An Adaptive Variable Neighborhood Search for a Heterogeneous Fleet Vehicle Routing Problem with Three-Dimensional Loading Constraints

An Australian company is faced with the logistics problem of distributing small quantities of fibre boards to hundreds of customers every day. The resulting Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-Dimensional Loading Constraints has to be solved within a single hour, hence the use of a heuristic instead of an exact method. In previous work, the loading was performed after optimising the routes, which in some cases generated infeasible solutions in need of a repair mechanism. In this work, the feasibility of the loading constraints is maintained during the route optimisation. Iterated Local Search has proved very effective at solving vehicle routing problems. Its success is mainly due to its biased sampling of locl optima. However, its performance heavily depends on the perturbation procedure. We trialled different perturbation procedures where the first one perturbs the given solution by moving deliveries that incur the highest cost on the objective function, whilst the second one moves deliveries that have been shifted less frequently by the local search in previous iterations. Our industry partner provided six sets of daily orders which have varied characteristics in terms of the number of customers, customer distribution, number of fibre boards and fibre boards’ sizes. Our investigations show that an instance becomes more constrained when the customer order contains many different board sizes, which makes it harder to find feasible solutions. The results show that the proposed perturbation procedures significantly enhances the performance of iterated local search specifically on such constrained problems.

A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints

A developed Tabu Search algorithm for heterogeneous fleet vehicle routing problem

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

In Southeast Asian cities, it is common for logistic companies to operate a heterogeneous fleet of delivery vehicles with motorcycles being the preferred vehicle to handle the final phase of delivery. In such scenarios, heterogeneous fleet vehicle routing problem (HFVRP) is generally applied to plan an optimal delivery. However, in many downtown cores of large and rapidly developing Southeast Asian cities, HFVRP is neither viable nor reliable because of road usage restrictions. The purpose of this article is to develop and test a different approach that accurately takes these restrictions into account and provides viable and more sustainable results. Restrictions in this paper refer to situations of urban areas in Vietnam where (i) certain vehicle types are prohibited in specified areas or where narrow alleyways limit the utilization of vehicles that exceed the road capacity and (ii) certain roads are exclusive to certain vehicle types. In networks, limited access and exclusive lanes are represented as links, or arcs, exclusive to one or another. Taking these limitations into consideration, we have developed a unique model, which we have termed Vehicle Routing Problem with Exclusive Links (VRP-EL). The model was validated and tested for its performance on scenarios with varying ratios of exclusive links. Scenarios up to 500 customers were tested on a meta-heuristic algorithm, simulated annealing. VRP-EL produces realistic outcomes. Limiting certain links to be selected according to vehicle types increases overall travel distance. However, this increase outweighs the cost of re-planning and rerouting had they not been constrained initially. The reduction in traveling distance leads to fossil fuel reduction for the overall system. The estimation of reduced carbon emissions through applying the proposed model is presented. Considering the severe traffic congestion and carbon emissions caused by motorcycles in Vietnam, the proposed model leads to a sustainable road environment.

Distribution is an action of supplying goods and services from one place to another. This company is an official agency which its main business is distributing subsidized Liquefied Petroleum Gas (LPG). Every day the company distributes to 29-agents that bounded by a company contract. The number of deliveries everyday varies depending on the agents’ demands. The company has 3 fleet vehicles, which are a six-wheel truck, 2 four-wheel trucks, and 2 three-wheel motorcycles. Those vehicles have different load capacity and some of them are able to distribute goods more than once in a day, therefore the company is facing Multiple Trips Heterogeneous Fleet Vehicle Routing Problem (MTHFVRP). At the moment the company does not know whether the vehicle routing they have now is the most effective and efficient. A solution is needed to determine a better distribution route in order to minimize the company's cost by using sweep algorithm to cluster all agents based on their vicinity. After clustering, establishment of distribution routes is created by using nearest neighbor algorithm with taking into account the minimum distance between the agents in order to produce an effective and efficient distribution route. Based on the result, distribution route created using sweep algorithm and nearest neighbor algorithm are able to generate effective and efficient distribution routes, so that the company can minimize the cost of current distribution route as much as 118,834.86 IDR/day or 2,852,036.64 IDR/month.

