours on two consecutive days, and 3) an arc should not be repeated on two consecutive days. The proposed model with real information received from Bank Shahr has been performed for all branches in Tehran. Because the VRP is an NP-Hard problem, a genetic algorithm was used to solve the problem. Different issues in various production dimensions were solved with GAMS and MATLAB software to show the algorithm solution quality. The results show that the difference between the genetic algorithm and the optimal solution is an average of 1.09% and a maximum of 1.75%. [ABSTRACT FROM AUTHOR]

The production capacity sharing problem was studied in this paper. Considering that the game is composed of a capacity provider and customers, in which the capacity provider and customers are self-interest, with different demands and different market relations. Nash bargaining theory was adopted to explore the sharing strategy of the production capacity. To be specific, the classic scheduling model and the asymmetric Nash bargaining model were combined to develop a production capacity sharing model, which was essentially a nonlinear integer program. To address the computational issue, a solving method based on Lagrangian relaxation was designed, and then, the bargaining results of production capacity sharing were given. Simulation analysis shows that the proposed algorithm performs well in most cases. It is found that when the capacity provider has a min-sum objective function, the capacity provider pays attention to the performance indicators of all customers, and the conict between the capacity provider and customers are particularly significant. With the increase of bargaining power of the capacity provider, the capacity provider index is optimized, but the customer performance index becomes worse. However, when the bargaining power of the capacity provider is very strong, it will lead to the uctuation of the overall efficiency of the system. Therefore, the game parties need to maintain a reasonable bargaining power. [ABSTRACT FROM AUTHOR]

Environmental concerns have called for several measures to be taken within the logistics and transportation fields. Among these measures is the adoption of electric vehicles instead of diesel-operated vehicles for personal and commercial-delivery use. The optimized routing of electric vehicles for the commercial delivery of products is the focus of this paper. We study the effect of several practical challenges that are faced when routing electric vehicles. Electric vehicle routing faces the additional challenge of the potential need for recharging while en route, leading to more travel time, and hence cost. Therefore, in this work, we address the issue of electric vehicle routing problem, allowing for partial recharging while en route. In addition, the practical mandate of the time windows set by customers is also considered, where electric vehicle routing problems with soft time windows are studied. Real-life experience shows that the delivery of customers' demands might be uncertain. In addition, real-time traffic conditions are usually uncertain due to congestion. Therefore, in this work, uncertainties in customers' demands and traffic conditions are modeled and solved using fuzzy methods. The problems of fuzzy real-time, fuzzy demand, and electric vehicle routing problems with soft time windows are addressed. A mixed-integer programming mathematical model to represent the problem is developed. A novel two-phase solution approach is proposed to solve the problem. In phase I, the classical genetic algorithm (GA) is utilized to obtain an optimum/near-optimum solution for the fuzzy demand electric vehicle routing problem with soft time windows (FD-EVRPSTW). In phase II, a novel fuzzy real-time-adaptive optimizer (FRTAO) is developed to overcome the challenges of recharging and real-time traffic conditions facing FD-EVRPSTW. The proposed solution approach is tested on several modified benchmark instances, and the results show the significance of recharging and congestion challenges for routing costs. In addition, the results show the efficiency of the proposed two-phase approach in overcoming the challenges and reducing the total costs. [ABSTRACT FROM AUTHOR]

Container transportation is pivotal in global supply chains, facilitating the exchange of goods between companies across different countries. Given the exceedingly high operational costs of transporting containers, optimizing itinerary schedules can yield significant benefits for logistics companies. In this paper, we delve into a real-world container transportation routing issue where trucks are scheduled to haul trailers, subsequently transporting containers amongst container depots, ports, and warehouses. Our research bridges the existing gap between academic literature and industrial practice by examining the versatile role of trailers. We specifically focus on factors like trailer capacity restrictions and the ability to detach. To encapsulate these intricacies, we introduce a mixed-integer linear programming model, incorporating new variables, invariants, and constraints pertinent to these requirements. We follow this with the proposition of an Approximate Adapted Large Neighborhood Search algorithm (A-ALNS) aimed at solving the model. Within this algorithm, six innovative operators and elimination strategies have been integrated to amplify the efficiency of solution searches and sidestep local optima. Moreover, we've established an adaptive scoring mechanism to expedite operator selection and deliver feasible solutions within constrained timeframes. Our empirical tests on 25 data sets underscore the efficacy of our algorithms; they serve between 90.9% to 100% of total requests across all instances. Impressively, our proposed framework can attain feasible solutions within an hour - a task that often spanned days with preceding methodologies. [ABSTRACT FROM AUTHOR]

