Multi-compartment Vehicle Routing Problem Research Articles

An Exact Approach to the Multi-Compartment Vehicle Routing Problem: The Case of a Fuel Distribution Company

Over the years, the vehicle routing problem has been studied by several authors, creating several extensions, such as the multi-compartment vehicle routing problem. Several studies in the literature have addressed this problem, but few have solved it through exact approaches owing to model convolution. In this way, a mathematical model is proposed for the multi-compartment vehicle routing problem with time windows, in which three types of fuel products are distributed to a set of customers using a limited homogeneous fleet. The model explicitly considers time windows, as well as regulatory rest times for the drivers and time limits for each trip and for working schedules, addressing a real company’s decision support requirements, which is scarce in the literature. The optimal solution determines, for each vehicle, the distribution route and time to carry out the deliveries with the corresponding loading of products to compartments, complemented by the calculation of carbon emissions. The main objective is to minimize the total distance traveled, which corresponds to the sum of the distances traveled by each one of the allocated vehicles. The results allow the assessment of the solution optimization applied to a set of instances for a Portuguese company to evaluate the performance and compare decision support improvements with current baseline company procedures.

An adaptive differential evolution algorithm to solve the multi-compartment vehicle routing problem: A case of cold chain transportation problem

This research paper introduces an adaptive differential evolution algorithm (ADE algorithm) designed to address the multi-compartment vehicle routing problem (MCVRP) for cold chain transportation of a case study of twentyeight customers in northeastern Thailand. The ADE algorithm aims to minimize the total cost, which includes both the expenses for traveling and using the vehicles. In general, this algorithm consists of four steps: (1) The first step is to generate the initial solution. (2) The second step is the mutation process. (3) The third step is the recombination process, and the final step is the selection process. To improve the original DE algorithm, the proposed algorithm increases the number of mutation equations from one to four. Comparing the outcomes of the proposed ADE algorithm with those of LINGO software and the original DE based on the numerical examples In the case of small-sized problems, both the proposed ADE algorithm and other methods produce identical results that align with the global optimal solution. Conversely, for larger-sized problems, it is demonstrated that the proposed ADE algorithm effectively solves the MCVRP in this case. The proposed ADE algorithm is more efficient than Lingo software and the original DE, respectively, in terms of total cost. The proposed ADE algorithm, adapted from the original, proves advantageous for solving MCVRPs with large datasets due to its simplicity and effectiveness. This research contributes to advancing cold chain logistics with a practical solution for optimizing routing in multi-compartment vehicles.

Solving the Multi Compartment Vehicle Routing Problem using a Hybridized Simulated Annealing Algorithm

Solving the Multi Compartment Vehicle Routing Problem using a Hybridized Simulated Annealing Algorithm

Multi-Compartment Vehicle Routing Problem Considering Traffic Congestion under the Mixed Carbon Policy

The use of multi-compartment vehicles (MCVs) in urban logistics distribution is increasing. However, urban traffic congestion causes high carbon emissions in the logistics distribution, resulting in unsustainable development in urban transportation. In addition, the application of the mixed carbon policy has gradually become the first choice for energy conservation and emission reduction in some countries and regions. The transportation industry is a major carbon-emitting industry, which needs to be constrained by carbon emission reduction policies. In this context, the research on the multi-compartment vehicle routing problem (MCVRP) considering traffic congestion under the mixed carbon policy is carried out. Firstly, a mathematical model of MCVRP considering traffic congestion under the mixed carbon policy is constructed. Secondly, a two-stage variable neighborhood threshold acceptance algorithm (VNS-TA) is proposed to solve the above mathematical model. Thirdly, 14 adapted standard examples of the MCVRP are used to verify the effectiveness and optimization ability of the two-stage VNS-TA algorithm. A simulation example of the MCVRP considering traffic congestion under the mixed carbon policy is used to conduct sensitivity analyses for different scenarios. Finally, the following conclusions are drawn: (1) the two-stage VNS-TA algorithm is effective and has strong optimization ability in solving the basic MCVRP, and (2) the two-stage VNS-TA algorithm can solve and optimize the MCVRP considering traffic congestion under the mixed carbon policy, which has the effects of cost saving and energy conservation and emission reduction.

