Loading Capacitated Vehicle Routing Problem Research Articles

Constraint programming-based solution approaches for three-dimensional loading capacitated vehicle routing problems

This paper presents constraint programming-based solution approaches for the three-dimensional loading capacitated vehicle routing problem (3l-CVRP) that consists of vehicle routing and three-dimensional loading problems in distribution logistics. Despite the practical benefits in the logistics world, the 3l-CVRP has not been extensively studied in the literature for its high combinatorial complexity. Therefore, we developed integrated and decomposed constraint programming-based solution methods in this study. The decomposed models outperformed the mixed-integer programming model proposed earlier in the literature for small-size problems. Furthermore, we solved the well-known benchmark problems with a decomposed model using constraint programming for the vehicle routing part of the problem and an evolutionary algorithm for the loading part. The computational study results show that the best-known results are improved in 36 of 93 problems.

Combination of nearest neighbor and heuristics algorithms for sequential two dimensional loading capacitated vehicle routing problem

Vehicle Routing Problem (VRP) is a method for determining the optimal route of vehicles in order to serve customers starting from depot. Combination of the two most important problems in distribution logistics, which is called the two dimensional loading vehicle routing problem, is considered in this paper. This problem combines the loading of the freight into the vehicles and the successive routing of the vehicles along the route. Moreover, an additional feature of last-in-first-out loading sequencesis also considered. In the sequential two dimensional loading capacitated vehicle routing problem (sequential 2L-CVRP), the loading must be compatible with the trip sequence: when the vehicle arrives at a customer i, there must be no obstacle (items for other customers) between the item of i and the loading door (rear part) of the vehicle. In other words, it is not necessary to move non-i’s items whenever the unloading process of the items of i. According with aforementioned conditions, a program to solve sequential 2L-CVRP is required. A nearest neighbor algorithm for solving the routing problem is presented, in which the loading component of the problem is solved through a collection of 5 packing heuristics.

Heuristic algorithms for a three-dimensional loading capacitated vehicle routing problem in a carrier

In this paper, we present heuristic algorithms for a three-dimensional loading capacitated vehicle routing problem arising in a real-world situation. In this problem, customers make requests of goods, which are packed in a sortment of boxes. The objective is to find minimum cost delivery routes for a set of identical vehicles that, departing from a depot, visit all customers only once and return to the depot. Apart of the usual 3D container loading constraints which ensure that the boxes are packed completely inside the vehicles and that the boxes do not overlap each other in each vehicle, the problem also takes into account constraints related to the vertical stability of the cargo and multi-drop situations. The algorithms are based on the combination of classical heuristics from both vehicle routing and container loading literatures, as well as two metaheuristic strategies, and their use in more elaborate procedures. Although these approaches cannot assure optimal solutions for the respective problems, they are relatively simple, fast enough to solve real instances, flexible enough to include other practical considerations, and normally assure relatively good solutions in acceptable computational times in practice. The approaches are also sufficiently generic to be embedded with algorithms other than those considered in this study, as well as they can be easily adapted to consider other practical constraints, such as the load bearing strength of the boxes, time windows and pickups and deliveries. Computational tests were performed with these methods considering instances based on the vehicle routing literature and actual customers’ orders, as well as instances based on a real-world situation of a Brazilian carrier. The results show that the heuristics are able to produce relatively good solutions for real instances with hundreds of customers and thousands of boxes.

A matheuristic algorithm for the three-dimensional loading capacitated vehicle routing problem (3L-CVRP)

This paper presents a hybrid algorithm for solving the Capacitated Vehicle Routing Problem with practical three-dimensional loading constraint. This problem is known as 3L-CVRP (Three-dimensional Loading Capacitated Vehicle Routing Problem). The proposed methodology consists of two phases. The first phase uses an optimization procedure based on cuts to obtain solutions for the well-known Capacitated Vehicle Routing Problem (CVRP). The second phase validates the results of the first phase of a GRASP algorithm (Greedy Randomized Adaptive Search Procedure). In particular, the GRASP approach evaluates the packing constraints for each performed route of the CVRP. The proposed hybrid algorithm uses a relaxation of the classical model of two sub-indices for the vehicle routing problem. Specifically different types of cuts are added: subtour elimination, capacity-cut constraints, and packing-cut constrains. The proposed algorithm is compared with the most efficient approaches for the 3L-CVRP on the set of benchmark instances considered in the literature. The computational results indicate that the proposed approach is able to obtain good solutions, improving some of the best-known solutions from the literature.