In pursuit of sustainable manufacturing and transportation paradigms, enterprises focus on ameliorating transportation costs while enhancing customer satisfaction by integrating forward and reverse logistics. However, existing research on sales-recycling models often overlooks constraints, leading to inaccuracies. This paper addresses this gap by introducing the 3L-MD-HFVRPSPD, a complex optimization challenge based on the Vehicle Routing Problem(VRP), which considers multiple depots, diverse vehicle fleets, dual stacking, simultaneous pick-up and delivery, and 3D loading limitations. A hybrid algorithm is formulated for problem resolution, employing the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) for vehicle routing and the heuristic Residual-Space-Optimized Algorithm (RSO) for load validation. Tests demonstrate that this approach outperforms traditional methods, delivering superior solutions more expeditiously.

The heterogeneous fleet vehicle routing problem with light loads and overtime: Formulation and population variable neighbourhood search with adaptive memory

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.

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.

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 vehicles while minimizing total travel distance. Compared with previous works which mainly focus on improving the performance of solving the routing problem, we propose a new least waste packing heuristic based approach for solving the loading subproblem, which is iteratively invoked by a simple tabu search algorithm for the routing. The proposed algorithm illustrates the state-of-the-art performance in terms of the solution quality and computational efficiency of our approach through the numerical experiments on the same test instances from literature.

The optimization of auto parts supply chain logistics plays a decisive role in the development of the automotive industry. To reduce logistics costs and improve transportation efficiency, this paper addresses the joint optimization problem of multi-vehicle pickup and delivery transportation paths under time window constraints, coupled with the three-dimensional loading of goods. The model considers mixed time windows, three-dimensional loading constraints, cyclic pickup and delivery paths, varying vehicle loads and volumes, flow balance, and time window constraints. Evaluation rules for the three-dimensional loading test of goods are also set, resulting in constructing a comprehensive optimization model for the inbound logistics of auto parts and components. In this study, a Greedy-Tabu Dual-Heuristic algorithm is proposed, which integrates an Improved Greedy Algorithm with an Enhanced Tabu Search Algorithm based on the -sampling strategy. The overall problem-solving process for the Improved Greedy Algorithm and the Tabu Search Algorithm is outlined. The superiority, efficiency, and stability of the improved algorithm are verified by solving cases of various sizes and analyzing the algorithm’s results before and after improvement. A case study involving the third-party logistics company R Enterprise compares the pickup and delivery-separated Milk-Run mode with the simultaneous delivery and pickup Milk-Run mode. The proposed method shows a 26.67% reduction in total distance traveled and a 46.60% decrease in waiting time compared to the traditional Milk-Run approach. Additionally, when evaluated against the standard 3D loading inspection method, the proposed approach improves average vehicle load utilization by 17% and vehicle volume utilization by 15%. These findings verify the applicability and superiority of the proposed algorithms and models in practical scenarios.

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.

Motivated by the so-called “Cloud Logistic”-concept as an innovative, line-based way for dealing with less than truck load (LTL) shipments in cooperation networks, this paper introduces a genetic algorithm as a heuristical approach for dealing with multi-objective optimization problems. Based on the implied optimization problem — the NP-hard multi-depot heterogeneous fleet vehicle routing problem with time windows and assignment restrictions (m-VRPTWAR) — four different optimization goals of the “CloudLogistic”-concept are introduced and a multi-step approach is motivated. Therefore, two different optimization steps are presented and transferred into a genetic algorithm. Additionally, two innovative problem-specific genetic operators are introduced by combining a generation-based approach and a usage-based approach in order to create a useful mutation process. A further usage-based approach is used to realize a problem-specific crossover operator. The presented genetic multi-step approach is a useful concept for dealing with multi-objective optimization problems without the need of a single combined fitness function.

To improve the efficiency of logistics distribution and balance the workload of drivers, this study introduces the standard deviation of workload time as an equilibrium measure and constructs a dual-objective mixed-integer programming model based on three-dimensional loading constraints to achieve the minimum total distance and workload balance. To solve the above model, a multi-stage hybrid algorithm is designed in this paper. Firstly, the clustering algorithm is used to effectively divide the distribution area, and then the non-dominated sorting genetic algorithm is used to solve the vehicle routing problem considering workload balance. At the same time, the constructive heuristic three-dimensional loading algorithm based on block loading is invoked to ensure the feasibility of cargo loading. Based on the historical data of a material flow distribution company, the feasibility of the constructed model and algorithm is verified. The research shows that the standard deviation of workload time can be reduced by 35.86%, and the average loading rate can be increased by 9.19% under the premise of increasing the distribution distance by only 1.6%. In addition, the proposed algorithm is compared with three other multi-objective optimization algorithms by constructing examples of different scales and using a series of standard example sets to verify its effectiveness and superiority.