Three-dimensional Loading Constraints Research Articles

生鲜农产品冷链集货车辆路径与货物配载联合优化研究

As a bridge connecting agricultural production and consumption, the circulation of agricultural products has the function of connecting supply and demand, guiding production and promoting consumption. However, the development of rural logistics in China is slow, and most logistics centers still rely on experience to plan the pick-up vehicle routings, resulting in long transport time and high cost. In order to improve the efficiency of pick-up and reduce transportation costs, a joint optimization model of cold-chain pick-up vehicle routing and cargo allocation for fresh agricultural products was proposed in this study. Soft time window constraint and three-dimensional loading constraints were considered, and the lowest pick-up cost was used as optimization goals in this model. In addition, adaptive large neighborhood search algorithm (ALNS) and heuristic depth-first search algorithm (HDFS) were combined to solve the model. A case study of Kunming International Flower Auction Center was conducted to compare the schemes of pick-up vehicle routing before and after optimization. Results demonstrate that the pick-up cost after optimization decreases by 9.6 %, the number of vehicles decreases by one, the total volume utilization rate of vehicles increases by 23 %, and the total load utilization rate of vehicles increases by 15 %. This study provides a model reference and solution method for enterprise operators to formulate schemes of pick-up vehicle routing quickly and reasonably.

The split delivery vehicle routing problem with time windows and three-dimensional loading constraints

The split delivery vehicle routing problem with time windows and three-dimensional loading constraints

Value of Cargo Pooling in On-Demand Intra-City Freight Logistics

On-demand intra-city freight logistics (ICFL) has recently emerged as a new freight service, where shippers can submit their shipping requests using smartphones and be matched to drivers in real time based on their locations and drivers’ availability. A major challenge faced by on-demand ICFL platforms is the shortage of vehicles during peak demand periods. Cargo pooling, the cargo version of carpooling, offers as a promising way to increase supply: cargoes heading in the same direction would share the cargo compartment of the same vehicle and be serviced simultaneously, which is achieved by careful sequencing of the pickup and delivery locations of the cargoes. We investigate models for cargo pooling for on-demand ICFL and quantify its benefit, which is new to the literature. The major difference between existing studies on ICFL and ours is that we no longer assume that demands are known beforehand. Instead, the demands arrive gradually throughout the day and we need to periodically match requests to drivers and re-optimize vehicle routes. We formulate the matching problem as a dynamic pickup and delivery problem with three-dimensional loading and time window constraints. To solve this model, we develop an algorithm based on large neighborhood search and tree search. The algorithm is tested with real freight data in a city in the Yangtze River Delta. Results show that the algorithm can reduce the total cost by 21.4% and reduce the total vehicle miles traveled by 36.0%.

Pickup capacitated vehicle routing problem with three-dimensional loading constraints: Model and algorithms

This study addresses the pickup capacitated vehicle routing problem with three-dimensional loading constraints (3L-PCVRP), which combined the container loading problem (CLP) and the capacitated vehicle routing problem (CVRP). A mixed-integer linear programming model for 3L-PCVRP is designed with the objective of minimizing the total transportation cost. The basic constraints of CLP and CVRP as well as the practical constraints imposed by the pickup operations are incorporated in 3L-PCVRP. An improved branch-and-price-based (B&P) algorithm is proposed to solve 3L-PCVRP. The 3L-PCVRP model is decomposed into the restricted master problem (RMP) for selecting routes and the subproblem (SP) for generating routes that satisfy the loading and routing constraints. A label-correcting-based algorithm (LCA) is presented to solve the SP, which employs a two-stage method and two enhanced loading algorithms to ensure the loading feasibility of the routes. The two loading algorithms (tree search and greedy heuristic algorithms) are improved by a new evaluation function and an improved space-merging method. The two-stage method is designed to call the two loading algorithms at different frequencies to investigate the route feasibility accurately and efficiently. Numerical experiments are designed to test the performance of the proposed algorithms. The efficiency and effectiveness of the improved loading algorithms are demonstrated in hundreds randomly generated instances. For small-scale 3L-PCVRP instances, the B&P algorithm can generate solutions that are not worse than those of the solver within 0.14% of the solver’s running time. The efficiency and effectiveness of the improved B&P algorithm are also validated in large-scale benchmark instances.

