Environmental Issues in Vehicle Routing Problems

Public consciousness on environmental sustainability and industry impact on environment has been increasing for the last few decades. As a result, more and more companies are taking pollution factor into account when planning their logistic activities. Pollution Routing Problem (PRP) is an extension of the classical Vehicle Routing Problem with Time Windows by determining a set of optimal routes and vehicle speed on each route segment for a fleet of vehicles serving a set of customers within specific time windows. In practice, many vehicle routing problems are addressed by a fleet of heterogeneous vehicles with different capacities and travel costs. Emission levels vary by vehicle type due to differences in curb weight and capacity. Therefore, Heterogeneous Fleet Pollution Routing Problem (HFPRP) has been proposed as an extension of Pollution Routing Problem (PRP). Its goal is to minimize the total costs of fuel, greenhouse gas (GHG) emissions, and vehicle variable cost put together in a more comprehensive objective function. This research developed a mathematical model and proposed a Simulated Annealing (SA) heuristic for HFPRP. The performance of the proposed SA heuristic was first verified using benchmark data of the Pollution Routing Problem. The result shows that SA performs better for 7 instances than previous method. SA was then used to solve HFPRP and the results were compared to those obtained by CPLEX. We found that the consideration of a heterogeneous fleet reduces total costs for all instances.

The simulated trading heuristic for solving vehicle routing problems

Vehicle routing problem with fuzzy time windows

In response to the rapid increase in e-commerce, distribution services, and smart technology, businesses need to solve the vehicle routing problem (VRP) and its variants to improve service quality and cut operating costs. In this paper, we introduce the VRP with time windows and time costs (VRPTWTC), which is a new but practical VRP variant that adds time windows of customers and time costs of service constraints into the optimization of the traditional VRP problem. Furthermore, we propose a masking algorithm and combine it into our proposed end-to-end and data-driven deep reinforcement learning framework to solve the VRPTWTC. Experimental results show a shorter tour length and reasonable processing time than benchmarks both on a simulated dataset and a real enterprise-level dataset. Besides, violation of time window and total time cost, which is one of the most important criterions in our problem formulation, never occurred in our experiment under the real road connection conditions when using a real map API. To the best of our knowledge, our framework is the first to effectively and efficiently solve a VRP variant problem with practical time windows and time costs constraints with a real map API to calculate routes of VRP considering real road connection conditions on an enterprise-level dataset.

The Vehicle Routing Problem (VRP) is a well-known combinatorial optimization problem where a number of customers must be served with a fleet of vehicles. The classical variation of the VRP is the Capacicated Vehicle Routing Problem (CVRP) with the additional constraint that each vehicle must have uniform capacity. Many Decision Support Systems (DSS) have been implemented to solve real life problems of the VRP and its’ variants, but they do not allow multiple decision makers to explore several scenarios of a given problem simultaneously and collaborate with each other in order to find the best possible solution. In this paper, we extend our previous work [35] and incorporate in our spatial DSS four variants of the CVRP: (i) Distance Constrained Vehicle Routing Problem (DVRP), (ii) Vehicle Routing Problem with Time Windows (VRPTW), (iii) Vehicle Routing Problem with Backhauls (VRPB), and (iv) Vehicle Routing Problem With Pickup and Delivery (VRPPD). This extension allows decision makers to solve specific routing problems according to their needs. The proposed collaborative spatial DSS allows two decision makers to collaborate with each other in order to find the best possible solution through a tangible interface. The locations are added through interactive Google Maps and other parameters through user-friendly forms that can be manipulated via tangible interfaces. The proposed DSS has been implemented using Java, TUIO protocol, jsprit, and Google Maps.

A vehicle routing problem involves finding a set of optimal route for a fleet of capacitated vehicles which are available at a location to service the demands of a set of customers. In its simplest form, a customer is required to be visited once and the capacity of a vehicle must not be exceeded. In this paper, a review of four common and applicable variants of the vehicle routing problem, namely, capacitated vehicle routing problem, vehicle routing problem with time windows, periodic vehicle routing problem and the dynamic vehicle routing problem, are considered based on formulation techniques, methods of solution and areas of application. A summary table is presented for each variant to emphasis some key features that represent direction of current research.

