A Greedy Tabu Dual Heuristic algorithm for the cyclic pickup and delivery problem with 3D loading constraints

The paper addresses the heterogeneous fleet vehicle routing problem with three-dimensional (3D) loading constraints (3L-HFVRP), a new practical variant of the combined routing and loading problem. In this problem, the loads consist of a set of three-dimensional, rectangular shaped items. The fleet is composed of heterogeneous vehicles with different weight and space capacities. The objective is to serve all customers by selecting a set of vehicles such that the total transportation cost is minimized. The cost consists of the fixed cost of the selected vehicles and their travel cost. In addition, loading sequence related constraints frequently encountered in realistic applications are respected when loading and unloading the items. To solve this challenging problem, we develop an adaptive variable neighborhood search (AVNS) which utilizes an extreme point based first fit heuristic to find a feasible loading pattern for each route. We design two strategies to accelerate the loading and routing processes. The Trie data structure is used to record the loading information of routes already visited and to control the computational effort spent for each route. The Fibonacci heap data structure is used to maintain all of the possible moves and vehicle type assignments, which avoids the duplicated evaluation of some moves and unnecessary loading check of unpromising solutions. The robustness and effectiveness of the proposed algorithm is validated by computational tests performed both on some newly generated 3L-HFVRP instances and well-known benchmark instances from the literature for two simplified VRP variants: the capacitated vehicle routing problem with 3D loading constraints (3L-CVRP) and the pure heterogeneous fleet vehicle routing problem (HFVRP). The numerical experiments show that the proposed AVNS outperforms other algorithms in 3L-CVRP and improves several best known solutions reported in the literature. The results obtained for the pure HFVRP are very close to the best known solutions.

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.

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

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.

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.

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.

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.

We propose a model for solving a parcel delivery problem with a fleet of trucks embedded with drones. When appropriate, drones are loaded with a parcel, launched directly from the truck, and sent to a client. Afterward, the drones autonomously return to the truck to be replenished and recharged. Inspired by the case of a large European logistics provider, the proposed modeling framework confronts realistic delivery problems involving time windows, limited drone autonomy, and the eligibility of clients to be served by drones. The considered global cost function includes fixed daily vehicle fares, driver wages, and the fuel and electricity consumption to power trucks and drones. To solve the problems at hand, we propose a mixed‐integer linear programming formulation and an adaptive large neighborhood search. Moreover, we introduce an efficient modeling framework to manage the numerous synchronization constraints induced by the simultaneous use of trucks and drones. We analyze the benefits of this new transportation concept for delivery problems involving up to 100 parcels. Results show that truck‐and‐drone solutions can reduce costs up to 34% compared to traditional truck‐only delivery. From a managerial perspective, we show that a certain percentage of client locations must be reachable by drone to make truck‐and‐drone solutions competitive (i.e., if the fixed costs of the drones are compensated for by the savings on truck routes) and compare the cost structures of truck‐and‐drone versus truck‐only solutions.

A Last Mile Delivery Problem with Multitrip and Time Window Constraints in E-Logistics

A vehicle routing problem with pickup and delivery time windows, and coordination of transportable resources

This paper provides a green vehicle routing problem with simultaneous pickup and delivery with time windows. The objective of this study is to minimize total costs including fuel cost and carbon emission cost while satisfying customer pickup and delivery demands simultaneously with time windows and capacity constraints. In this paper, fuel consumption is computed considering vehicle load and distance. Firstly, a mathematical model is developed to describe the VRPSPDTW problem. This study proposes a genetic algorithm to optimize cost. The computational experiments are conducted under three crossover (one point, two point and cyclic crossover) and two mutation (swap and inverse) operator. The computation between swap and inverse mutation under three crossover are compared and the results show that swap mutation perform better than inverse mutation under every crossover operator.

Minimizing fuel consumption and carbon emissions through vehicle routing is a critical objective for logistics companies, especially in light of stringent greenhouse gas emission policies enforced by various countries. To address this challenge, numerous studies have proposed robust vehicle routing problem models. Many of these focus on heterogeneous vehicle routing with time window constraints, aiming to reduce fuel consumption and emission costs. However, most research treats delays in customer time windows merely as penalty costs, giving limited attention to the impact of these delays on CO 2 emissions and their associated costs. Such delays—often caused by traffic congestion and rerouting—are significant contributors to excess CO 2 emissions. This paper addresses this overlooked aspect by proposing a model that accounts for the additional fuel consumption and CO 2 emissions resulting from delayed deliveries. It explores uncertainty in delivery schedules by analyzing three critical traffic scenarios: (1) vehicles idling in standstill traffic, (2) vehicles moving in slow traffic, and (3) vehicles being rerouted because of traffic uncertainties—all of which exacerbate CO 2 emissions from late deliveries. We propose a heterogeneous vehicle routing problem with carbon penalty, which optimizes routing to minimize CO 2 emissions for both on-time and delayed deliveries. A mathematical model and a robust genetic algorithm are developed, with their effectiveness validated through practical scenarios. The results offer valuable insights for logistics providers seeking to enhance both sustainability and operational efficiency.

One-to-one Pickup and Delivery Problem (PDP) with loading constraints is studied. Mathematical model is presented using combinatorial configurations approach for pickup and delivery and the phi-function technique for loading constraints. Two-stage solution strategy is used. The first stage has two levels: a) clustering the set of pickup and delivery points regarding to the set of vehicles and b) solving the PDP problem with 3D loading constraints for each vehicle within the appropriate cluster. The second stage improves the solution found at the previous stage and is based on the cyclic transfer approach and cyclic permutations. Computational results are presented to support efficiency of the approach.

In the near future, gasoline-fueled vehicles are expected to be replaced by electrical vehicles (EVs) to save energy and reduce carbon emissions. A large penetration of EVs threatens the stability of the electric grid but also provides a potential for grid ancillary services, which strengthens the grid, if well managed. This paper incorporates grid-to-vehicle (G2V) and vehicle-to-grid (V2G) options in the travel path of logistics sector EVs. The paper offers a complete solution methodology to the multivariant EV routing problem rather than considering only one or two variants of the problem like in previous research. The variants considered include a stochastic environment, multiple dispatchers, time window constraints, simultaneous and nonsimultaneous pickup and delivery, and G2V and V2G service options. Stochastic demand forecasts of the G2V and V2G services at charging stations are modeled using hidden Markov model. The developed solver is based on a modified custom genetic algorithm incorporated with embedded Markov decision process and trust region optimization methods. An agent-based communication architecture is adopted to ensure peer-to-peer correspondence capability of the EV, customer, charging station, and dispatcher entities. The results indicate that optimal route for EVs can be achieved while satisfying all constraints and providing V2G ancillary grid service.