Multiple Vehicle Routing Problem Research Articles

Nested benders decomposition for a deterministic biomass feedstock logistics problem

AbstractIn this paper, we address a biomass feedstock logistics problem to supply biomass from production fields to satellite storage locations (SSLs) and from there to bioenergy plants (BePs) and then to a biorefinery. It entails a new problem feature of routing load-out equipment sets among the SSLs to perform loading/unloading of biomass and/or its pre-processing operations. The ownership of the loading equipment is a very capital-intensive link of the ethanol production supply chain, which when loaded onto trucks and routed along the logistics chain significantly brings down the ethanol production costs. This will make ethanol a cost-competitive alternative to fossil fuels, lead to sustainable use of fossil fuels and add to the overall relevance of the bioenergy sector. In this regard, the objective of our problem is to minimize the total cost incurred due to the ownership of equipment sets, fixed setups, and land rental cost, as well as the cost of transporting biomass from the fields to the BePs and biocrude oil from the BePs to the refinery. A mixed-integer mathematical model of the problem is presented, and a nested Benders decomposition-based solution approach is developed which involves decomposing this large problem into three stages. Stage 1 deals with the selection of fields, BePs, and SSLs, and assignment of fields to the SSLs. The remaining model consists of multiple Capacitated Vehicle Routing Problems (CVRPs) that are separable over individual BePs. For each BeP, the CVRP is further decomposed into Stage 2 and Stage 3 sub-problems where the Stage 2 problem is an allocation problem that assigns SSLs to tours associated to each BeP, and the Stage 3 problem is a variant of Traveling Salesman Problem (TSP) that determines the sequence in which equipment is routed over the predesignated set of SSLs for each tour. These sub-problems are integer programs rather than linear programs. First novelty of our proposed approach is to effectively handle the integrality of variables arising due to the consideration of the routing of load-out equipment. Second is solution methodology and in the use of proposed multi-cut version of optimality cuts that capture the solution value at an integer solution for the sub-problems. These cuts aid in faster convergence and are shown to be stronger than those proposed in the literature. The applicability of the proposed methodology is demonstrated by applying it to a real-life problem that utilizes available GIS data for the catchment area of regions around Gretna and Bedford in Virginia. We then solved a set of varying problem size instances using the state-of-the-art CPLEX® Branch-and-Bound and Benders Strategy methods. The CPLEX® algorithms struggled to solve instances even 10 times smaller than the real-life problem size instances; with MIP optimality gaps ranging from 5.85% to 82.79% in the allowed time limit of 10,000 s. On the other hand, our proposed nested Benders decomposition algorithm was able to achieve faster convergence and provided optimal solutions for all the considered problem instances with an average CPU run-time of around 3,700 s. This validates the efficacy and superiority of our solution approach. Lastly, we summarize our work and point out some interesting potential future research opportunities.

Reinforcement Learning for Solving Multiple Vehicle Routing Problem with Time Window

Vehicle routing problem with time window (VRPTW) is of great importance for a wide spectrum of services and real-life applications, such as online take-out and car-hailing platforms. A promising method should generate high-qualified solutions within limited inference time, and there are three major challenges: (a) directly optimizing the goal with several practical constraints; (b) efficiently handling individual time-window limits; and (c) modeling the cooperation among the vehicle fleet. In this article, we present an end-to-end reinforcement learning framework to solve VRPTW. First, we propose an agent model that encodes constraints into features as the input and conducts harsh policy on the output when generating deterministic results. Second, we design a time penalty augmented reward to model the time-window limits during gradient propagation. Third, we design a task handler to enable the cooperation among different vehicles. We perform extensive experiments on two real-world datasets and one public benchmark dataset. Results demonstrate that our solution improves the performance by up to 11.7% compared to other RL baselines and could generate solutions for instances within seconds, while existing heuristic baselines take for minutes as well as maintain the quality of solutions. Moreover, our solution is thoroughly analyzed with meaningful implications due to the real-time response ability.

