Heterogeneous Fleet Vehicle Routing Problem Research Articles

Multi-period heterogeneous fleet vehicle routing problem with self-pickup point selection: a last-mile delivery scenario in urban and rural areas

Multi-period heterogeneous fleet vehicle routing problem with self-pickup point selection: a last-mile delivery scenario in urban and rural areas

Mathematical problems for designing a short-distance relief goods distribution network in urban areas

In the humanitarian relief efforts after an earthquake strikes, local capabilities are critical in the first hours to assess the situation and deliver relief supplies to the victims. Usually, the relief goods required by victims are unlikely to be found in the impacted areas, and resources from other places need time to be mobilized to the affected areas. Often in earthquakes in cities in developing countries, relief goods do not arrive on time causing victims to suffer even more. In this paper, we present the mathematical formulations and solutions techniques for designing a short-distance distribution network of relief goods, which can be managed by local governments. In the preparation phase, as a part of the immediate response plan based on scenarios, the facilities location and the preliminary distribution paths must be determined. Hence, a p-median problem and a multi-depot heterogeneous fleet vehicle routing problem (MDHFVRP) must be solved. These problems are usually small and there is time to find a solution. However, in the response phase, a dynamical VRP must be solved.

Optimization of vehicle routing problem using guided local search and simulated annealing

Transportation concerns in the supply chain are important because they have the potential to greatly raise logistical requirements. The proposed solution to the issue is the vehicle routing problem. The Heterogeneous Fleet Vehicle Routing Problem (HFVRP) model will be implemented in this study using the metaheuristic methodology together with the Guided Local Search (GLS) and Simulated Annealing (SA) approaches for case studies. Python 3.10 software was used to analyze the SA and GLS, and the Google OR-Tools module was used. Implementing the SA and GLS algorithm based on data from the case study in a logistics company involved in the distribution of chicken feed and gas is the goal of this project. By doing so, it will be possible to determine whether the current situation is ideal or if it could be improved to reduce the number of vehicles used, find the best route, lower shipping costs, and increase efficiency. The findings of this study show that when compared to the GLS algorithm, research employing SA produces better outcomes in terms of cost and route management. According to actual data, SA increases income by an average amount between 3% and 10%.

A multiobjective mathematical model for a humanitarian logistics multimodal transportation problem

PurposeThe purpose of this paper is to introduce a three-echelon multimodal transportation problem applied to a humanitarian logistic case study that occurred in Mexico.Design/methodology/approachThis study develops a methodology combining a transshipment problem and an adaptation of the multidepot heterogeneous fleet vehicle routing problem to construct a mathematical model that incorporates the use of land-based vehicles and drones. The model was applied to the case study of the Earthquake on September 19, 2017, in Mexico, using the Gurobi optimization solver.FindingsThe results ratified the relevance of the study, showing an inverse relationship between transportation costs and delivery time; on the flip side, the model performed in a shorter CPU time with medium and small instances than with large instances.Research limitations/implicationsWhile the size of the instances limits the use of the model for big-scale problems, this approach manages to provide a good representation of a transportation network during a natural disaster using drones in the last-mile deliveries.Originality/valueThe present study contributes to a model that combines a vehicle routing problem with transshipment, multiple depots and a heterogeneous fleet including land-based vehicles and drones. There are multiple models present in the literature for these types of problems that incorporate the use of these transportation modes; however, to the best of the authors’ knowledge, there are still no proposals similar to this study.

A simulated annealing with variable neighborhood descent approach for the heterogeneous fleet vehicle routing problem with multiple forward/reverse cross-docks

With a greater awareness of the challenges regarding environmental, societal, political, and economic factors, where reverse logistics has become a significant part of supply chain networks, this paper presents an integrated forward and reverse logistics network, named the Heterogeneous Fleet Vehicle Routing Problem with Multiple Forward/Reverse Cross-Docks (HF-VRPMFRCD). We consider a heterogeneous fleet of vehicles with different loading capacities and transportation costs. We also consider multiple cross-docks with two different operations: forward and reverse processes. The former focuses on delivering the demand from suppliers to customers, while the latter aims at returning unsold products from customers to suppliers. We propose a Simulated Annealing with Variable Neighborhood Descent (SAVND) algorithm for solving HF-VRPMFRCD, where Variable Neighborhood Descent (VND) is a local search heuristic embedded in the framework of Simulated Annealing (SA). SAVND outperforms the state-of-the-art algorithm in solving the Heterogeneous Fleet Vehicle Routing Problem with Multiple Cross-Docks (HF-VRPMCD), where the VND heuristic significantly improves the quality of solutions. For HF-VRPMFRCD benchmark instances, SAVND provides optimal solutions for small-scale instances and better solutions than those of the GUROBI solver for remaining larger instances. Lastly, we present and discuss the benefits of integrating the forward and reverse processes.

