Generalized Vehicle Routing Problem Research Articles

An exact method for vehicle routing problem with backhaul discounts in urban express delivery network

The surge in e-commerce has led to an increased demand for urban express services, requiring the strategic development of delivery networks that are both efficient and cost-effective. This study addresses a practical vehicle routing problem (VRP) in an urban express delivery network to minimize transportation costs. Specifically, it considers the implementation of backhaul discounts, a factor disregarded in the existing literature. This VRP is further complicated by various realistic constraints, including pickup and delivery, time windows, multiple trips, heterogeneous fleets, and docking capacity limitations, which make most general VRP solvers inapplicable. This study proposes a trip-based formulation to overcome this challenge and develop a tailored branch-and-price algorithm. Feasible trips are classified into four types to simplify the computation of backhaul discounts, thereby enhancing solution efficiency. Validation with real-world data from SF Express substantiates the efficacy of our method and yields insights for sustainable city logistics management. Moreover, our simplified column generation algorithm exhibits competitive performance, achieving optimal solutions expeditiously for the tested instances.

Mathematical models and exact algorithms for the Colored Bin Packing Problem

This paper focuses on exact approaches for the Colored Bin Packing Problem (CBPP), a generalization of the classical one-dimensional Bin Packing Problem in which each item has, in addition to its length, a color, and no two items of the same color can appear consecutively in the same bin. To simplify modeling, we present a characterization of any feasible packing of this problem in a way that does not depend on its ordering. This allows us to describe the problem with a simple mathematical model. Furthermore, we present four exact algorithms for the CBPP. First, we propose a generalization of Valério de Carvalho’s arc flow formulation for the CBPP using a graph with multiple layers, each representing a color. Second, we present an improved arc flow formulation that uses a more compact graph and has the same linear relaxation bound as the first formulation. And finally, we design two exponential set-partition models based on reductions to a generalized vehicle routing problem, which are solved by a branch-cut-and-price algorithm through VRPSolver. To compare the proposed algorithms, a varied benchmark set with 574 instances of the CBPP is presented. Experimental results show that our best model, the improved arc flow formulation, was able to solve instances of up to 500 items and 37 colors. The set-partition models are also shown to exceed their arc flow counterparts in instances with a very small number of colors.

Generalized vehicle routing problem: Contemporary trends and research directions

Generalized Vehicle Routing Problem (GVRP) is a challenging operational research problem which has been widely studied for nearly two decades. In this problem, it is assumed that graph nodes are grouped into a number of clusters, and serving any node of a cluster eliminates the need to visit the other nodes of that cluster. The general objective of this problem is to find the set of nodes to visit and determine the service sequence to minimize the total traveling cost. In addition to these general conditions, GVRP can be formulated with different assumptions and constraints to practically create different sub-types and variants. This paper aims to provide a comprehensive survey of the GVRP literature and explore its various dimensions. It first encompasses the definition of GVRP, similar problems, mathematical models, classification of different variants and solution methods developed for GVRPs, and practical implications. Finally, some useful suggestions are discussed to extend the problem. For this review study, Google Scholar, Scopus, Science Direct, Emerald, Springer, and Elsevier databases were searched for keywords, and 160 potential articles were extracted, and eventually, 45 articles were judged to be relevant.

Dynamics between warehouse operations and vehicle routing

When scheduling the distribution of ordered items from a warehouse to customers, the transportation planning is generally done first and serves as input for planning warehouse operations. Such a sequential approach can lead to substantial inefficiencies when the customer deliveries are restricted by time windows, and the warehouse has limited resources available (both order pickers and space in the staging area). This paper studies the trade‐offs between warehouse operations and transportation planning. The goal is to understand the impact of three specific managerial interventions: adopting an integrated planning approach, expanding the available staging space, and expanding the delivery time windows. To this end, we propose a mathematical model for a general vehicle routing problem that incorporates order batching, order picker scheduling, staging, and vehicle loading. We introduce a novel idea to express the picking time of an order batch as a function of the batch size and develop a metaheuristic to solve this integrated problem. Furthermore, we develop exact algorithms to provide optimal solutions for the individual warehouse and transportation problems in a sequential planning approach. Managerial insights are distilled from case studies in two warehouses, one for ambient products and the other for refrigerated products, of a leading grocery retailer in the Netherlands. Our results show that integrated planning outperforms the other managerial interventions and generates cost savings between 9% and 11%. Savings are generally realized by executing larger order batch sizes to be picked in the warehouses at the expense of additional routing cost (around 2–3%). The second intervention in the form of time window expansions of only 15 minutes for customer deliveries can lead to cost savings between 4% and 6%, which results from a reduction in both transportation and warehousing cost. Expanding the capacity of the staging area is only meaningful when the staging space is highly utilized and only results in cost savings for the warehouse operations.