Discovering Lin-Kernighan-Helsgaun heuristic for routing optimization using self-supervised reinforcement learning

Vehicle routing optimization is a crucial responsibility of transportation service providers, which can significantly reduce operating expenses and improve client satisfaction. Learning to tackle routing optimization problems automatically can be the next significant step forward in optimization technology. Despite recent advancements in automatically learned heuristics for routing optimization problems, state-of-the-art traditional methods such as Lin-Kernighan-Helsgaun (LKH) still outperform machine learning-based approaches. To narrow this gap, we propose a novel technique called self-supervised reinforcement learning (SSRL), which combines self-supervised learning with the LKH heuristic. We provide a node decoder and an edge decoder corresponding to reinforcement learning and self-supervised learning for learning node penalties and edge scores, respectively. The self-supervised part with cross-entropy loss offers strong gradient signals for parameter updates. At the same time, the reinforcement learning component functions as a regularizer to drive the supervised part, which focuses on particular rewards. SSRL learns and replicates all of the LKH’s significant components, improving the original LKH’s generalization and performance. Through experiments on multiple vehicle routing problems, SSRL has demonstrated superior accuracy and efficiency compared to existing methods. Our results provide empirical evidence of SSRL’s effectiveness and potential as a promising solution for optimizing complex routing problems.

Program untuk permasalahan multiple trip vehicle routing problem (MTVRP) menggunakan algoritma memetic pada proses pendistribusian

In everyday life almost all problems require the help of mathematics, one of them on the transportation or on the distribution prosess. Multiple Trip Vehicle Routing Problem (MTVRP) is one of the problems related to the transportation or distribution prosess. Multiple Trip Vehicle Routing Problem (MTVRP) is defined as the problem of the Vehicle Routing Problem (VRP) with the expansion and the addition of multiple trips on the each vehicle when it distributes goods and the time window of customer service. One algorithm to solve the Multiple Trip Vehicle Routing Problem (MTVRP) is memetic algorithms. Memetic algorithm is a combination of genetic algorithm and local search procedures that intensify the search. Memetic algorithms procedures are: initialization process, evaluation process, selection, crossover process, mutation process, repair process, local search, vehicle allocation, and the best route is formed. To facilitate the search for the solution of the Multiple Trip Vehicle Routing Problem (MTVRP) especially at the time had to submit to many customers, memetic algorithms implemented in the language programming Borland Delphi. By using an program application be made, produced together with the results obtained manually route 0 – 1 – 3 – 4 – 0 – 5 – 2 – 0 with a travel time "1.1675" hours and uses a vehicle. This program is designed applications up to 50 points in the Multiple Trip Vehicle Routing Problem (MTVRP) using memetic algorithms, which is already in trials with 11 points, 22 points, and 50 points in attachment. So that the application program can be used to solve the Multiple Trip Vehicle Routing Problem (MTVRP) using memetic algorithms on the transportation or on the distribution prosess.

Heuristics for Multi-Vehicle Routing Problem Considering Human-Robot Interactions

Autonomous mobile robots (AMRs) are being used extensively in civilian and military applications for applications such as underground mining, nuclear plant operations, planetary exploration, intelligence, surveillance and reconnaissance (ISR) missions and manned-unmanned teaming. We consider a multi-objective, multiple-vehicle routing problem in which teams of manned ground vehicles (MGVs) and AMRs are deployed respectively in a leader-follower framework to execute missions with differing requirements for MGVs and AMRs while considering human-robot interactions (HRI). HRI studies highlight the costs of managing a team of follower AMRs by a leader MGV. This paper aims to compute feasible visit sequences, replenishments, team compositions and number of MGV-AMR teams deployed such that the requirements for MGVs and AMRs for the missions are met and the routing, replenishment, HRI and team deployment costs are at minimum. The problem is first modeled as a a mixed-integer linear program (MILP) that can be solved to optimality by off-the-shelf commercial solvers for small-sized instances. For larger instances, a variable neighborhood search algorithm is offered to compute near optimal solutions and address the challenges that arise when solving the combinatorial multi-objective routing optimization problem. Finally, computational experiments that corroborate the effectiveness of the proposed algorithms are presented.