A Column Generation Based Heuristic for the Capacitated Vehicle Routing Problem with Three-dimensional Loading Constraints

This paper addresses an integrated problem of routing and loading known as the three-dimensional loading capacitated vehicle routing problem (3L-CVRP). 3L-CVRP consists of finding feasible routes with minimum total travel cost while satisfying customers’ demands expressed in terms of cuboid and weighted items. Practical constraints related to connectivity, stability, fragility, and LIFO are considered as parts of the problem. 3L-CVRP is addressed by using a column generation (CG) technique based heuristic. To generate new columns, an integrated approach using the shortest path problem and 3D loading problem is applied. To speed up the CG technique, fast CG is also carried out by applying a heuristic pricing method. The CG technique outperforms the efficient tabu search technique proposed in the literature in terms of solution quality and execution time.

Using biased randomization for solving the two-dimensional loading vehicle routing problem with heterogeneous fleet

This paper discusses the two-dimensional loading capacitated vehicle routing problem (2L-CVRP) with heterogeneous fleet (2L-HFVRP). The 2L-CVRP can be found in many real-life situations related to the transportation of voluminous items where two-dimensional packing restrictions have to be considered, e.g.: transportation of heavy machinery, forklifts, professional cleaning equipment, etc. Here, we also consider a heterogeneous fleet of vehicles, comprising units of different capacities, sizes and fixed/variable costs. Despite the fact that heterogeneous fleets are quite ubiquitous in real-life scenarios, there is a lack of publications in the literature discussing the 2L-HFVRP. In particular, to the best of our knowledge no previous work discusses the non-oriented 2L-HFVRP, in which items are allowed to be rotated during the truck-loading process. After describing and motivating the problem, a literature review on related work is performed. Then, a multi-start algorithm based on biased randomization of routing and packing heuristics is proposed. A set of computational experiments contribute to illustrate the scope of our approach, as well as to show its efficiency.

A Review on the Bin Packing Capacitated Vehicle Routing Problem

This paper introduced the Bin Packing Capacitated Vehicle Routing Problem. It introduced the constraints and differences between algorithms of two-dimensional and three-dimensional loading capacitated vehicle routing problem. It gave a review of models and algorithms for Bin Packing Capacitated VRP. Finally, it prospected future research orientations and possible improvement in this area.

An effective tabu search approach with improved loading algorithms for the 3L-CVRP

In this paper, we consider the Three-Dimensional Loading Capacitated Vehicle Routing Problem(3L-CVRP) which combines the routing of a fleet of vehicles and the loading of three-dimensional shaped goods into the vehicles while minimizing the total travel distance incurred. Apparently, 3L-CVRP is a combination of capacitated vehicle routing and three-dimensional bin packing problem and thus of high complexity. Different from most of previous works, we propose an innovative approach, called improved least waste heuristic for solving the loading subproblem, which is iteratively invoked by a simple tabu search algorithm for the routing. The good performance in terms of the solution quality and computational efficiency of our approach is shown through the numerical experiments on the benchmark instances from literature.

Local search techniques for a routing-packing problem

We propose a complex real-world problem in logistics that integrates routing and packing aspects. It can be seen as an extension of the Three-Dimensional Loading Capacitated Vehicle Routing Problem (3L-CVRP) introduced by Gendreau, Iori, Laporte, and Martello (2006). The 3L-CVRP consists in finding a set of routes that satisfies the demand of all customers, minimizes the total routing cost, and guarantees a packing of items that is feasible according to loading constraints. Our problem formulation includes additional constraints in relation to the stability of the cargo, to the fragility of items, and to the loading and unloading policy. In addition, it considers the possibility of split deliveries, so that each customer can be visited more than once. We propose a local search approach that considers the overall problem in a single stage. It is based on a composite strategy that interleaves simulated annealing with large-neighborhood search. We test our solver on 13 real-world instances provided by our industrial partner, which are very diverse in size and features. In addition, we compare our solver on benchmarks from the literature of the 3L-CVRP showing that our solver performs well compared to other approaches proposed in the literature.