A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints

This paper addresses the issue of ship routing design for collecting and transporting the oily liquid waste from a number of ports to a waste treatment center. The aim is simultaneously to construct a set of ship routes and to determine the number and the types of ships in a fleet at the minimum total cost. The problem is considered as a vehicle routing problem with heterogeneous fleet of vehicles and multiple trips (VRPHMT). The VRPHMT is a combination of two variants of the classical vehicle routing problem (VRP) by including two additional features. The first is the heterogeneous fleet of vehicles where number and types of vehicles have to be determined, and the second is multiple trips where vehicles may perform more than one route or trip as long as the total duration of each vehicles does not exceed the planning period.

In today's competitive market, manufacturers and service providers are continuously seeking ways to reduce costs and save time to gain a competitive edge. One of the most significant challenges they face is the vehicle routing problem (VRP), which is crucial due to its direct impact on the delivery time of services or products. Efficient vehicle routing not only enhances delivery performance but also optimizes the overall network, resulting in reduced operational costs. This study focuses on evaluating the VRP specifically for trucks while incorporating sustainability indicators into the analysis. The key sustainability indicators considered include social, economic, and environmental aspects. By integrating these indicators, the study aims to address multiple objectives simultaneously: reducing delivery time, minimizing costs, and mitigating the environmental impact of vehicle operations.The primary objective of this research is to minimize overall costs, fuel consumption, and route complexity associated with truck deliveries. Given the growing concern over environmental issues, there is a strong emphasis on improving methods to reduce greenhouse gas (GHG) emissions and streamline logistics processes. The research addresses these concerns by proposing a model that not only aims to enhance operational efficiency but also contributes to environmental protection and social responsibility.To achieve these objectives, the study employs advanced optimization techniques, specifically the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO). These methods are utilized to solve the VRP while balancing the trade-offs between various objectives, such as cost reduction, fuel efficiency, and route optimization.The results of the study indicate that the proposed model successfully improves aspects of environmental protection and social responsibility while simultaneously addressing economic concerns. The integration of sustainability indicators into the vehicle routing problem provides a comprehensive approach to optimizing logistics operations, highlighting the importance of considering environmental and social factors alongside economic performance.Overall, this research contributes to the field by offering a refined model for tackling the VRP, with a focus on sustainability. The findings underscore the potential for optimization algorithms to drive improvements in both operational efficiency and environmental stewardship, ultimately supporting more sustainable and socially responsible practices in the transportation and logistics industry.

This paper proposes an efficient algorithm, with a reduced number of parameters, for solving the two‐dimensional loading‐capacitated vehicle routing problem (2L‐CVRP). This problem combines two of the most important issues in logistics, that is, vehicle routing and packing problems. Our approach contemplates unrestricted loading including the possibility of applying 90° rotations to each rectangular‐shaped item while loading it into the vehicle, which is a realistic assumption seldom considered in the existing literature. The algorithm uses a multistart approach that is designed to avoid local minima and also to make the algorithm an easily parallelizable one. At each restart, a biased randomization of a savings‐based routing algorithm is combined with an enhanced version of a classical packing heuristic to produce feasible good solutions for the 2L‐CVRP. The proposed algorithm has been compared with the classical benchmarks for two different 2L‐CVRP variants, that is, with and without item rotations. Experimental results show that our approach outperforms several best‐known solutions from previous work, both in terms of quality and the computational time needed to obtain them.