An optimization model for vehicle routing problem in last-mile delivery

Due to rapid urbanization, timely delivery using vehicle routing is the most pressing issue for E-commerce logistics and distribution. In this study, we articulate multiple vehicle routing problems with a maximum capacity constraint and no time constraint. A brief literature review is conducted to identify the widely used optimization models for perishable goods delivery in the last mile. We have implemented and compared optimization algorithms such as Intra-Route Local Search, Inter-Route Local Search, and Tabu Search that provide a suboptimal solution to the greedy solution of this NP-hard problem. We compared the solution provided by these algorithms with the optimal solution that can be obtained in exponential time using processing time and precision. The results demonstrate that Tabu search outperforms other techniques for larger instance sizes, but for smaller instance sizes, Local search can produce results that are comparable to TABU search in a significantly shorter amount of time. In addition, the impact of instance size on the performance of the aforementioned algorithms is evaluated. The real-life evaluation is done to understand the use cases of this problem for an e-commerce company that will repeatedly face this challenge during warehouse storage management, last-mile delivery planning, and execution. A comprehensive performance comparison of various algorithms is presented to optimize last-mile delivery for future cases in order to reduce the overall carbon footprint and achieve profitability through the use of sustainable modes of distribution.

Modified Ant Colony Optimization with Route Elimination and Pheromone Reset for Multiple Pickup and Multiple Delivery Vehicle Routing Problem with Time Window

The vehicle routing problem (VRP) has many applications in goods distribution and goods transportation. Today, many companies have requirements for VRP with multiple pickup and multiple delivery within due time. This problem is called multiple pickup and multiple delivery vehicle routing problem with time window (PDPTW). PDPTW has many constraints and ant colony optimization (ACO) has been used to solve it although ACO creates too many infeasible routes. Moreover, it often gets trapped in local optimum. To solve these problems, this paper proposed an improved ACO by using the route elimination technique and the pheromone reset technique. The ACO with route elimination technique, it has proven to solve the PDPTW problem with increased performance. The proposed technique was tested on datasets from the Li & Lim’s PDPTW benchmark problems and provided more satisfactory results compared to other ACO techniques.

Co-Simulation of Multiple Vehicle Routing Problem Models

Complex systems are often designed in a decentralized and open way so that they can operate on heterogeneous entities that communicate with each other. Numerous studies consider the process of components simulation in a complex system as a proven approach to realistically predict the behavior of a complex system or to effectively manage its complexity. The simulation of different complex system components can be coupled via co-simulation to reproduce the behavior emerging from their interaction. On the other hand, multi-agent simulations have been largely implemented in complex system modeling and simulation. Each multi-agent simulator’s role is to solve one of the VRP objectives. These simulators interact within a co-simulation platform called MECSYCO, to ensure the integration of the various proposed VRP models. This paper presents the Vehicle Routing Problem (VRP) simulation results in several aspects, where the main goal is to satisfy several client demands. The experiments show the performance of the proposed VRP multi-model and carry out its improvement in terms of computational complexity.

Optimizing the multiple trip vehicle routing plan for a licensee green tea dealer in Sri Lanka

PurposeThis 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.Design/methodology/approachThe 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.FindingsThe 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.Research limitations/implicationsThis study contributes to the three index mixed-integer programing model formulation through in-depth analysis and combination of several extensions of vehicle routing problem.Practical implicationsThis 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.Social implicationsThe 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.Originality/valueDeveloping 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.