Modelling and heuristically solving three-dimensional loading constrained vehicle routing problem with cross-docking

Cross-docking is a logistics strategy widely applied in numerous enterprises, where vehicle scheduling is one of the most important factor in operational level for cost reduction. In sight of the widespread applications of the three-dimensional loading on the vehicle scheduling, this study addresses a vehicle routing problem with cross-docking and three-dimensional loading constraints (3L-VRPCD). A relaxation mixed integer linear programming (MILP) model is proposed for solving the 3L-VRPCD. In order to effectively solve large-scale 3L-VRPCD instances, a hybrid heuristic algorithm is then proposed, which combines adaptive large neighbourhood search (ALNS) and multi-order local search packing (LSP) algorithm. In addition, a storage-pool-based strategy is integrated into the proposed algorithm for efficiency enhancement. A large number of 3L-VRPCD instances with wide-ranging properties are generated to test the feasibility and effectiveness of the proposed MILP model and heuristic method. Experimental results demonstrate remarkable advantages of the proposed heuristic over the MILP-based method with respect to solution quality and computational efficiency, especially for medium to large-scale instances. Meanwhile, the results verify that the proposed storage-pool-based strategy is capable of accelerating the search process and reducing the computational burden of the heuristic. Furthermore, the impacts of different properties (e.g., loading conditions) on the solution of 3L-VRPCD have been analysed and discussed.

Optimization of Simultaneous Pickup and Delivery Vehicle Routing with Three-Dimensional Balanced Loading Constraints

In order to promote the cost reduction and efficiency improvement of the logistics distribution process and to guarantee the safety of goods transportation, this paper studies the portfolio optimization of goods loading and the problem of simultaneous pickup and delivery vehicle routing. A balanced loading constraint was introduced to restrict loading through two aspects of axle weight bearing and lateral center-of-gravity offset. With the shortest total route length as the objective, this paper constructs a simultaneous pickup and delivery vehicle routing model with three-dimensional (3D) balanced loading constraints (3BL-VRPSPD). Additionally, a hybrid tabu search (TS) algorithm embedded loading test was proposed to solve this problem. Firstly, a heuristic insertion method was applied to determine the initial routing scheme, and the node swapping and relocation operators were designed to construct the tabu neighborhood scheme for routing optimization. On this basis, the 3D balanced loading was incorporated into the routing iteration process. A balanced loading algorithm, combining multiple-indicator ordering and maximum space division strategies (MOMD), was formulated to develop a 3D-balanced loading plan for goods with a pickup and delivery vehicle routing scheme. Finally, standard instances verified the effectiveness of the method. The results show that the proposed method can effectively optimize 3BL-VRPSPD and outperform other algorithms.

Logistics Distribution Vehicle Routing Problem with Time Window under Pallet 3D Loading Constraint

As an important support of the e-commerce industry, the express delivery industry is particularly important in national development. Low loading rates caused by numerous types of containers and cost increases caused by low loading and unloading efficiency are still remaining issues in the process of goods delivery and packing. This study introduced the pallet with telescopic support height as the middle to address these issues and proposed a distribution scheme based on the constraints of three-dimensional pallet loading with a time window. First, combining the path optimization of the time window and cargo loading, a solution model was established to solve the existing express delivery problem with the lowest total delivery cost and the highest average vehicle loading rate. In addition, the multi-objective problem was transformed through the multi-objective linear weighting method. Second, we cluster the customer nodes. In order to solve the large number of gaps generated by the hierarchy theory, we adopt the descending order of cargo volume as the initial sequence and design the coding and decoding for path optimization and pallet loading, solving the problem through the simulated anneal-genetic algorithm. Finally, the effectiveness of the algorithm is obtained through the comparison with other algorithms and the simple three-dimensional loading and distribution scheme by using examples. It is proved that the optimization of three-dimensional packing for express delivery using pallets as carriers can not only meet the high loading rate but also improve the loading and unloading speed, reduce the time penalty cost, and improve the operability of loading. This paper provides decision reference and method support for path optimization under three-dimensional loading constraints.

