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As a critical problem in sophisticated distribution systems, vehicle routing plays a pivotal role in dealing with time windows and capacities constraints. The purpose of this paper is to addresses a new integrated model to incorporate both three-dimensional and time windows aspects of the routing problem. First, capacitated vehicle routing decisions are made subject to a soft time interval to meet the customers’ demands. Afterward, these decisions are entered into the three-dimensional loading problem.

The problem is solved using generalized algebraic modeling system software in small-size problems. The problem is NP-hard and requires an efficient solution methodology. For this purpose, a hybrid algorithm has been proposed to solve the large-size problems. The efficiency of this algorithm is checked by making comparisons with exact solutions for small and medium size test problems, and with the related literature for large size problems.

The numerical experiments show that the proposed model covers more effectively the broader aspects of the transportation problem. Furthermore, the proposed algorithm supports competitive and satisfactory results by giving reasonable outputs in comparison with previous studies.

The main purpose of this integration is to achieve minimum total transportation costs, which cannot be guaranteed without applying two referred constraints, simultaneously.

This paper aims to optimize the halal product distribution by minimizing the transportation cost while ensuring halal integrity of the product. The problem is considered as a capacitated vehicle routing problem (CVRP), based on the assumption that two different types of vehicles are used for distribution: vehicles dedicated for halal product distribution and vehicles dedicated for nonhalal products distribution. The problem is modeled as an integer linear program (ILP), termed CVRP-halal and nonhalal products distribution (CVRP-HNPD). It is solved using tabu-search (TS)-based algorithm and is suitable for application to real-life sized halal product distribution.

Two approaches are used in solving the problem: exact approach (integer-linear program) and approximate approach (TS). First, the problem is modeled as ILP and solved using CPLEX Solver. To solve life-sized problems, a TS-based algorithm is developed and run using MATLAB.

The experiments on numerical data and life-sized instances validate the proposed model and algorithm and show that cost-minimizing routes for HNPD are developed while ensuring the halal integrity of the products.

The proposed model and algorithm are suitable as decision support tools for managers responsible for distribution of halal products as they facilitate the development of minimum cost distribution routes for halal and nonhalal products while maintaining the integrity of halal products. The model and algorithm provide a low transportation cost strategy at the operational level of halal products distribution while fulfilling the halal logistics requirement.

To the best of the author’s knowledge, this is the first study that specifically deals with the CVRP of halal products distribution by proposing CVRP-HNPD model and TS-CVRP-HNPD algorithm. The proposed model and algorithm ensure the integrity of halal products along the distribution chain, from the warehouse (distribution center) to the retailer, while achieving lowest transportation cost.

The purpose of this paper is to reduce the distribution cost of an Indian cooperative dairy. The reduction of cost was achieved with the application of the clustering method (k-means clustering) and capacitated vehicle routing problem (cheapest link algorithm (CLA)).

Capacitated k-means clustering was used to split delivery locations into similar size groups (i.e. clusters) based on proximity without exceeding a specified total cluster capacity. Each cluster would be served by a local stockist. CLA was then used to find delivery routes from dairy (i.e. depot) to stockist in each cluster and from stockist to all other delivery locations within the cluster.

K-means clustering and CLA suggested optimal delivery routes on which vehicles will run. The complete algorithm was able to provide a solution within 30 s.

Clustering of delivery locations and use of heterogeneous fleet of delivery vehicles can result in considerable savings in daily operational cost.

Most of the research related to the use of demand clustering to improve distribution routes has been theoretical, which do not take into account real-world limitations like vehicle’s specific limitations. The authors tried to address that gap by taking a real-world case of a cooperative dairy and compared the result with existing distribution routes used by dairy. This work can be used by other dairies or distribution companies according to their scenario.

This paper studies a concept for protecting vulnerable population groups during pandemics using direct home deliveries of essential supplies, from a distribution logistics perspective. The purpose of this paper is to evaluate feasible and resource-efficient home delivery strategies, including collaboration between retailers and logistics service providers based on a practical application.

A food home delivery concept in urban areas during pandemics is mathematically modeled. All seniors living in a district of Berlin, Germany, represent the vulnerable population supplied by a grocery distribution center. A capacitated vehicle routing problem (CVRP) is developed in combination with a k-means clustering algorithm. To manage this large-scale problem efficiently, mixed-integer programming (MIP) is used. The impact of collaboration and additional delivery scenarios is examined with a sensitivity analysis.