Solving the multi-compartment vehicle routing problem by an augmented Lagrangian relaxation method

In real-world routing applications such as waste collection or fuel distribution, multiple products that cannot be mixed should be jointly collected or delivered. Multi-compartment vehicles are applied with great flexibility in routing and assignment decisions for these real-world applications. This study concentrates on the multi-compartment vehicle routing problem with fixed compartment size and fixed assignment products to compartments. For this problem, we develop two new formulations in the space–time network and state-space–time network. For the state-space–time network formulation, we dualize the task allocation constraints to the objective function and decompose the Lagrangian relaxed problem (LR) into a series of identical routing subproblems. To produce high-quality feasible solutions, the augmented Lagrangian relaxed problem (ALR) with superior convergence and feasibility is further applied to this problem. The ALR is decomposed into many solvable routing subproblems by alternating direction method of multipliers. A time-dependent dynamic programming algorithm is developed to settle the obtained subproblems of the LR and ALR. The subgradient optimization method solves the Lagrangian dual problems. The solution quality can be evaluated by the relative gap between the global lower and upper bounds at each iteration. In numerical experiments, the proposed method produces solutions with good integrality gaps. Based on Lagrangian relaxation and decomposition techniques, this research provides a novel solving scheme for the multi-compartment vehicle routing problem.

Multi-trip multi-compartment vehicle routing problem with backhauls

Multi-trip multi-compartment vehicle routing problem with backhauls

A multi-compartment VRP model for the health care waste transportation problem

Health-care waste (HCW) is a special category of refuse generated when providing health care and can comprise materials with infectious and/or toxic characteristics. The disposal of this waste involves its transport from health-care facilities to treatment centers. This step can be threatening to humans and the environment if not managed with the utmost care. To ensure the safe management of HCW, this article proposes a new model for HCW transportation that separates hazardous from non-hazardous waste along the transportation route. The proposed model is based on the multi-compartment vehicle routing problem, where each type of waste is carried in a dedicated compartment, and the objective is to minimize the total route cost. Considering the NP-hardness of the problem, an adaptive genetic algorithm is proposed based on the results of statistical pre-post testing of the population. The experimental study, conducted on benchmark instances and real data instances, show the efficiency of the proposed approach against state-of-the-art algorithms.

A dynamic approach for the multi-compartment vehicle routing problem in waste management

Urban areas worldwide face a significant environmental challenge which is increasing municipal solid waste rate. Addressing its negative consequences necessitates advancements in waste management systems. Although the previous research focused on the static routing approach in the collection phase, this paper adds a dynamic municipal solid waste collection scheme to optimize vehicle routing, accounting for fluctuations in waste generation and changes in transportation systems. This study employs, for the first time, the application of a discrete choice model (DCM) to streamline the process of re-optimization in dynamic vehicle routing problems (DVRP). At each decision epoch, DCM is applied to determine the likelihood of choosing the next geographical zone to visit bins based on current waste generation levels and traveling costs. Moreover, the multi-compartment vehicles are considered to preserve waste segregation during transportation, thereby increasing operational efficiency and regulatory compliance. Another contribution of this paper is to determine visiting priority for each bin by adjusting the time window based on the threshold waste level. Hence, this paper proposes a framework for sustainable, efficient, and effective waste management practices by integrating the benefits of dynamic and multi-compartment routing. Furthermore, a hybrid Genetic and Particle Swarm Optimization algorithm has been designed to find the best solution for the studied problem as well as some of the latest and most proficient metaheuristic algorithms. Finally, the Best Worst Method is applied to find the best-proposed algorithm to solve the presented problem, indicating that the hybrid algorithm has the highest performance in providing high-quality route plans.