Use of heuristic methods for the optimisation of truck loading in a steel company

The correct layout of goods, objects or cargo, in the container's available space is considered a complex task. The study was motivated by the need to implement a solution to optimise container use in a steel industry company in the South of Brazil. This article has contributed to synthesising research on the three-dimensional container loading problem, highlighting classifications, constraints, and algorithms used in its resolution. A framework is presented and may be used as a road map for practical implementation as used in this research. As a practical contribution, this article presents several instances of one actual case application. Results showed reducing of formatting loads processing time in comparison with the traditional company approach.

A clustering-based extended genetic algorithm for the multidepot vehicle routing problem with time windows and three-dimensional loading constraints

Since the multidepot vehicle routing problem with time windows and three-dimensional loading constraints (MDVRPTW-TDLC) is a multiconstraint and combinatorial optimization problem, this study proposes a resource sharing scheme on the basis of customer clustering to achieve a balance of spatial resource spatial distributions, thereby reducing the operating costs in a collaborative multidepot logistics network. Moreover, this study proposes a vehicle compartment partition strategy based on cargo characteristics such as type and sizes to increase vehicle loading rates, after which the proposed MDVRPTW-TDLC is formulated as a bi-objective mixed-integer programming model to minimize the total operating costs while maximizing the average loading rate of vehicles. Subsequently, a two-stage hybrid algorithm combining a three-dimensional (3D) k-harmonic means clustering algorithm and extended nondominated sorting genetic algorithm-II (ENSGA-II) is developed to find the Pareto optimal solutions and solve the MDVRPTW-TDLC optimization model, followed by an introduction of the 3D k-harmonic means clustering algorithm to cluster customers, thereby reducing computational complexity. The proposed ENSGA-II, integrating the improved Clarke–Wright savings algorithm and NSGA-II is then used to obtain the final optimal solutions, followed by the application of a selective exchange mechanism between the clustering algorithm and ENSGA-II to enhance the global and local optimization capability, enabling fast and efficient computation of optimal solutions. Based on our investigations revealed through an algorithm comparison using the multiobjective harmony search algorithm, multiobjective evolution algorithm, multiobjective particle swarm optimization, monarch butterfly optimization, Runge Kutta optimizer, and Harris hawks optimization, ENSGA-II demonstrates better performance in reaching high-quality objective function values. Finally, a real-world case study of Chongqing City, China is employed to verify the efficiency of the proposed model and optimization algorithm, after which a comparison of the optimization results among different vehicle compartment partition strategies demonstrates the efficiency of the proposed method. We also discuss 16 scenarios with and without the vehicle compartment partition strategy with computational results showing an improved vehicle loading rate and reduced logistics operating costs with the adopted vehicle compartment partition strategy. Therefore, our results confirm that the proposed MDVRPTW-TDLC can facilitate the sustainable development of logistics operations, and providing decision support for constructing intelligent logistics systems smart cities.

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.

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

This paper proposes a matheuristic algorithm based on a column generation structure for the capacitated vehicle routing problem with three-dimensional loading constraints (3L–CVRP). In the column generation approach, the master problem is responsible for managing the selection of best-set routes. In contrast, the slave problem is responsible for solving a shorter restricted route problem (CSP, Constrained Shortest Path) for generating columns (feasible routes). The CSP is not necessarily solved to optimality. In addition, a greedy randomized adaptive search procedure (GRASP) algorithm is used to verify the packing constraints. The master problem begins with a set of feasible routes obtained through a multi-start randomized constructive algorithm (MSRCA) heuristic for the multi-container loading problem (3D–BPP, three-dimensional bin packing problem). The MSRCA consists of finding valid routes considering the customers' best packing (packing first-route second). The efficiency of the proposed approach has been validated by a set of benchmark instances from the literature. The results show the efficiency of the proposed approach and conclude that the slave problem is too complex and computationally expensive to solve through a MIP.