Roughly 45 medically vulnerable persons can be served by one delivery vehicle in the baseline scenario. Operational measures allow a drastic decrease in required resources by reducing service quality. In this way, home delivery for the vulnerable population of Berlin can be achieved. This requires collaboration between grocery and parcel services and public authorities as well as overcoming accompanying challenges.

Developing a home delivery concept for providing essential goods to urban vulnerable groups during pandemics creates a special value. Setting a large-scale CVRP with variable fleet size in combination with a clustering algorithm contributes to the originality.

Nowadays, global warming, due to large-scale emissions of greenhouse gasses, is among top environmental issues. The purpose of this paper is to present a problem involving the incorporation of environmental aspects into logistics, which provides a comparison between pollution reduction and distance-based approaches.

In green vehicle routing problem (VRP), the aim is to model and solve an optimization problem in order to minimize the fuel consumption which results in reducing energy consumption as well as air pollution. The Gravitational Search Algorithm (GSA) is adapted and used as a powerful heuristic.

Here, it is shown that a set of routes with minimum length is not an optimal solution for FCVRP model since the total distance is not the only effective factor for fuel consumption and vehicle's load plays an important role too. In many cases, a considerable reduction in emissions can be achieved by only an insignificant increase in costs.

Green transportation is a policy toward reducing carbon emissions. This research focussed on routes problem and introduce FCVRP model. GSA is used as a powerful heuristic to obtain high quality routes in a reasonable time. Considering other factors that affecting fuel consumption could make this study more realistic.

When a distribution center receives all the information it needs about the demand from all the retail stores it supplies, a VRP is produced. So the models are valid for use by all goods producers and distributors. The preliminary assessment of the proposed model and method carried out on benchmark problems up to 200 nodes.

Fuel consumption is one of the most influential factors in transportation costs. This paper introduces an innovative decision-making framework to obtain optimum routes in a vehicle routes problem considering air pollution. The results were compared from fuel consumption as well as total travel distance viewpoints.

A variant of Kohonen's algorithm for the self‐organizing map (SOM) is used to solve a continuous location‐routing problem that can be applied to identify potential sites for subsequent selection by a discrete finite set model. The paper aims to show how the algorithm may be customized to fit the problem structure in a way that allows aspects of location and routing to be integrated into the solution procedure.

A set of test instances is used to compare the solutions of the neural network to those obtained by sequential approaches based on a savings procedure.

Compared to the results of the sequential approaches, the neural network yields good results.

Future work may cover the expansion of the neural approach to multi‐depot and multi‐stage problems. Additionally, application of procedures other than the savings procedure should be evaluated with respect to their potential for further enhancing the solution quality of the sequential approaches.

This paper shows that strategic location decisions in practical applications with long‐term customer relationships can be taken using simultaneously generated routing information on an operational level.

The paper provides a new variety of applications for SOM as well as high quality results for the specific type of problem considered.

With the increasing awareness of global warming and the important role of last mile distribution in logistics activities, the purpose of this paper is to build an environmental and effective last mile distribution model considering fuel consumption and greenhouse gas emission, vehicle capacity and two practical delivery service options: home delivery (HD) and pickup site service (PS). This paper calls the problem as the capacitated pollution-routing problem with pickup and delivery (CPRPPD). The goal is to find an optimal route to minimize operational and environmental costs, as well as a set of optimal speeds over each arc, while respecting capacity constraints of vehicles and pickup sites.

To solve this problem, this research proposes a two-phase heuristic algorithm by combining a hybrid ant colony optimization (HACO) in the first stage and a multiple population genetic algorithm in the second stage. First, the HACO is presented to find the minimal route solution and reduce distribution cost based on optimizing the speed over each arc.

To verify the proposed CPRPPD model and algorithm, a real-world instance is conducted. Comparing with the scenario including HD service only, the scenario including both HD and PS option is more economical, which indicates that the CPRPPD model is more efficient. Besides, the results of speed optimization are significantly better than before.

The developed CPRPPD model not only minimizes delivery time and reduces the total emission cost, but also helps logistics enterprises to establish a more complete distribution system and increases customer satisfaction. The model and algorithm of this paper provide optimal support for the actual distribution activities of logistics enterprises in low-carbon environment, and also provide reference for the government to formulate energy-saving and emission reduction policies.