Flooding, a pervasive and severe natural disaster, significantly damages environments and infrastructure and endangers human lives. In affected regions, disruptions to transportation networks often lead to critical shortages of essential supplies, such as food and water. The swift and adaptable delivery of relief goods via vehicle is vital to sustain life and facilitate community recovery. This paper introduces a novel model, the Vehicle Routing Problem for Relief Item Distribution under Flood Uncertainty (VRP-RIDFU), which focuses on optimizing the speed of route generation and minimizing waiting times for aid delivery in flood conditions. The Genetic Algorithm (GA) is employed because it effectively handles the uncertainties typical of NP-Hard problems. This model features a dual-population strategy: random and enhanced populations, with the latter specifically designed to manage uncertainties through anticipated route performance evaluations, incorporating factors like waiting times and flood risks. The Population Sizing Module (PSM) is implemented to dynamically adjust the population size based on the dispersion of affected nodes, using standard deviation assessments. Introducing the Complete Subtour Order Crossover (CSOX) method improves solution quality and accelerates convergence. The model's efficacy is validated through simulated flood scenarios that emulate various degrees of uncertainty in road conditions, affirming its practicality for real-life rescue operations. Focusing on prioritizing waiting times over travel times in routing decisions has proven effective. The model has been tested using standard CVRP problems with 20 distinct sets, each with varying node numbers and patterns, demonstrating superior performance and efficiency in generating vehicle routing plans compared to the shortest routes, which serve as the benchmark for optimal solutions. The results highlight the model's capability to deliver high-quality solutions more rapidly across all tested scenarios. [ABSTRACT FROM AUTHOR]

Multi-objective transportation problems (MOTPs) are mathematical optimization problems that involve simultaneously considering multiple, often conflicting objectives in transportation planning. Unlike traditional transportation problems, which typically focus on minimizing a single objective such as cost or distance, MOTPs aim to balance multiple objectives to find the optimal solution. These problems appear in various real-world applications such as logistics, supply chain management, and transportation, where decision-makers need to consider multiple criteria when designing transportation networks, routing vehicles, or scheduling deliveries. The primary challenge lies in the uncertainty in real-world transportation scenarios, where logistics involve factors beyond cost and distance. We investigated a multi-choice solid fractional multi-objective transportation problem (MCSF-MOTP) based on supply, demand, and conveyance capacity, where the coefficients of the objective functions were of the multi-choice type due to uncertainty. To address this uncertainty, the proposed model employed the Newton divided difference interpolation polynomial method, and the suitability of this model was validated through a numerical illustration employing a ranking approach. [ABSTRACT FROM AUTHOR]

A fleet of drones is considered in the routing problems with an offshore drone base station, considering the simultaneous movements of drones and ships. A model, entitled meeting model, between a drone and a moving ship is devised, and an extended model is developed based on the vehicle routing problem model. A genetic algorithm based on a sequential insert heuristic (SIH) is designed to solve the model as a holistic framework with two strategies to determine the sequential assignments of ships to drones, namely, the D r o n e B y D r o n e , and S h i p B y S h i p strategies. The proposed models and solution algorithms are demonstrated and verified by experiments. Numerical studies show that the D r o n e B y D r o n e strategy can overperform the S h i p B y S h i p strategy regarding traveling distances. In addition, when considering the simultaneous movement of the ship and drone, improving the drone flying speeds can reduce the flying time of drones rather than optimizing the ship's moving speed. The managerial implications and possible extensions are discussed based on modeling and experimental studies. [ABSTRACT FROM AUTHOR]