The split heterogeneous vehicle routing problem with three-dimensional loading constraints on a large scale

This paper introduces a complex real-world problem on a large scale that combines the split delivery heterogeneous vehicle routing problem with three-dimensional loading and considers new routing and loading constraints. The problem aims to find a set of routes with minimum transportation cost by satisfying the demand of all customers and loading constraints. We propose a column generation-based heuristic algorithm that employs three heuristic algorithms to solve the subproblem and a hybrid algorithm for loading. Computational experiments on the literature instances indicate that the proposed algorithm can produce very near solutions to the literature algorithm's solutions in significantly shorter running times. This paper introduces real-world instances with 230 to 850 customers, several times larger than the existing benchmarks. The results of the proposed algorithm for real-world instances are effective, and compared to the current situation, it leads to a reduction of 20% in the average total cost of transportation. Also, the average number of vehicles is reduced by 36%.

Vehicle routing problem with three-dimensional loading constraints: Experimentations and evaluation

Abstract This paper treats the integration of 3D loading constraints in Vehicle Routing Problems (VRP) and highlights its impact on the feasibility of VRP solutions. The Heterogeneous Fleet Vehicle Routing Problems (HFVRP) is the variant of the VRP class problem that is the subject of this study. Its objective is to construct a set of vehicle routes in order to minimize the sum of the costs. A brief overview of the most practical loading constraints is presented as well as our proposed approach to solve the considered problem. Besides, experimentations on some benchmark instances were performed to prove the efficiency of our algorithm, which has led to very good results. Finally, an evaluation is addressed to show the impact of considering 3D loading constraints when solving a vehicle routing problem.

A Double Traveling Salesman Problem With Three-Dimensional Loading Constraints for Bulky Item Delivery

This article considers bulky item delivery problems in which multiple items are retrieved and loaded onto a vehicle from different warehouses and then delivered. This problem is described as a double traveling salesman problem with three-dimensional container loading constraints with multiple stacks. The double TSP with multiple stacks is used to determining the shortest route performing pickups and deliveries in two separated networks (one for pickups and one for deliveries) using only one container. Repacking is not allowed after loading the items into the container. An integer linear programming model is proposed to solve this problem, a standard genetic algorithm and an improved genetic algorithm is designed. In the improved genetic algorithm, a Lin-Kernighan algorithm is used to improve the delivery route, a k-means clustering algorithm, and a heuristic packing scheme improvement rules work together to improve the loading route. The results show that the improved genetic algorithm is superior to the standard genetic algorithm in large scale problems.

The Split Delivery Vehicle Routing Problem with Three-Dimensional Loading and Time Windows Constraints

Besides routing and packing plans, synthetically considering the requirements of customers about service time is absolutely necessary. An order split delivery plan can not only better satisfy the service time requirements, but also improve the full-load rate of vehicles. The split delivery vehicle routing problem with three-dimensional loading constraints (3L-SDVRP) combines vehicle routing and three-dimensional loading with additional packing constraints. In the 3L-SDVRP splitting deliveries of customers is basically possible, i.e., a customer can be visited in two or more tours. The vehicle routing problem with three-dimensional loading constraints that are based on the time window and considering split delivery of orders (3L-CVRPTWSDO) and its optimization algorithm are studied in this paper. We established mathematical model of the problem and designed the tabu search algorithm. Based on the examples used in Gendreau et al. (2006), examples was constructed to test our algorithm. The experimental results have expressed that, in the 3L-CVRP problem, the results of split delivery is better than those of non-split delivery, and it is easier to satisfy the time window constraints. The algorithm in this paper generates high quality solutions, it provides a effective method to solve the 3L-CVRPTWSDO problems.

A hybrid algorithm for the vehicle routing problem with three-dimensional loading constraints and mixed backhauls

In this paper, a variant of the vehicle routing problem with mixed backhauls (VRPMB) is presented, i.e. goods have to be delivered from a central depot to linehaul customers, and, at the same time, goods have to be picked up from backhaul customers and brought to the depot. Both types of customers can be visited in mixed sequences. The goods to be delivered or picked up are three-dimensional (cuboid) items. Hence, in addition to a routing plan, a feasible packing plan for each tour has to be provided considering a number of loading constraints. The resulting problem is the vehicle routing problem with three-dimensional loading constraints and mixed backhauls (3L-VRPMB). The simultaneous transport of linehaul and backhaul items presents a particular challenge of the problem. We consider two different loading variants in order to avoid any reloading during the tour: (i) rear loading with separate linehaul and backhaul sections and (ii) loading at a long side. In order to solve the problem, we propose a hybrid metaheuristic consisting of a reactive tabu search for the routing problem and different packing heuristics for the loading problem. Numerical experiments are reported with benchmark instances from the literature for the one-dimensional VRPMB to examine the performance of the routing algorithm and with newly generated instances for the 3L-VRPMB.