Heuristics for the strip packing problem with unloading constraints

This article addresses the Strip Packing Problem with Unloading Constraints (SPU). In this problem, we are given a strip of fixed width and unbounded height, and n items of C different classes. As in the well-known two-dimensional Strip Packing problem, we have to pack all items minimizing the used height, but now we have the additional constraint that items of higher classes cannot block the way out of lower classes items. This problem appears as a sub-problem in the Two-Dimensional Loading Capacitated Vehicle Routing Problem (2L-CVRP), where one has to optimize the delivery of goods, demanded by a set of clients, that are transported by a fleet of vehicles of limited capacity based at a central depot. We propose two approximation algorithms and a GRASP heuristic for the SPU problem and provide an extensive computational experiment with these algorithms using well know instances for the 2L-CVRP problem as well as new instances adapted from the Strip Packing problem.

An exact algorithm for the three-dimensional loading capacitated vehicle routing problem

The three-dimensional loading capacitated vehicle routing problem is a strong NP-hard problem. Most existing algorithms for the problem are heuristic or meta-heuristic algorithms. In this paper, an exact algorithm is proposed for the problem. For solving the loading sub-problem, we use an effective method to generate possible points for loading items, which greatly reduce the search scope. Then we proposed an exact algorithm witch iteratively calls a branch-and-bound algorithm based on set partition. The validity of the proposed algorithm is examined by comparing the present results with those of published algorithms using the same data.

A hybrid genetic algorithm for the vehicle routing problem with three-dimensional loading constraints

This paper addresses a Three-Dimensional Loading Capacitated Vehicle Routing Problem (3L-CVRP) which combines a three-dimensional loading problem and vehicle routing problem in distribution logistics. The problem requires the combinatorial optimization of a feasible loading solution and a successive routing of vehicles to satisfy client demands, where all vehicles must start and terminate at a central depot. In spite of its clear practical significance in the real world of distribution management, 3L-CVRP in literature is very limited for its high combinatorial complexity. We solve this problem by a hybrid approach which combines Genetic Algorithm and Tabu Search (GATS). Genetic algorithm is developed for vehicle routing and tabu search for three-dimensional loading, while these two algorithms are integrated for the combinatorial problem. We computationally evaluate this hybrid genetic algorithm on all publicly available test instances, and obtain new best solutions for several instances.

A hybrid approach for the vehicle routing problem with three-dimensional loading constraints

This paper addresses a recently practical combinatorial problem named Three-Dimensional Loading Capacitated Vehicle Routing Problem, which combines three-dimensional loading problem and vehicle routing problem in distribution logistics. The problem requires a combinatorial optimization of a feasible loading and successive routing of vehicles to satisfy customer demands, where all vehicles must start and finish at a central depot. The goal of this combinatorial problem is to minimize the total transportation cost while serving customers. Despite its clearly practical significance in the real world distribution management, for its high combinatorial complexity, published papers on this problem in literature are very limited.We present a hybrid approach which combines Honey Bee Mating Optimization and six loading heuristics, one for vehicle routing and the other for three-dimensional loading, to solve the integrated problem. We computationally evaluate this hybrid approach on all publicly available test instances, and obtain new best solutions for several scenarios.