A multi-objective vehicle routing optimization model is established to minimize total cost and equilibrium degree for multi-objective vehicle routing problem with time windows, and a hybrid multi-objective grey wolf algorithm is proposed to solve the problem. Mainly design three strategies: (1) A new encoding and decoding method is designed to achieve the conversion of continuous grey wolf position vectors to discrete customer sequences. (2) Convergence and distribution indicators are used to select decision individuals. (3) Multiple deletion and insertion operators have been designed to implement local routing optimization. To demonstrate the effectiveness of the algorithm, some numerical examples in Solomon are used as examples to experimentally compare the proposed algorithm with MOIGA and improved ACO algorithms. Experimental results show that the hybrid multi-objective grey wolf algorithm proposed in this paper can find a better Pareto solution, and its performance is better than other evolutionary algorithm. [ABSTRACT FROM AUTHOR]

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Rising traffic congestion and fuel costs pose significant challenges for supply chains with numerous retailers. This paper addresses these challenges by optimizing transportation routes for processed tomatoes within a long-haul and intercity distribution network. We use the heterogeneous capacitated vehicle routing problem framework to create a new quadratically constrained mixed-integer non-linear programming model that aims to meet demand at multiple destinations while minimizing transportation costs. Our model incorporates real-time data and route optimization strategies that consider traffic conditions based on freight time and route diversions for expedited deliveries. It aims to devise an optimal transportation schedule that minimizes fuel, operational, and maintenance costs while ensuring efficient delivery of tomato paste. By applying this model to a real-world case study, we estimate a significant 27.59% reduction in transportation costs, dropping them from GH¢20,270 ($1,638.91) to GH¢14,676 ($1,186.61) on average. This highlights the effectiveness of our strategy in lowering costs while maintaining smooth and efficient deliveries.

Effective waste management is essential for maintaining a clean and sustainable urban environment. This paper addresses the waste collection challenges in Torreón, Coahuila, Mexico, by integrating data mining techniques with the vehicle routing problem (VRP). The goal is to optimize waste collection routes and schedules to minimize costs, reduce fuel consumption, and enhance operational efficiency. The study leverages historical waste collection data, demographic information, and geographic data to comprehensively understand waste generation patterns, population density, and infrastructure layout. The data mining process involves exploratory analysis, clustering, and classification techniques to identify critical variables and patterns that influence waste generation and collection. This information is used to design efficient collection routes, considering factors such as distance, capacity constraints, traffic patterns, and time windows. The VRP model is then applied to allocate waste collection vehicles optimally, ensuring that each route is serviced within the designated timeframe. The model aims to minimize the number of vehicles used, optimize capacity utilization, and reduce travel distances. Additionally, real-time data on vehicle status, traffic conditions, and waste generation rates are integrated to adjust routes and schedules to improve operational efficiency dynamically. This approach provides waste management authorities in Torreón with valuable insights and tools to enhance waste collection operations. By leveraging data mining and VRP techniques, the study aims to improve waste management practices, reduce environmental impact, and promote a cleaner, healthier environment for residents of Torreón, Coahuila, Mexico.

The vehicle routing problem (VRP) is a combinatorial optimization problem that determines optimal routes to enhance distribution efficiency. One of the most popular strategies in freight distribution is multi-echelon distribution. Multi-echelon distribution networks often apply to supply chain management, land transportation, the maritime industry, aviation, etc., and rely on VRP. This comprehensive review systematically analyses 382 papers retrieved through the Scopus database. We use a bibliometric and network analysis tool to complete a systematic literature mapping identifying key interrelationships and research clusters. The analysis depicts five main research clusters: green logistics and decision analysis, scheduling and inventory optimization, VRP for city logistics, mathematical modeling and optimization, and outbound logistics and customer service, identified based on author keywords of the systematically derived paper pool. Each cluster is provided with foundational knowledge, concepts, theories, and employed techniques. Finally, future studies are suggested to explore more comprehensive investigation in highly discussed domains like city logistics problems in e-commerce, vehicle routing problems for sustainable logistics, and technological advancement-based applications.