A hybrid iterated local search algorithm for the multi-compartment vehicle routing problem

Multi-compartment vehicle routing problem (MCVRP) is an extension of the classical capacitated vehicle routing problem where products with different characteristics are transported together in one vehicle with multiple compartments. This paper deals with this problem, whose objective is to minimize the total travel distance while satisfying the capacity and maximum route length constraints. We proposed a hybrid iterated local search metaheuristic (HILS) algorithm to solve it. In the framework of iterated local search, the current solution was improved iteratively by five neighborhood operators. For every obtained neighborhood solution after the local search procedure, a large neighborhood search-based perturbation method was executed to explore larger solution space and get a better neighborhood solution to take part in the next iteration. In addition, the worse solutions found by the algorithm were accepted by the nondeterministic simulated annealing-based acceptance rule to keep the diversification of solutions. Computation experiments were conducted on 28 benchmark instances and the experimental results demonstrate that our presented algorithm finds 17 new best solutions, which significantly outperforms the existing state-of-the-art MCVRP methods.

Solving a heterogeneous fleet multi-compartment vehicle routing problem:a case study

Vehicle Routing Problem (VRP) is a complex optimisation problem in the field of supply chain management, especially in the Oil & Gas sector. Due to the rising cost of fuel, effective planning of transportation routes has become a crucial success factor for distribution companies, increasing operational efficiency as well as the corresponding service level. In this paper, we present an optimisation model to solve a heterogeneous fleet multi-compartment vehicle routing problem (MCVRP), a variant of the conventional vehicle routing problem (VRP). Real data are obtained from a medium size oil distribution company, operating in Greece and incorporates 19 petrol stations served from a central oil depot using a fleet of various multi-compartment tanker trucks. The main objective of this research is to design an optimum set of routes minimising distance and truck operating costs. The MCVRP with a heterogeneous fleet of vehicles is modelled as a Mixed-Integer Linear Programming (MILP) problem and the proposed solution determines the number of assigned vehicles, the planning of daily routes and the allocation of different fuels to vehicles compartments, while satisfying customer demand following specific requirements, as detailed in the Carriage of Dangerous Goods (ADR) Regulations.

Dynamic Multi-Compartment Vehicle Routing Problem for Smart Waste Collection

The rapid increase in urbanization results in an increase in the volume of municipal solid waste produced every day, causing overflow of the garbage cans and thus distorting the city’s appearance; for this and environmental reasons, smart cities involve the use of modern technologies for intelligent and efficient waste management. Smart bins in urban environments contain sensors that measure the status of containers in real-time and trigger wireless alarms if the container reaches a predetermined threshold, and then communicate the information to the operations center, which then sends vehicles to collect the waste from the selected stations in order to collect a significant waste amount and reduce transportation costs. In this article, we will address the issue of the Dynamic Multi-Compartmental Vehicle Routing Problem (DM-CVRP) for selective and intelligent waste collection. This problem is summarized as a linear mathematical programming model to define optimal dynamic routes to minimize the total cost, which are the transportation costs and the penalty costs caused by exceeding the bin capacity. The hybridized genetic algorithm (GA) is proposed to solve this problem, and the effectiveness of the proposed approach is verified by extensive numerical experiments on instances given by Valorsul, with some modifications to adapt these data to our problem. Then we were able to ensure the effectiveness of our approach based on the results in the static and dynamic cases, which are very encouraging.

Metaheuristic algorithm for the location, routing and packing problem in the collection of recyclable waste

The increasing accumulation of solid waste worldwide has made it necessary to look for alternatives that improve the operation of recyclable waste collection systems to make waste treatment more profitable and eco-friendlier. This paper introduces a new variant of the multi-compartment vehicle routing problem (MCVRP) that considers the rearrangement or relocation of collection points and packing the demand. This problem is called the location packing multi-compartment vehicle routing problem (LPMCVRP) and is developed for a waste collection system using vehicles with flexible compartments. A mathematical formulation of the problem is proposed. A two-phase metaheuristic algorithm based on a tabu search without packing considerations and a variant that integrates a tabu search and a greedy randomized adaptive search procedure (GRASP) scheme with packing constraints have been proposed. A set of instances adapted from the literature is generated to validate the proposed solution strategy. The results obtained show the efficiency of the proposed solution scheme for optimizing collection systems.