Vehicle routing with heterogeneous service types: Optimizing post-harvest preprocessing operations for fruits and vegetables in short food supply chains

This study focuses on the post-harvest preprocessing of fruits and vegetables, aiming to provide an effective way to conduct preprocessing operations in short food supply chains. We consider both a heterogeneous fleet of mobile preprocessing units and the possibility to pick up products for centralized preprocessing. The resulting problem is a variant of the classic heterogeneous fleet vehicle routing problems with time windows (HFVRPTW), with the additional consideration of multi-depot and heterogeneous service types, which we refer to as HFVRPTW-MDHS. These additional considerations are important to include in the development of more efficient food supply chains, but lead to a challenging routing problem. In this paper, we formulate the HFVRPTW-MDHS using a mixed-integer linear programming model. Due to the complexity of the model, we propose a customized adaptive large neighborhood search (ALNS) metaheuristic. We design a multi-level struct-based solution representation to improve the efficiency of the ALNS and develop customized methods for solution evaluation, feasibility checks, and neighborhood search. Comparing our results with the results of an exact algorithm and solutions in the existing literature, we find that our ALNS algorithm can obtain high-quality solutions quickly when solving HFVRPTW-MDHS and related variants of the VRP. Finally, we study the application of our approach in the case of precooling, which is a commonly used preprocessing operation, to illustrate the effectiveness of our approach in a relevant practical context.

Scheduling multi-pattern precooling service resources for post-harvest fruits and vegetables using the adaptive large neighborhood search

This study focuses on the multi-pattern precooling service resources scheduling (MPPSRS) issue recently derived from the practice of small-scale farming. In this issue, a heterogeneous fleet of vehicles belonging to different service pattens is considered to fulfil precooling requests of farmers in the service time windows. The studied issue is regarded as a variant of heterogeneous fleet vehicle routing problem with time windows (HFVRPTW) in which heterogeneous service efficiencies among vehicles are considered. To the best of our knowledge, this is the first time that such a characteristic of vehicles’ heterogenous service efficiencies is considered in vehicle routing problems. This new characteristic increases the potential combination ways of nodes in the temporal aspect, which expands the search space of the problem and leads to a more challenging optimization issue. This study formulates the MPPSRS issue using a mixed-integer programming model in which details from the real world are considered. Motivated by the challenge of computational time, an adaptive large neighborhood search (ALNS) metaheuristic is proposed to solve the model. Results obtained from a case study of the apple industry from Luochuan County, China show advantages of using multi-pattern precooling service resources in reducing total operating cost.

The Heterogeneous Fleet Vehicle Routing Problem with Draft Limits

Over the past two decades, international maritime transport has been characterized by the advent of ever larger ships. This phenomenon is known as naval gigantism. If, on the one hand, naval gigantism allows to reduce transport costs by exploiting the economies of scale achievable by large ships, on the other hand, it implies a series of operational issues. Indeed, due to their large draft, such giant vessels are not allowed to enter small ports when fully or near-fully loaded, and in some cases, they cannot enter such small ports at all. In fact, their draft can strongly vary depending on the load on board. This implies restrictions for vessels in accessing ports, which impact not only at the strategical level on the fleet sizing problem, but also at the tactical/operational level, on the sequence of port visits among each route. In fact, given a set of ports that a ship has to visit, determining the optimal sequence of visits becomes a very challenging issue, as the sequence that gives the shortest travel distance (i.e., the smallest travel cost) may prove infeasible due to draft limit restrictions for accessing ports. Furthermore, the same sequence of ports, which may be infeasible for a large ship, may become viable if operated by a smaller ship. On the other hand, due to the economy of scale, travel costs per load unit are generally much lower for large ships than for small ones. Therefore, the draft restrictions also affect the fleet sizing problem. In this paper, we introduce the Heterogeneous Fleet Vehicle Routing Problem with Draft Limits (HF-VRP-DL). We propose a mixed integer programming formulation and several valid inequalities to strengthen it. Since the mathematical model is able to handle only small-sized instances, to address larger instances we propose a Large Neighborhood Search matheuristic (LNS) and an Iterated Local Search matheuristic (ILS). Computational tests carried out show excellent performances of the proposed approach. Further analysis is provided on the impact of the instance layout on the computation time required to solve the problem to optimality.