STUDI ALGORITMA IGVNS, ALGORITMA GVNS, DAN ALGORITMA ABC PADA MULTIPLE TRIP VEHICLE ROUTING PROBLEM (MTVRP)

The Multiple Trip Vehicle Routing Problem (MTVRP) is one of the VRP variants with vehicle capacity constraints, and the limited number of vehicles allows each vehicle to distribute more than one route so as to minimize the number of vehicles used. The algorithm used in this study is the Improved General Variable Neighborhood Search (IGVNS) algorithm. The IGVNS algorithm is a hybrid between the GVNS algorithm and the VNS algorithm. The calculation results of the IGVNS algorithm will be compared with the GVNS algorithm and the ABC algorithm. The main stages of the IGVNS and GVNS algorithms are initial solution formation, perturbation, and solution improvement. The main stages of the ABC algorithm are initialization, solution improvement and optimization. Based on manual calculations using 8 points, the ABC algorithm produces a distance of 86 km and a service time of 1.47 hours, the GVNS algorithm produces a distance of 80 km and a service time of 1.37 hours, the IGVNS algorithm produces a distance of 79 km and service time is 1.35 hours. Based on one example of the ABC algorithm, the calculation solution using the IGVNS algorithm shows more optimal results. Based on the results of parameter testing, the v max parameter affects the calculation results, that is the greater the v max value, the more optimal the resulting solution. While the a max parameter does not affect the calculation results because it shows constant results in two successive iterations carried out.

Ant Colony Optimization for Multiple Pickup and Multiple Delivery Vehicle Routing Problem with Time Window and Heterogeneous Fleets

This study focuses on solving the vehicle routing problem (VRP) of E-logistics service providers. In our problem, each vehicle must visit some pick up nodes first, for instance, warehouses to pick up the orders then makes deliveries for customers in the list. Each pickup node has its own list of more than one customers requiring delivery. The objective is to minimize the total travelling cost while real-world application constraints, such as heterogeneous vehicles, capacity limits, time window, driver working duration, etc. are still considered. This research firstly proposes a mathematical model for this multiple pickup and multiple delivery vehicle routing problem with time window and heterogeneous fleets (MPMDVRPTWHF). In the next step, the ant colony optimization algorithm is studied to solve the problem in the large-scale.

Planejamento de entregas em áreas urbanas considerando recarregamento intermediário, veículos com múltiplos compartimentos e restrição de acesso

Face ao aumento da demanda por transporte de mercadorias por comércios e residências nos últimos anos e, considerando as restrições de entrada de caminhões de grande porte impostas pelas cidades, faz-se necessário planejar as entregas de maneira diferente. Assim, esse artigo propõe o planejamento da entrega de mercadorias considerando recarregamento intermediário na rota, veículos com múltiplos compartimentos, alocação independente das caixas, período de atendimento e restrições de acesso nos clientes. Para planejar as entregas em áreas urbanas, é proposta uma nova classe de problema denominada Site Dependent Multiple Compartment Vehicle Routing Problem with Intermediate Replenishment Facilities and Time Windows com objetivo de minimizar o custo total do transporte. Foi analisado o problema de uma empresa que está em implantação na cidade de Vitória, ES. Utilizou-se o CPLEX 12.8 para resolver o modelo e os resultados mostraram que a disponibilidade de mais armazéns intermediários é a estratégia mais econômica.

Application of Modified Flower Pollination Algorithm to Multiple Vehicle Routing Problems with Time Constraints

The aim of this research is to apply the modified flower pollination algorithm (MoFPA) to the multiplevehicle routing problems (MVRP) with the time constraints. As one of the latest enhanced versions of the originalflower pollination algorithm (FPA), the MoFPA utilizes the randomly switching probability for selection betweenlocal (self) and global (cross) pollinations in order to search for the better solutions and improve its searchperformance. In this paper, the MoFPA is applied to solve the MVRP problems with the time constraints basedon the modern optimization approach. Ten standard MVRP problems with the time constraints consisting ofapproximately 100–500 destinations are selected and solved by the MoFPA. Results obtained by the MoFPA arecompared with those obtained by original FPA, genetic algorithm (GA), tabu search (TS) and particle swarmoptimization (PSO). Results reveals that the MoFPA can provide optimal solutions of all ten selected MVRPproblems with shorter total distance than FPA, PSO, TS and GA, respectively. In addition, the execution timeconsumed by FPA and MoFPA are less than PSO, TS and GA, respectively.