This article discusses the process of conducting a comprehensive rate study in the water industry, specifically focusing on the cost of service analysis. The cost of service analysis involves understanding the costs associated with providing water service and allocating those costs to appropriate customers. By grouping customers into classes based on common usage characteristics, water utilities can distribute costs in proportion to each user's respective use of the system. This ensures that rates are fair and that no class of customers is subsidizing another. The article outlines a standard approach for conducting a cost of service analysis, including categorizing revenue requirements, allocating functional costs, developing units of service, and deriving the unit cost of service for each customer class. The results of the analysis allow utilities to determine the specific revenue requirements for each component of their water system and create a comprehensive rate structure that ensures all customers pay their fair share. [Extracted from the article]

This paper studies a new variant of integrated production scheduling and vehicle routing problem where production of customer orders are performed under job-shop environment and order deliveries are made by a heterogeneous fleet of vehicles, each of which is allowed to take multiple trips. Two conflicting objectives are considered, namely minimisation of the total amount of CO2 emitted by the vehicles and minimisation of maximum tardiness resulting from late deliveries. To this end, we present a bi-objective mixed-integer programming formulation. Augmented ε-Constraint (Augmecon) method is implemented to find Pareto optimal solutions. Due to problem complexity, Augmecon cannot provide solutions even with small-sized problems. Thus, we adopt Pareto Local Search (PLS) and non-dominated sorting genetic algorithm-II (NSGA-II) for practical sized instances. For small-sized instances involving 5, 6, and 7 customers, experimental results indicate that CPU time of Augmecon are 11, 84, and 524 sec, respectively with an average number of Pareto efficient solution of 3.5. In terms of hypervolume index, Augmecon shows the best performance, followed by NSGA-II with 11.32% and PLS with 20.75% degradation for small-sized instances. For medium and large-sized instances, PLS shows worse performance than NSGA-II by 16.87% and 40.48%. [ABSTRACT FROM AUTHOR]

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in real-world VRP applications, Machine Learning (ML) methods have been used in combination with analytical approaches to enhance problem formulations and algorithmic performance across different problem solving scenarios. However, the relevant papers are scattered in several traditional research fields with very different, sometimes confusing, terminologies. This paper presents a first, comprehensive review of hybrid methods that combine analytical techniques with ML tools in addressing VRP problems. Specifically, we review the emerging research streams on ML-assisted VRP modelling and ML-assisted VRP optimisation. We conclude that ML can be beneficial in enhancing VRP modelling, and improving the performance of algorithms for both online and offline VRP optimisations. Finally, challenges and future opportunities of VRP research are discussed. [ABSTRACT FROM AUTHOR]

The Inventory-Routing Problem (IRP) deals with the joint optimisation of inventory and the associated routing decisions. The IRP with time windows (IRPTW) considers time windows for the deliveries to the customers. Due to its importance and several real-world applications, in this paper, we develop an intricate solution algorithm for this problem. A combination of tools ranging from established groups of valid inequalities, pre-processing techniques, local search procedures, and a local branching algorithm is utilised to solve the IRPTW efficiently. We compare the performance of our algorithm on a benchmark set of instances and show how our solution algorithm provides promising results against a competing algorithm from the literature. Moreover, the results of our study provide an overview of the performance of several already proposed techniques and their integration in the literature. [ABSTRACT FROM AUTHOR]

In modern banks, establishing efficient and quality customer services plays a crucial role to achieve the business success. There are a large number of customers to be served daily; however, required service resources (in particular, customer service representatives) can be rather limited. Therefore, customer service representative scheduling is a challenging problem for bank managers. In the present paper, we focus on a customer service representative scheduling problem considering the stochastic customer arrival time and service duration to minimise the total cost including two parts: (i) the loss concerning the customer waiting and (ii) cost of providing service representatives. We formulate this scheduling problem as an integer programming problem and employ an adapted water wave optimization (WWO) algorithm to solve this problem efficiently. We adapt the propagation and refraction operators of WWO according to the solution space of this problem. The results of the conducted computational experiments demonstrate that the adapted WWO algorithm outperforms the considered state-of-the-art evolutionary algorithms in solving a set of test instances. [ABSTRACT FROM AUTHOR]