An adaptive iterated local search heuristic for the Heterogeneous Fleet Vehicle Routing Problem

The Heterogeneous Fleet Vehicle Routing Problem (HFVRP) is an important variant of the classical Capacitated Vehicle Routing Problem (CVRP) that aims to find routes that minimize the total traveling cost of a heterogeneous fleet of vehicles. This problem is of great interest given its importance in many industrial and commercial applications. In this paper, we present an Adaptive Iterated Local Search (AILS) heuristic for the HFVRP. AILS is a local search-based meta-heuristic that achieved good results for the CVRP. The main characteristic of AILS is its adaptive behavior that allows the adjustment of the diversity control of the solutions explored during the search process. The proposed AILS for the HFVRP was tested on benchmark instances containing up to 360 customers. The results of computational experiments indicate that AILS outperformed state-of-the-art metaheuristics on 87% of the instances.

A tabu search based approach for the Heterogeneous Fleet Vehicle Routing Problem with three-dimensional loading constraints

This paper studies a particular integration of the Heterogeneous Fleet Vehicle Routing Problem with three-dimensional loading constraints (3L-HFVRP), which considers rectangular-shaped items to be delivered to customers and loading constraints to be satisfied. The resolution of this problem consists of assigning a loading plan to each used vehicle, while minimizing the total transportation cost. Clearly, the 3L-HFVRP is a combination of Heterogeneous Fleet Vehicle Routing Problem (HFVRP) and Three Dimensional Single Container Loading Problem (3D-SCLP). In order to solve this problem, we propose a hybrid meta-heuristic approach based on a developed Tabu Search (TS) algorithm for the routing aspect and a modified Extreme Point based First Fit Decreasing (EP-FFD) heuristic for the loading sub-problem. New procedures have been proposed in the framework of this approach. Afterwards, numerical experiments on available sets of benchmark instances show that our new approach outperforms the current best algorithm for several instances. Indeed, the different experiments performed showed that our algorithm was able to find good solutions on 76% of the cases, which confirms the efficiency and performance of our approach in terms of solution quality.

Sustainable Transportation Networks Incorporating Green Modes for Urban Freight Delivery

The sustainability of transportation networks is threatened by growing amounts of emissions generated by vehicles. Urban freight delivery is one of the major sources of these emissions. Cargo cycles are attracting increasing attention for urban delivery owing to their numerous benefits, such as being less pollutant, requiring less space on roads, and high maneuverability. Electric vans have also been proposed as another green mode of freight delivery with a larger delivery capacity and range relative to cargo cycles. In this study, urban freight delivery is targeted through a heterogeneous fleet vehicle routing problem. The proposed framework is used to capture the optimal configuration of a mixed freight delivery fleet offering cargo cycles (i.e., pedal-assisted bikes and trikes as well as electric bikes and trikes) alongside the often-used diesel or gasoline vans or small trucks and electric vans. The formulated problem aims to minimize the delivery costs for companies, including maintenance, purchase, fuel, and labor costs and noise and emission taxes. The methodological contribution of this study is to develop a new metaheuristic algorithm, based on variable neighborhood search and simulated annealing, that finds a better solution with up to 7% lower objective function value and 50% to 80% lower solution times relative to the existing approaches in the literature. This study also demonstrates that bikes and trikes are selected at short delivery distances in the Chicago downtown network. Electric vans are more suitable for large distances, while cargo vans are selected for medium distances. Imposing an emission tax would change the model from cargo vans to electric vans. The results also show that increasing tax levels does not necessarily reduce societal costs because the delivery company tends to maintain its profit margin by increasing delivery costs for customers.