Integrated Tomato Picking and Distribution Scheduling Based on Maturity

Agriproducts have the characteristics of short lifespan and quality decay due to the maturity factor. With the development of e-commerce, high timelines and quality have become a new pursuit for agriproduct online retailing. To satisfy the new demands of customers, reducing the time from receiving orders to distribution and improving agriproduct quality are significantly needed advancements. In this study, we focus on the joint optimization of the fulfillment of online tomato orders that integrates picking and distribution simultaneously within the context of the farm-to-door model. A tomato maturity model with a firmness indicator is proposed firstly. Then, we incorporate the tomato maturity model function into the integrated picking and distribution schedule and formulate a multiple-vehicle routing problem with time windows. Next, to solve the model, an improved genetic algorithm (the sweep-adaptive genetic algorithm, S-AGA) is addressed. Finally, we prove the validity of the proposed model and the superiority of S-AGA with different numerical experiments. The results show that significant improvements are obtained in the overall tomato supply chain efficiency and quality. For instance, tomato quality and customer satisfaction increased by 5% when considering the joint optimization, and the order processing speed increased over 90% compared with traditional GA. This study could provide scientific tomato picking and distribution scheduling to satisfy the multiple requirements of consumers and improve agricultural and logistics sustainability.

Solving Multiple Vehicle Routing Problems with Time Constraintsby Flower Pollination Algorithm Optimization

The multiple vehicle routing problem (MVRP) with the time constraint is one of the most importantreal-world problems in industrial and logistic engineering. The MVRP problems can be considered as a class ofthe non-polynomial (NP) time-complete combinatorial optimization problem. Such the MVRP problems aim tofind the set of routes with the shortest total distance for overall minimum route cost serving all the givendemands by the fleet of vehicles. Based on modern optimization, the MVRP problems can be optimally solvedby the potential metaheuristic optimization techniques. The flower pollination algorithm (FPA) is one of themost efficient metaheuristic optimizers proposed for solving the combinatorial optimization problems. Withfew searching parameters, the algorithm of the FPA is not complex and ease of use. In this paper, the FPA isapplied to solve five selected benchmark MVRP problems with the time constraints consisting of 50-100destinations. Results obtained by the FPA will be compared with those obtained by genetic algorithm (GA), tabusearch (TS) and particle swarm optimization (PSO). From results, the FPA can provide optimal solutions of allfive selected problems. Optimal results obtained by the FPA are superior to PSO, TS and GA, respectively,with shorter total distance and computational time consumed

A heuristic algorithm for multiple trip vehicle routing problems with time window constraint and outside carrier selection

Purpose In this paper, the authors introduced a real world new problem, the multi-trip vehicle routing problem with time windows and the possible use of a less-than-truckload carrier to satisfy customer demands. The purpose of this paper is to develop a heuristic algorithm to route the private trucks with time windows and to make a selection between truckload and less-than-truckload carriers by minimizing a total cost function. Design/methodology/approach Both mathematical model and heuristic algorithm are developed for routing the private trucks with time windows and for selecting of less-than-truckload carriers by minimizing the total cost function. Findings In all, 40 test problems were examined with the heuristics. Computational results show that the algorithm obtains the optimal or near-optimal solutions efficiently in terms of time and accuracy. Originality/value The research described in this paper differs from the previous one on fleet planning or vehicle routing, in that it modifies the Clarke and Wright method by shifting the performance measure from a distance to cost and also incorporates the fixed cost of different types of trucks into the model. In addition, the authors simultaneously consider the multiple trip vehicle routing problems with time windows and the selection of less-than-truckload carriers that is an integrated scenario of real-world application. To the best of the authors’ knowledge, this scenario has not been considered in the literature.