This paper provides a great space for the improvement of carbon emissions in the last mile distribution. The results show that the distribution arrangement including HD and PS services in the last mile adopting speed optimization can significantly reduce the carbon emission. Additionally, an integrated real-world instance is applied in this paper to illustrate the validity of the model and the effectiveness of this method.

The vehicle routing problem (VRP) has been widely investigated during last decades to reduce logistics costs and improve service level. In addition, many researchers have realized the importance of green logistic system design in decreasing environmental pollution and achieving sustainable development.

In this paper, a bi-objective mathematical model is developed for the capacitated electric VRP with time windows and partial recharge. The first objective deals with minimizing the route to reduce the costs related to vehicles, while the second objective minimizes the delay of arrival vehicles to depots based on the soft time window. A hybrid metaheuristic algorithm including non-dominated sorting genetic algorithm (NSGA-II) and teaching-learning-based optimization (TLBO), called NSGA-II-TLBO, is proposed for solving this problem. The Taguchi method is used to adjust the parameters of algorithms. Several numerical instances in different sizes are solved and the performance of the proposed algorithm is compared to NSGA-II and multi-objective simulated annealing (MOSA) as two well-known algorithms based on the five indexes including time, mean ideal distance (MID), diversity, spacing and the Rate of Achievement to two objectives Simultaneously (RAS).

The results demonstrate that the hybrid algorithm outperforms terms of spacing and RAS indexes with p-value <0.04. However, MOSA and NSGA-II algorithms have better performance in terms of central processing unit (CPU) time index. In addition, there is no meaningful difference between the algorithms in terms of MID and diversity indexes. Finally, the impacts of changing the parameters of the model on the results are investigated by performing sensitivity analysis.

In this research, an environment-friendly transportation system is addressed by presenting a bi-objective mathematical model for the routing problem of an electric capacitated vehicle considering the time windows with the possibility of recharging.

The purpose of this paper is to solve the capacitated location routing problem (CLRP), which is an NP-hard problem that involves making strategic decisions as well as tactical and operational decisions, using a hybrid particle swarm optimization (PSO) algorithm.

PSO, which is a population-based metaheuristic, is combined with a variable neighborhood strategy variable neighborhood search to solve the CLRP.

The algorithm is tested on a set of instances available in the literature and gave good quality solutions, results are compared to those obtained by other metaheuristic, evolutionary and PSO algorithms.

Local search is a time consuming phase in hybrid PSO algorithms, a set of neighborhood structures suitable for the solution representation used in the PSO algorithm is proposed in the VNS phase, moves are applied directly to particles, a clear decoding method is adopted to evaluate a particle (solution) and there is no need to re-encode solutions in the form of particles after applying local search.

This research is designed to optimize the business process of a green tea dealer, who is a key supply chain partner of the Sri Lankan tea industry. The most appropriate trips for each vehicle in multiple trip routing systems are identified to minimize the total cost by considering the traveling distance.

The study has followed the concepts in vehicle routing problems and mixed-integer programming mathematical techniques. The model was coded with the Python programming language and was solved with the CPLEX Optimization solver version 12.10. In total, 20 data instances were used from the subjected green tea dealer for the validation of the model.

The result of the numerical experiment showed the ability to access supply over the full capacity of the available fleet. The model achieved optimal traveling distance for all the instances, with the capability of saving 17% of daily transpiration cost as an average.

This study contributes to the three index mixed-integer programing model formulation through in-depth analysis and combination of several extensions of vehicle routing problem.

This study contributes to the three index mixed-integer programming model formulation through in-depth analysis and combination of several extensions of the vehicle routing problem.

The proposed model provides a cost-effective optimal routing plan to the green tea dealer, which satisfies all the practical situations by following the multiple trip vehicle routing problems. Licensee green tea dealer is able to have an optimal fleet size, which is always less than the original fleet size. Elimination of a vehicle from the fleet has the capability of reducing the workforce. Hence, this provides managerial implication for the optimal fleet sizing and route designing.

Developing an optimization model for a tea dealer in Sri Lankan context is important, as this a complex real world case which has a significant importance in export economy of the country and which has not been analyzed or optimized through any previous research effort.