An efficient approach for the petrol station replenishment problem: an Algerian case study

In a logistic process, the goods distribution is an important task. It is also a critical activity that needs to be optimised according to company policy. The petrol station replenishment problem (PSRP) is one of the transportation problems concerned with replenishing a set of fuel stations with the different petroleum products. This problem presents a particular case of the multi-compartment vehicle routing problem (MC-VPR). In this paper, a new bi-objective approach is proposed in order to treat the PSRP. A novel MILP model is proposed based on a real life case study (the Algerian company of fuel distribution NAFTAL). Two objectives are considered: gain maximisation and carbon emissions minimisation. The economic objective is optimised independently of the environmental one, and then they are joined by adapting a multi-objective method 'LP-metric'. Finally, computational results are presented in order to show the efficiency of our green approach for a sustainable transportation system.

Heuristic algorithms for solving the multi-compartment vehicle routing problem with time windows and heterogeneous fleet

Heuristic algorithms for solving the multi-compartment vehicle routing problem with time windows and heterogeneous fleet

WITHDRAWN: An improved genetic algorithm for multi-compartment vehicle selection with time window

The main problem to be solved in this article is how to choose a mixed fleet of single and multi-compartment vehicles when delivering multiple orders, and when considering the time-dependence, time window, and deterioration loss, to minimize the total distribution cost of the distribution center, namely the time dependence of multi-compartment vehicle selection problem TDMCVRPTWs. By establishing the heuristic algorithm pre self-organized clustering improved genetic algorithm (SOMGA), and based on the framework of SOMGA algorithm, We build a pre self-organizing clustering improved genetic algorithm of vehicle type selection (SOMGAs), SOMGAs to solve the hybrid fleet that can make the distribution cost the lowest. In order to verify the rationality of SOMGA algorithm, this paper will check the calculation through Solomon’s 25, 50 and 100 customer sets with time windows, and compare the results with HPSO improved particle swarm optimization algorithm. In addition, the optimal values of ACS, HAC, HVANS and HABC are compared. Through analysis, SOMGA algorithm has strong algorithm advantages. In order to verify the feasibility of the pre-self-organization cluster genetic algorithm of vehicle type selection (SOMGAs) based on the framework of SOMGA algorithm, through the Solomon 50 customer, 100 customer set, the hybrid fleet can significantly reduce the distribution cost. And in the process of vehicle class selection, the vehicle path of each vehicle is optimized. Finally, it is concluded that SOMGAs algorithm can solve a reasonable mixed fleet in 80% of cases, reducing the total distribution cost by 0% to 24%. • A new algorithm for solving the multi-compartment vehicle routing problem is proposed. • It provides a new method for studying hybrid fleet. • Various traffic environmental factors and food environmental factors are considered.

A three-dimensional ant colony optimization algorithm for multi-compartment vehicle routing problem considering carbon emissions

A three-dimensional ant colony optimization algorithm (TDACO) is proposed to solve the multi-compartment vehicle routing problem (MCVRP) arising in many industries, such as petrol station replenishment, cold chain logistics, and waste collection. The objective of this problem to be minimized is the total transportation cost including the consideration of carbon emissions (TC_CE). In TDACO, a new three-dimensional pheromone concentration matrix is first presented to learn and accumulate the valuable information from excellent individuals or ants. Then, to make the algorithm have high-quality search in the initial stage, five heuristic rules are designed to initialize the pheromone concentration matrix and construct the initial population or colony. In addition, the vehicle capacity rate and carbon emissions are brought into the state transition rule to reasonably guide the global search towards the promising solutions or regions. Moreover, an adaptive local search with the speed-up search strategy and the first move strategy is devised to perform effective exploitation from the promising regions. Finally, comparative experiments on benchmark problem instances with different scales are conducted, and the superior performance of the proposed TDACO is verified.