A new approach to the joint order batching and picker routing problem with alternative locations

Abstract Accepted by: M. Zied Babai The clustered and generalized vehicle routing problem (CGVRP) extends the well-known vehicle routing problem by grouping the demand points into multiple distinct zones, and within each zone, further separation is made by forming clusters. The objective of the CGVRP is to determine the optimal routes for a fleet of vehicles dispatched from a depot, visiting all zones within each cluster. This requires making two simultaneous optimization decisions. Firstly, each zone must be visited by exactly one node, and secondly, all zones within a cluster must be visited by the same vehicle. In this paper, we introduce two mixed-integer linear programming formulations for the CGVRP, aimed at solving a joint order batching and picker routing problem with alternative locations in a warehouse environment featuring mixed-shelves configuration. Both formulations are tested on three scenarios of randomly generated small- and medium-sized instances. Additionally, we propose a general rule approach for calculating a cost matrix in a rectangular environment. The results demonstrate the effectiveness of the proposed mathematical formulations in efficiently solving problems with up to 180 nodes.

Planning methods and decision support systems in vehicle routing problems for timber transportation: a review

ABSTRACT In the forest industry, transportation accounts for a significant part of the operational costs. Reducing transportation costs through advanced planning and improved efficiency has motivated considerable research efforts. A substantial part of the research has been devoted to planning methodology and decision support systems development to solve large complex vehicle routing problems in forest timber or roundwood transportation. This paper reviews the scientific contributions to timber transportation vehicle routing planning methodologies and decision support systems used in case studies found in the literature. The challenges of their deployment are discussed and future research opportunities are presented. Vehicle routing problems in timber transportation differ from general vehicle routing problems in many aspects. This paper also describes the industrial context, in which various timber transportation vehicle routing problems (TTVRPs) are intrinsic. Several attributes are identified that characterize the TTVRPs, for which various planning and solution methodologies have been implemented.

Constrained Local Search for Last-Mile Routing

Last-mile routing refers to the final step in a supply chain, delivering packages from a depot station to the homes of customers. At the level of a single van driver, the task is a traveling salesman problem. But the choice of route may be constrained by warehouse sorting operations, van-loading processes, driver preferences, and other considerations rather than a straightforward minimization of tour length. We propose a simple and efficient penalty-based local search algorithm for route optimization in the presence of such constraints, adopting a technique developed by Helsgaun to extend the Lin–Kernighan–Helsgaun algorithm for the traveling salesman problem to general vehicle routing problems. We apply his technique to handle combinations of constraints obtained from an analysis of historical routing data, enforcing properties that are desired in high-quality solutions. Our code is available under the open-source Massachusetts Institute of Technology license. An earlier version of the code received the $100,000 top prize in the Amazon Last Mile Routing Research Challenge organized in 2021. History: This paper has been accepted for the Transportation Science Special Issue on Machine Learning Methods and Applications in Large-Scale Route Planning Problems.

A unified exact approach for Clustered and Generalized Vehicle Routing Problems

The Clustered Vehicle Routing Problem (CluVRP) and the Generalized Vehicle Routing Problem (GVRP) are variants of the classic capacitated vehicle routing where customers are partitioned into clusters. In the first problem, all customers in the same cluster must be visited in sequence by a single route. In the second problem, all customers in a cluster are served by visiting a single customer in it. This article proposes a model for GVRP, together with new reduction tests. Then, three different models for CluVRP are proposed and discussed. The best performing CluVRP model is actually a reduction of the problem to a GVRP. All models are implemented and solved by the branch-cut-and-price algorithm in the VRPSolver package. The computational results show that the new approach can solve instances with up to 1,200 customers, much larger than those that could be solved by previous exact algorithms.