The Split Delivery Vehicle Routing Problem with three-dimensional loading constraints

The Split Delivery Vehicle Routing Problem with three-dimensional loading constraints (3L-SDVRP) combines vehicle routing and three-dimensional loading with additional packing constraints. In the 3L-SDVRP splitting deliveries of customers is basically possible, i.e. a customer can be visited in two or more tours. We examine essential problem features and introduce two problem variants. In the first variant, called 3L-SDVRP with forced splitting, a delivery is only split if the demand of a customer cannot be transported by a single vehicle. In the second variant, termed 3L-SDVRP with optional splitting, splitting customer deliveries can be done any number of times. We propose a hybrid algorithm consisting of a local search algorithm for routing and a genetic algorithm and several construction heuristics for packing. Numerical experiments are conducted using three sets of instances with both industrial and academic origins. One of them was provided by an automotive logistics company in Shanghai; in this case some customers per instance have a total freight volume larger than the loading space of a vehicle. The results prove that splitting deliveries can be beneficial not only in the one-dimensional case but also when goods are modeled as three-dimensional items.

A hybrid algorithm for the vehicle routing problem with backhauls, time windows and three-dimensional loading constraints

This paper deals with a special vehicle routing problem with backhauls where customers may want to receive items from a depot and, at the same time, return items back to the depot. Moreover, time windows are assumed and three-dimensional loading constraints are to be observed, i.e. the items are three-dimensional boxes and packing constraints, e.g. regarding load stability, are to be met. The resulting problem is the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), time windows and three-dimensional loading constraints (3L-VRPSDPTW). This problem occurs, for example, if retail stores are supplied by a central warehouse and wish to return packaging material. A particular challenge of the problem consists of transporting delivery and pickup items simultaneously on the same vehicle. In order to avoid any reloading effort during a tour, we consider two different approaches for loading the vehicles: (i) loading from the back with separation of the loading space into a delivery section and a pickup section and (ii) loading from the (long) side. A hybrid algorithm is proposed for the 3L-VRPSDPTW consisting of an adaptive large neighbourhood search for the routing and different packing heuristics for the loading part of the problem. Extensive numerical experiments are conducted with VRPSDP instances from the literature and newly generated instances for the 3L-VRPSDPTW.

An Heuristic Approach to Solving the one-to-one Pickup and Delivery Problem with Threedimensional Loading Constraints

An Heuristic Approach to Solving the one-to-one Pickup and Delivery Problem with Threedimensional Loading Constraints

Solving the pickup and delivery problem with three-dimensional loading constraints and reloading ban

In this paper, we extend the classical Pickup and Delivery Problem (PDP) to an integrated routing and three-dimensional loading problem, called PDP with three-dimensional loading constraints (3L-PDP). We are given a set of requests and a homogeneous fleet of vehicles. A set of routes of minimum total length has to be determined such that each request is transported from a loading site to the corresponding unloading site. In the 3L-PDP, each request is given as set of rectangular boxes and the vehicle capacity is replaced by a 3D loading space.This paper is the second one in a series of articles on 3L-PDP. As in the first paper we are dealing with constraints which guarantee that no reloading effort will occur. Here the focus is laid on the reloading ban, a packing constraint that ensures identical placements of same boxes in different packing plans. The reloading ban allows for better solutions in terms of travel distance than a routing constraint that was used in the first paper to preclude any reloading effort. To implement this packing constraint a new type of packing procedure is needed that is capable to generate a series of interrelated packing plans per route. This packing procedure, designed as tree search algorithm, and the corresponding concept of packing checks is the main contribution of the paper at hand. The packing procedure and a large neighborhood search procedure for routing form a hybrid algorithm for the 3L-PDP. Computational experiments were performed using 54 3L-PDP benchmark instances.