This paper presents a novel bi-objective multi-product capacitated vehicle routing problem with uncertainty in demand of retailers and volume of products (UCVRP) and heterogeneous vehicle fleets. The first of two conflict fuzzy objective functions is to minimize the cost of the used vehicles, fuel consumption for full loaded vehicles and shortage of products. The second objective is to minimize the shortage of products for all retailers. In order to get closer to a real-world situation, the uncertainty in the demand of retailers is applied using fuzzy numbers. Additionally, the volume of products is applied using robust parameters, because the possible value of this parameter is not distinct and belongs to a bounded uncertainty set. The fuzzy-robust counterpart model may be larger than the deterministic form or the uncertain model with one approach and it has with further complexity; however, it provides a better efficient solution for this problem. The proposed fuzzy approach is used to solve the bi-objective mixed-integer linear problem to find the most preferred solution. Moreover, it is impossible to improve one of the objective functions without considering deterioration in the other objective functions. In order to show the conflict between two objective functions in an excellent fashion, a Pareto-optimal solution with the e-constraint method is obtained. Some numerical test problems are used to demonstrate the efficiency and validity of the presented model.

The field of grain logistics transport vehicle route has seen the development of a variety of mathematical techniques, and the practical application of these techniques has depended on the use of spatial information, such as regional allocation information of road network. Vehicle Routing Problem (VRP) is regarded as the key of grain logistics distribution. In this paper, firstly, focus on the grain logistics VRP with time windows, then VRP model is successful constructed. In order to reduce the cost of grain logistics distribution, to combine the VRP model to geographic information system (GIS) by analyzing the VRP model. GIS takes into account for grain logistics, and the Particle Swarm Optimization (PSO) is used for the identification of optimal routes. And the optimal route for grain distribution is urgent since it has been calculated that, of the total cost for transportation. It improves the efficiency of grain logistics distribution and gets a better effect.

The Capacitated Vehicle Routing Problem with Time-Dependent Demands (CVRPTD) is a significant optimization challenge in the logistics and transportation domain, characterized by dynamic customer demands, strict time windows, and heterogeneous vehicle fleets. This study focuses on urban parcel delivery operations as the primary object of research. The problem addressed involves the inefficiency of conventional vehicle routing strategies in adapting to time-varying customer demands and operational constraints, which often lead to increased costs and service delays. This study aims to minimize total operational costs while ensuring compliance with capacity constraints, service continuity, and demand fluctuations. A comprehensive mathematical model is developed based on a fully connected, directed acyclic graph G=(V, A), incorporating decision variables that represent vehicle routing sequences, timing, and vehicle type assignments. This study addresses the Capacitated Vehicle Routing Problem with Time-Dependent Demands (CVRPTD) in urban parcel delivery, where traditional routing methods struggle with dynamic demands and operational constraints. A mathematical model using a directed acyclic graph is developed, optimized via a gradient-based method with Hessian approximation, LU decomposition, and quasi-Newton techniques. Experiments on datasets with up to 200 customers and 20 vehicles with reductions ranging from 1.79% to 12.75%. The most significant improvement was observed in Sidorame Timur, where the optimization distance decreased by 12.75%, indicating high accuracy in route optimization. For the SCP, the proposed algorithm achieved a 6.46% improvement in solution quality over traditional greedy algorithms

The vehicle routing problem (VRP) is a crucial group of transportation problems, and traditional capacitated VRP (CVRP) directly handles external logistics with a homogeneous vehicle fleet. This paper examines the CVRP from an in-plant logistic view with a heterogeneous fleet in an automotive factory. The homogeneous and heterogeneous vehicle fleets are compared to address the factory's actual in-plant logistics issues. Firstly, simulated annealing (SA), tabu search (TS) algorithms and mathematical modeling were utilized. Then, a hybrid approach was proposed, and all suggested meta-heuristic algorithms were evaluated for homogeneous and heterogeneous vehicle fleets. According to the results, the reduction rates using CVRP with the heterogeneous fleet are 17% and 36% for fleet area and distribution costs, respectively. Also, to examine the effect of the hybrid algorithm parameters on the result, traveling distance was calculated for different scenarios, and multiple regression analyses were applied. According to the multiple regression analysis, the hybrid algorithm's most affected parameter was the cooling coefficient.

A tabu search heuristic for the vehicle routing problem with time windows and split deliveries