A two-level based genetic algorithm for solving the soft-clustered vehicle routing problem

The soft-clustered vehicle routing problem (Soft-CluVRP) is a relaxation of the clustered vehicle routing problem (CluVRP), which in turn is a variant of the generalized vehicle routing problem (GVRP). The aim of the Soft-CluVRP is to look for a minimum cost group of routes starting and ending at a given depot to a set of customers partitioned into a priori defined, mutually exclusive and exhaustive clusters, satisfying the capacity constraints of the vehicles and with the supplementary property that all the customers from the same cluster have to be supplied by the same vehicle. The considered optimization problem is NP-hard, that is why we proposed a two-level based genetic algorithm in order to solve it. The computational results reported on a set of existing benchmark instances from the literature, prove that our novel solution approach provides high-quality solutions within acceptable running times.

A column generation based heuristic for the generalized vehicle routing problem with time windows

The generalized vehicle routing problem with time windows (GVRPTW) is defined on a directed graph G=(V,A) where the vertex set V is partitioned into clusters. One cluster contains only the depot, where is located a homogeneous fleet of vehicles, each with a limited capacity. The other clusters represent customers. A demand is associated with each cluster. Inside a cluster, the vertices represent the possible locations of the customer. A time window is associated with each vertex, during which the visit must take place if the vertex is visited. The objective is to find a set of routes such that the total traveling cost is minimized, exactly one vertex per cluster is visited, and all the capacity and time constraints are respected. This paper presents a set covering formulation for the GVRPTW which is used to provide a column generation based heuristic to solve it. The proposed solving method combines several components including a construction heuristic, a route optimization procedure, local search operators and the generation of negative reduced cost routes. Experimental results on benchmark instances show that the proposed algorithm is efficient and high-quality solutions for instances with up to 120 clusters are obtained within short computation times.

ANALISIS PERBANDINGAN ALGORITMA WARSHALL DAN DIJKSTRAA PADA METODE GVRP DALAM PENENTUAN RUTE TERPENDEK (STUDI KASUS : PT YAKULT CABANG SUMBAWA)

Yakult is one of the large industrial companies engaged in the manufacturing sectorfermented milk. This company has business activities, namely selling anddistributing fermented milk to shops. The purpose of this research isanalyze the comparison between Warshall and Dijkstraa's Algorithm on the GVRP method indetermination of the shortest route. The General Vehicle Routing Problem (GVRP) methodused to make it easier to classify the many shops (vertek) intovarious groups (clusters) so as to determine the optimal route and costsminimal. The Warshall algorithm is a method that makes it easy to determinethe shortest route from all points to all points and has a simple method andeasy to implement. While Dijkstraa's algorithm is a method for searchingshortest path between 2 points from starting point to destination point. In this study analyzedthat the Warshall and Dijkstraa algorithms for determining the shortest route have a waycalculations and results that are almost the same as the difference between the total distance of 800 meters withdifference in cost of IDR 645 in one go. The different routes are only in cluster 6 andcluster 9. The conclusion of this study shows that both the Warshall Algorithm andDijkstraa's algorithm has a calculation method that is almost the same as the total distance andcosts have a relatively small difference.

Application of the CGVRP model and the 0-1 linear programming determines the RASKIN (subsidized rice) distribution route

Distribution is one of the important aspects to run a business or enterprise. BULOG is a state-own enterprise that operates in the food security sector. One of its services is to distribute RASKIN (subsidized rice) to all district in Indonesia. Sumbawa is one of the big district in Indonesia has a BULOG Regional sub-division to distr So far, the distribution of Raskin carried out by BULOG in the district of Sumbawa still relies on the experience of drivers in distributing RASKIN to destination villages and the application of the heuristic method has never been applied to optimize distribution routes, considering that a large number of distribution areas creates many combinations of distribution channels. This study aims to propose the optimal distribution route for RASKIN for BULOG in Sumbawa district, Alas warehouse so that the distribution time and costs can be more optimal. In this study, this problem was solved using the Cluster General Vehicle Routing Problem (CGVRP) model and the 0-1 linear programming. The result shows that only 3 of 4 vehicles can be used to distribute RASKIN, whereas previously, BULOG use 4 vehicles. The total route of the three vehicles is 206.52 miles.