A two-stage tabu search algorithm with enhanced packing heuristics for the 3L-CVRP and M3L-CVRP

The Three-Dimensional Loading Capacitated Vehicle Routing Problem (3L-CVRP) addresses practical constraints frequently encountered in the freight transportation industry. In this problem, the task is to serve all customers using a homogeneous fleet of vehicles at minimum traveling cost. The constraints imposed by the three-dimensional shape of the goods, the unloading order, item fragility, and the stability of the loading plan of each vehicle are explicitly considered. We improved two well-known packing heuristics, namely the Deepest-Bottom-Left-Fill heuristic and the Maximum Touching Area heuristic, for the three-dimensional loading sub-problem and provided efficient implementations. Based on these two new heuristics, an effective tabu search algorithm is given to address the overall problem. Computational experiments on publicly available test instances show our new approach outperforms the current best algorithms for 20 out of 27 instances. Our approach is also superior to the existing algorithm on benchmark data for the closely related problem variant M3L-CVRP (which uses a slightly different unloading order constraint compared to 3L-CVRP).

Heuristics and memetic algorithm for the two-dimensional loading capacitated vehicle routing problem with time windows

This work deals with a new combinatorial optimization problem, the two-dimensional loading capacitated vehicle routing problem with time windows which is a realistic extension of the well known vehicle routing problem. The studied problem consists in determining vehicle trips to deliver rectangular objects to a set of customers with known time windows, using a homogeneous fleet of vehicles, while ensuring a feasible loading of each vehicle used. Since it includes NP-hard routing and packing sub-problems, six heuristics are firstly designed to quickly compute good solutions for realistic instances. They are obtained by combining algorithms for the vehicle routing problem with time windows with heuristics for packing rectangles. Then, a Memetic algorithm is developed to improve the heuristic solutions. The quality and the efficiency of the proposed heuristics and metaheuristic are evaluated by adding time windows to a set of 144 instances with 15–255 customers and 15–786 items, designed by Iori et al. (Transport Sci 41:253–264, 2007) for the case without time windows.

A multi-start evolutionary local search for the two-dimensional loading capacitated vehicle routing problem

This paper addresses an extension of the capacitated vehicle routing problem where customer demand is composed of two-dimensional weighted items (2L-CVRP). The objective consists in designing a set of trips minimizing the total transportation cost with a homogenous fleet of vehicles based on a depot node. Items in each vehicle trip must satisfy the two-dimensional orthogonal packing constraints. A GRASP×ELS algorithm is proposed to compute solutions of a simpler problem in which the loading constraints are transformed into resource constrained project scheduling problem (RCPSP) constraints. We denote this relaxed problem RCPSP-CVRP. The optimization framework deals with RCPSP-CVRP and lastly RCPSP-CVRP solutions are transformed into 2L-CVRP solutions by solving a dedicated packing problem. The effectiveness of our approach is demonstrated through computational experiments including both classical CVRP and 2L-CVRP instances. Numerical experiments show that the GRASP×ELS approach outperforms all previously published methods.

Metaheuristics for vehicle routing problems with three-dimensional loading constraints

Abstract This paper addresses an important combination of three-dimensional loading and vehicle routing, known as the Three-Dimensional Loading Capacitated Vehicle Routing Problem. The problem calls for the combined optimization of the loading of freight into vehicles and the routing of vehicles along a road network, with the aim of serving customers with minimum traveling cost. Despite its clear practical relevance in freight distribution, the literature on this problem is very limited. This is because of its high combinatorial complexity. We solve the problem by means of an Ant Colony Optimization algorithm, which makes use of fast packing heuristics for the loading. The algorithm combines two different heuristic information measures, one for routing and one for packing. In numerical tests all publicly available test instances are solved, and for almost all instances new best solutions are found.

Heuristics for Two-Dimensional Loading Capacitated Vehicle Routing Problem with Time Windows

Abstract This work concerns the two-dimensional loading capacitated vehicle routing problem with time windows. We present for this problem two heuristics. The first one combines an adaptation of the constructive algorithm of Alvarez-Valdes et al. and the famous insertion heuristic of Solomon. The second heuristic uses the touching perimeter algorithm of Lodi et al. and the heuristic of Solomon. There exist two variants of the problem : unrestricted and sequential. We are interested in the unrestricted case, which is known to be NP-hard. To test the quality and the efficiency of the proposed heuristics, some test problems were created based on Iori et al. test problems. Preliminary results are presented and the two methods are compared.