Multi-compartment vehicle routing optimization based on a hybrid Genetic Algorithm

To solve the problem of efficient distribution of convenience store chains, this paper creates a multi-compartment vehicle routing problem model with time- windows (MCVRP-TW) to meet the goal of minimizing the total distribution cost. The solution is based on a hybrid genetic algorithm, which using the “destruction” and “repair” operators of the large-scale neighborhood search algorithm and the Metropolis criterion of simulated annealing for local search operations. The results show that the proposed multi-compartment vehicle routing model with time windows and the hybrid algorithm can meet the requirement of practical route design and reduce the total distribution cost.

Variable Neighborhood Descent for Multi-Compartment and Multi-Objective Vehicle Routing Problem in Refined Product Distribution

Refined product distribution is an application of the Multi-compartment Vehicle Routing Problem (MCVRP), which simultaneously considers the vehicle routing, the assignment of heterogonous vehicles and loading policies of multi-compartment. First, we develop an optimization model with the objective of delivering on-time and minimizing transportation cost. Then we propose a Multi-objective Variable Neighborhood Descent Algorithm (MOVND), where the [Formula: see text]-constraint method transforms the original problem into a series of sub-problems of single objective with constraints. Finally, the efficiency of the proposed algorithm is verified by conducting a large number of small and large instances. Mainly including (i) compared with the classical NSGA-2 algorithm for multi-objective VRP, MOVND provides better performance in terms of convergence, spread and distribution; (ii) the multi-compartment vehicles are able to carry a variety of products simultaneously, which can improve the effective utilization of vehicle space and meet the needs of different customers in a single transportation. In addition, heterogonous vehicles that take full advantage of the characteristics of different vehicles are superior to homogeneous ones in terms of operating cost in the practice of the refined product distribution.

Exact algorithms for the multi-compartment vehicle routing problem with flexible compartment sizes

The multi-compartment vehicle routing problem with flexible compartment sizes is a variant of the classical vehicle routing problem in which customers demand different product types and the vehicle capacity can be separated into different compartments each dedicated to a specific product type. The size of each compartment is not fixed beforehand but the number of compartments is limited. We consider two variants for dividing the vehicle capacity: On the one hand the vehicle capacity can be discretely divided into compartments and on the other hand compartment sizes can be divided continuously. The objective is to minimize the total distance of all vehicle routes such that all customer demands are met and vehicle capacities are respected. Modifying a branch-and-cut algorithm based on a three-index formulation for the discrete problem variant from the literature, we introduce an exact solution approach that is tailored to the continuous problem variant. Moreover, we propose two other exact solution approaches, namely a branch-and-cut algorithm based on a two-index formulation and a branch-price-and-cut algorithm based on a route-indexed formulation, that can tackle both problem variants with small adaptions and can be combined into an effective two-stage approach. Extensive computational tests have been conducted to compare the different algorithms. For the continuous variant, we can solve instances with up to 50 customers to optimality and for the discrete variant, several previously open instances can now be solved to proven optimality. Moreover, we analyze the cost savings of using continuously flexible compartment sizes instead of discretely flexible compartment sizes.

Çok Bölmeli Araç Rotalama Problemi için Bir Melez Genetik Algoritma

In this study, a Multi-Compartment Vehicle Routing Problem (MC-VRP) was studied. In daily life, markets, companies and organizations need to load their certain products into different compartments in vehicles during the delivery or collecting of these products. Some of the products need to be carried in cold temperature while others in ambient temperature. Some wastes, chemical products or fuel types need to be transported in the same vehicle separately. Therefore, the transportation fleet must have vehicles with separate compartments and the different products must be either delivered or collected in related compartments of these vehicles. The MC-VRP studied in this paper was taken into consideration with three scenarios of vehicles with one-, two-, or three-compartments. As the solution method, a hybrid Genetic Algorithm (GA) was used and applied on a well-known problem instance set in Vehicle Routing Problem (VRP) literature. As a result, new benchmark results were obtained for the version of MC-VRP in this study and these results were evaluated.