Hybridizing large neighborhood search and exact methods for generalized vehicle routing problems with time windows

Delivery options are at the heart of the generalized vehicle routing problem with time windows (GVRPTW) allowing that customer requests are shipped to alternative delivery locations which can also have different time windows. Recently, the vehicle routing problem with delivery options was introduced into the scientific literature. It extends the GVRPTW by capacities of shared locations and by specifying service-level constraints defined by the customers’ preferences for delivery options. The vehicle routing problem with delivery options also generalizes the vehicle routing problem with home roaming delivery locations and the vehicle routing problem with multiple time windows. For all these GVRPTW variants, we present a widely applicable matheuristic that relies on a large neighborhood search (LNS) employing several problem-tailored destruction operators. Most of the time, the LNS performs relatively small and fast moves, but when the solution has not been improved for many iterations, a larger destruction move is applied to arrive in a different region of the search space. Moreover, an adaptive layer of the LNS embeds two exact components: First, a set-partitioning formulation is used to combine previously found routes to new solutions. Second, the Balas-Simonetti neighborhood is adapted to further improve already good solutions. These new components are in the focus of our work and we perform an exhaustive computational study to evaluate four configurations of the new matheuristic on several benchmark instances of the above-mentioned variants. On all the benchmark sets, our matheuristic is competitive with the previous state-of-the-art methods. In summary, the four configurations provide 81 new best-known solutions. • Matheuristic for variants of the generalized VRP with time windows. • Adaptive layer of the large neighborhood search embeds two exact components. • First component uses set-partitioning model, second dynamic programming. • Exhaustive computational study evaluates four configurations of matheuristic. • 81 new best-known solutions found.

Optimizing Vehicle Routing for Simultaneous Delivery and Pick-Up Considering Reusable Transporting Containers: Case of Convenience Stores

Previous studies have proposed various frameworks and algorithms to optimize routes to reduce total transportation cost, which accounts for over 29.4% of overall logistics costs. However, it is very hard to find cases in which mathematical models or algorithms are applied to practical business environment cases which require reusable packaging, especially daily operating logistics services like convenience store support systems. Most previous studies have considered developing an optimal algorithm which can solve the mathematical problem within a practical amount of time while satisfying all constraints, such as the capacity of delivery and pick-up, and hard or soft time windows. For daily delivery and pick-up services, like those supporting several convenience stores, it is required to consider the unit transporting the container, as well as the demand, capacity of trucks, travel distance, and traffic congestion. In particular, reusable transport containers and trays should be regarded as important assets of logistics centers. However, if the mathematical model focuses on only satisfying constraints related to delivery and not considering the cost of trays, it is often to leave the empty trays on the pick-up points when there is not enough space in the track. In this study, we propose a mathematical model for optimizing delivery and pick-up plans by extending the general vehicle routing problem of simultaneous delivery and pick-up with time windows, while considering left-over cost. With numerical experiments it has been proved that the proposed model may reduce the total delivery cost. Also, it seems possible to apply the proposed approach to the various logistics businesses which require reusable transport containers like shipping containers, refrigerating containers, trays, and pallets.

On the Selective Vehicle Routing Problem

The Generalized Vehicle Routing Problem (GVRP) is an extension of the classical Vehicle Routing Problem (VRP), in which we are looking for an optimal set of delivery or collection routes from a given depot to a number of customers divided into predefined, mutually exclusive, and exhaustive clusters, visiting exactly one customer from each cluster and fulfilling the capacity restrictions. This paper deals with a more generic version of the GVRP, introduced recently and called Selective Vehicle Routing Problem (SVRP). This problem generalizes the GVRP in the sense that the customers are divided into clusters, but they may belong to one or more clusters. The aim of this work is to describe a novel mixed integer programming based mathematical model of the SVRP. To validate the consistency of the novel mathematical model, a comparison between the proposed model and the existing models from literature is performed, on the existing benchmark instances for SVRP and on a set of additional benchmark instances used in the case of GVRP and adapted for SVRP. The proposed model showed better results against the existing models.