Urban hazmat transportation with multi-factor

In this paper, an urban hazmat transportation problem considering multiple factors that tangle with real-world applications (i.e., weather conditions, traffic conditions, population density, time window, link closure and half link closure) is investigated. Based on multiple depot capacitated vehicle routing problem, we provide a multi-level programming formulation for urban hazmat transportation. To obtain the Pareto optimal solution, an improved biogeography-based optimization (improved BBO) algorithm is designed, comparing with the original BBO and genetic algorithm, with both simulated numerical examples and a real-world case study, demonstrating the effectiveness of the proposed approach.

The multiple trip vehicle routing problem with backhauls in random fuzzy environment: using (α,β)-cost minimization model under the Hurwicz criterion

ABSTRACTIn the literature on VRP issues, many works have been studied in deterministic environments. Such proposed models cannot show the appropriate demands of different customers in the real world. One of the most important VRP problems that are widely applicable in real life is nondeterministic multiple trip vehicle routing problem with backhauls (MT-VRPB). In this paper, we focus on MT-VRPB in the random fuzzy environment using cost minimization model under the Hurwicz criterion. This model can deal with various MT-VRPB in random, fuzzy and random fuzzy environments. Regarding to the structure of the proposed model and in order to solve it, a hybrid intelligent algorithm based on the integration of the simplex algorithm, fuzzy simulations, and a firefly algorithm is proposed. The effectiveness and sensitive analysis of the proposed algorithm is demonstrated by solving some numerical examples.

An Enhanced Approach for the Multiple Vehicle Routing Problem with Heterogeneous Vehicles and a Soft Time Window

The vehicle routing problem (VRP) is a challenging combinatorial optimization problem. This research focuses on the problem under which a manufacturer needs to outsource materials from other suppliers and to ship the materials back to the company. Heterogeneous vehicles are available to ship the materials, and each vehicle has a limited loading capacity and a limited travelling distance. The purpose of this research is to study a multiple vehicle routing problem (MVRP) with soft time window and heterogeneous vehicles. Two models, using mixed integer programming (MIP) and genetic algorithm (GA), are developed to solve the problem. The MIP model is first constructed to minimize the total transportation cost, which includes the assignment cost, travelling cost, and the tardiness cost, for the manufacturer. The optimal solution can present multiple vehicle routing and the loading size of each vehicle in each period. The GA is next applied to solve the problem so that a near-optimal solution can be obtained when the problem is too difficult to be solved using the MIP. A case of a food manufacturing company is used to examine the practicality of the proposed MIP model and the GA model. The results show that the MIP model can obtain the optimal solution under a short computational time when the scale of the problem is small. When the problem becomes non-deterministic polynomial hard (NP-hard), the MIP model cannot find the optimal solution. On the other hand, the GA model can obtain a near-optimal solution within a reasonable amount of computational time. This paper is related to several important topics of the Symmetry journal in the areas of mathematics and computer science theory and methods. In the area of mathematics, the theories of linear and non-linear algebraic structures and information technology are adopted. In the area of computer science, theory and methods, and metaheuristics are applied.

Integrated production and multiple trips vehicle routing with time windows and uncertain travel times

We study the integrated production and multiple trips vehicle routing problem with time windows and uncertain travel times involving two phases. The first phase considers scheduling a set of jobs on parallel machines with machine-dependent ready times, and the second phase focuses on the delivery of completed jobs by a fleet of identical vehicles, which may differ in their ready times. In addition, the travel times in distribution are uncertain. The objective is to minimize the total cost comprising the travel cost and penalty cost caused by tardiness. We present a robustness approach, known as “Elastic p-Robustness”, to deal with travel time variations when historical risk data are limited or non-existent, and develop a memetic algorithm with an effective search strategy to solve the problem. We conduct numerical studies on randomly generated data based on real experience to assess the effectiveness and efficiency of the proposed method. The computational results show that the proposed solution approach yields relatively good solutions in comparison with current mainstream heuristic algorithms.