Mathematical Model and Simulated Annealing Algorithm for the Two-Dimensional Loading Heterogeneous Fixed Fleet Vehicle Routing Problem

This paper addresses the two-dimensional loading heterogeneous fixed fleet vehicle routing problem, which is a complex and unstudied variant of the classical vehicle routing problem and has a wide range of applications in transportation and logistics fields. In this problem, each customer demands a set of rectangular two-dimensional items, and the objective is to find the minimum cost delivery routes for a limited set of vehicles with different capacities, fixed and variable operating costs, and rectangular two-dimensional loading surfaces. We formulate a mixed integer linear programming model to obtain optimal solutions for small-scale problems. To obtain solutions for large-scale problems, we develop an algorithm based on simulated annealing and local search, which uses a collection of packing heuristics to address the loading constraints, and we also propose three new heuristics. We conduct experiments on benchmark instances derived from the two-dimensional loading heterogeneous fleet vehicle routing problem. The results indicate that the proposed model correctly describes the problem and can solve small-scale problems, that the new packing heuristics are effective in improving the collection of packing heuristics, and that the proposed simulated annealing algorithm can find good solutions to large-scale problems within an acceptable computational time. Hence, it can be used by logistic companies using a heterogeneous fixed fleet in the integrated planning of vehicle loading and routing.

A Granular Local Search Matheuristic for a Heterogeneous Fleet Vehicle Routing Problem with Stochastic Travel Times

A Granular Local Search Matheuristic for a Heterogeneous Fleet Vehicle Routing Problem with Stochastic Travel Times

Multi-depot heterogeneous fleet vehicle routing problem with time windows: Airline and roadway integrated routing

In transportation, the multi-depot heterogeneous fleet vehicle routing problem with time windows (MDHFVRPTW) is one of the hard-to-solve real-life problems. In the study, a new node-based MDHFVRPTW has been developed. Unlike other studies in the literature, heterogeneous fleets including both airline and roadway vehicles are used for routing. In the model, real-life data of the airline and roadway are taken into consideration. In particular, important aviation constraints such as the range of the aircraft, landing and take-off cycle (LTO) cost according to the engine type, and the penalty cost are presented in the model. The problem is analysed by using narrow and wide time windows, which is the realization of fast and normal demand. A new hybrid genetic algorithm with variable neighborhood search (HGA-VNS) has been proposed for the solution of the MDHFVRPTW model. In the solution of the model, remarkable results have been obtained with the HGA-VNS algorithm compared to the genetic algorithm and off-the-shelf solvers. Also, the HGA-VNS algorithm has been tested with small and large-scale instances and compared with other studies in the literature. It is thought that the proposed MDHFVRPTW model and the developed HGA-VNS algorithm will bring a different perspective to transportation.

A Hybrid Simulated Annealing with Variable Neighborhood Search for the Heterogeneous Fleet Vehicle Routing Problem with Multiple Forward/Reverse Cross-Docks

A Hybrid Simulated Annealing with Variable Neighborhood Search for the Heterogeneous Fleet Vehicle Routing Problem with Multiple Forward/Reverse Cross-Docks

Optimasi rute distribusi gas LPG 3 kg menggunakan metode tabu search pada PT. SPI

PT. SPI is one of the agents of 3 kg LPG gas in the Karawang area, where there are problems in the process of distributing 3 kg LPG gas, because the route chosen for delivery is based on the intuitiveness of the driver who carries out the distribution process. PT. SPI has 11 vehicles where there are differences in vehicle capacity, therefore the problem of PT. SPI is a type of Heterogeneous Fleet Vehicle Routing Problem. This study aims to determine the optimal distribution route, calculate the distribution costs required by PT. SPI to the base and compare the company's existing route with the proposed route that is formed based on the total distance traveled and the costs to be incurred. The method used in this research is the method Clarke and Wright savin g as the initial solution assignment which is then optimized by the method Tabu search . The results obtained in this study are the method Tabu search can form a route that is close to optimal with a total distance of 1323.4 kilometers with the search process using a maximum of 60 iterations can reduce the total distance traveled on Monday to Saturday, the difference from the total existing mileage with the proposed route is 141.2 kilometers with a percentage of the decrease in the existing total mileage with the total proposed mileage as a whole is 9.6% In addition, it can provide a total distribution cost of Rp. 24,015,811,- /week, and the difference between the existing total distribution costs and the proposed distribution costs is Rp. 1,758,994 and can be presented as a decrease in total distribution costs of 6.8%.