The exponential multi-insertion neighborhood for the vehicle routing problem with unit demands

In this paper, we extend, analyze and evaluate the exponential multi-insertion neighborhood for the vehicle routing problem with unit demands, originally proposed by Angel et al. (2008). In this neighborhood, a neighbor solution is obtained by the removal of a set of mobile nodes from a solution and a subsequent best reinsertion. At first, we examine theoretical properties of the neighborhood, such as its connectivity and the question how many nodes may be chosen as mobile. Furthermore, we prove that finding a best set of mobile nodes is NP-hard. Then, we present a two-stage approach in which first mobile nodes are selected heuristically and reinserted in an optimal way afterwards. Finally, this approach is embedded into a simulated annealing procedure and compared to other heuristics known for the more general vehicle routing problem with arbitrary demands.

A note on the lifted Miller–Tucker–Zemlin subtour elimination constraints for routing problems with time windows

We propose lifted versions of the Miller–Tucker–Zemlin subtour elimination constraints for routing problems with time windows (TW). The constraints are valid for problems such as the travelling salesman problem with TW, the vehicle routing problem with TW, the generalized travelling salesman problem with TW, and the general vehicle routing problem with TW. They are corrected versions of the constraints proposed by Desrochers and Laporte (1991).

An approach to the optimal timber transport scheduling

An approach to the optimal timber transport scheduling is described in the paper. A description of this problem is given, a multi-criteria mathematical model is created. It is noted that the problem belongs to the class of General vehicle routing problems (GVRP) associated with the job-shop scheduling. A hybrid algorithm for solving this problem based on the decomposition method using the simplex method and the genetic algorithm is developed. Testing of the proposed approach using real data from wood harvesting enterprises showed its effectiveness. The algorithm was implemented in “Opti-Wood” decision support system for wood harvesting planning and management, developed by Opti-Soft company (Russia).

Analisa Optimasi Rute Transportasi Antar Jemput Siswa Menggunakan Model CGVRP dan Algoritma Dijkstra di SDIT Darus Sunnah

School transportation is one of the facilities provided by the school in the process of picking up students. In the process of picking up, taking the optimal route is needed to save costs and time. The purpose of this study is to develop a model School transportation routes using the Clustered Generalized Vehicle Routing Problem (CGVRP ) model and the Dijkstra algorithm to get a more optimal route from the route that has been used. Furthermore, comparing the real distance from the shuttle transportation routes with the distance from the results of this case study using the CGVRP model and the Dijkstra algorithm. From the research results obtained by using the CGVRP model and the Djikstra algorithm which is applied to the case study of shuttle students at Darus Sunnah SDIT We found that our result has shorter distance when compared to the distance of the usual route.. The total distance on the SDIT Darus Sunnah route is 2.746.416 meters and costs Rp. 2.214.288 in a month. While the distance from the proposed route obtained 2.333.616 meters for at Rp. 1.881.478 in a month. Therefore the difference in the distance from the real route and the proposed route is 357.288 meters with a difference in cost of Rp. 332.820, - in a month.

Solving Generalized Vehicle Routing Problem With Occasional Drivers via Evolutionary Multitasking.

With the emergence of crowdshipping and sharing economy, vehicle routing problem with occasional drivers (VRPOD) has been recently proposed to involve occasional drivers with private vehicles for the delivery of goods. In this article, we present a generalized variant of VRPOD, namely, the vehicle routing problem with heterogeneous capacity, time window, and occasional driver (VRPHTO), by taking the capacity heterogeneity and time window of vehicles into consideration. Furthermore, to meet the requirement in today's cloud computing service, wherein multiple optimization tasks may need to be solved at the same time, we propose a novel evolutionary multitasking algorithm (EMA) to optimize multiple VRPHTOs simultaneously with a single population. Finally, 56 new VRPHTO instances are generated based on the existing common vehicle routing benchmarks. Comprehensive empirical studies are conducted to illustrate the benefits of the new VRPHTOs and to verify the efficacy of the proposed EMA for multitasking against a state-of-art single task evolutionary solver. The obtained results showed that the employment of occasional drivers could significantly reduce the routing cost, and the proposed EMA is not only able to solve multiple VRPHTOs simultaneously but also can achieve enhanced optimization performance via the knowledge transfer between tasks along the evolutionary search process.