Optimizing the Heterogeneous Fleet Vehicle Routing Problem with Time Window on Urban Last Mile Delivery

The growth of the e-commerce business in Indonesia during the COVID-19 pandemic has increased the demand for last mile delivery (LMD) services. LMD activities with a large frequency of trips can increase logistics operational costs if operational handling is not carried out optimally. Optimization of LMD distribution routes is applied as an operational handling and also as a solution to the vehicle routing problem (VRP). VRP is an important problem to consider in transportation modeling where an optimum route plan is desired to obtain the minimum cost. The purpose of this paper is to optimize the last mile delivery route using the Heterogeneous Fleet Vehicle Routing Problem with Time Window (HFVRP-TW) model in urban areas. The route optimization process is carried out by developing and applying the HFVRP-TW model using data from one of the express delivery companies in Jakarta, Indonesia, and then simulating and forming several operational scenarios. The results of the analysis show that the application of route optimization with variations in vehicle types reduced operating costs by an average of 58.46% - 65.98% compared to the existing conditions. Scenario evaluation is carried out to obtain the scenario with the lowest operational cost. The evaluation results show that the best scenario is a scenario that has the closest characteristics to existing conditions, where there is no change in the type of vehicle used and optimization is only applied to operational routes. However, several other scenarios using a variety of different vehicle types still resulted in a reduction in operating costs of more than 50%.

Simplified Swarm Optimization for the Heterogeneous Fleet Vehicle Routing Problem with Time-Varying Continuous Speed Function

Transportation planning has been established as a key topic in the literature and practices of social production, especially in urban contexts. To consider traffic environment factors, more and more researchers are taking time-varying factors into account when scheduling their logistic activities. The time-dependent vehicle routing problem (TDVRP) is an extension of the classical Vehicle Routing Problem with Time Windows (VRPTW) by determining a set of optimal routes serving a set of customers within specific time windows. However, few of them use the continuous speed function to express the time-varying. In practice, many vehicle routing problems are addressed by a fleet of heterogeneous vehicles with different capacities and travel costs including fix costs and variable costs. In this study, a Heterogeneous Fleet Vehicle Routing Problem (HFPRP) Time-Varying Continuous Speed Function has been proposed. The objective is to minimize distribution costs, which contained fixed costs of acquiring and variable fuel costs. To address this problem, our research developed a mathematical model and proposed a Simplified Swarm Optimization (SSO) heuristic for HFVRP with Time-Varying Continuous Speed Function.

A POPMUSIC matheuristic for the capacitated vehicle routing problem

This work proposes a partial optimization metaheuristic under special intensification conditions (POPMUSIC) for the classical capacitated vehicle routing problem. The proposed approach uses a branch-cut-and-price algorithm as a powerful heuristic to solve subproblems whose dimensions are typically between 25 and 200 customers. The whole algorithm can be seen as the application of local search over very large neighborhoods, starting from a single initial solution. The main computational experiments were carried out on instances having between 302 and 1000 customers. Using initial solutions generated by some of the best available metaheuristics for the problem, POPMUSIC was able to obtain consistently better solutions for long runs of up to 32 h. Starting from the best known solutions available in CVRP library (CVRPLIB), POPMUSIC was able to find new best solutions for several instances, including some very large ones. In a final experiment, we successfully applied the same POPMUSIC framework to tackle the heterogeneous fleet vehicle routing problem and the vehicle routing problem with backhauls.

Managing pharmaceuticals delivery service using a hybrid particle swarm intelligence approach

Medicines or drugs have unique characteristics of short life cycle, small size, light weight, restrictive distribution time and the need of temperature and humidity control (selected items only). Thus, logistics companies often use different types of vehicles with different carrying capacities, and considering fixed and variable costs in service delivery, which make the vehicle assignment and route optimization more complicated. In this study, we formulate the problem to a multi-type vehicle assignment and mixed integer programming route optimization model with fixed fleet size under the constraints of distribution time and carrying capacity. Given non-deterministic polynomial hard and optimal algorithm can only be used to solve small-size problem, a hybrid particle swarm intelligence (PSI) heuristic approach, which adopts the crossover and mutation operators from genetic algorithm and 2-opt local search strategy, is proposed to solve the problem. We also adapt a principle based on cost network and Dijkstra’s algorithm for vehicle scheduling to balance the distribution time limit and the high loading rate. We verify the relative performance of the proposed method against several known optimal or heuristic solutions using a standard data set for heterogeneous fleet vehicle routing problem. Additionally, we compare the relative performance of our proposed Hybrid PSI algorithm with two intelligent-based algorithms, Hybrid Population Heuristic algorithm and Improved Genetic Algorithm, using a real-world data set to illustrate the practical and validity of the model and algorithm.