The design of the layout of Vertical Lift Module (VLM) warehouses is a non-trivial process that involves selecting dimensions, internal configuration, and allocation of each tray to avoid space loss while satisfying logistic constraints. Our contribution in this context is a two-phase matheuristics –an algorithm that combines exact mathematical methods and heuristics– to simplify the design of VLMs layout. The proposed matheuristics relies on three Mixed-Integer Linear Programming models, addressing the internal configuration of trays and the allocation of trays into columns based on industrial logistic constraints. This approach requires as input parameters the items features, predetermined tray types with different dimensions, matheuristic settings, and a priority rule for tray allocation. The algorithm outputs to the logistics operator types and quantities of trays needed, internal partitioning, item positions in each tray, and tray positions in each column. Extensive testing demonstrates the effectiveness of our approach under realistic scenarios. Additionally, we introduce a comprehensive set of priority rules for allocating trays into columns, providing a comparison to assist logistics operators in selecting the most suitable for specific scenarios. Note to Practitioners—VLMs are closed structures composed of columns that house a variable number of sliding trays and a lift-mounted module that handles the trays. Their operation revolves around the so-called “goods to the man” principle, where goods are automatically brought to the operator using a dedicated access bay. This design ensures that stored items are easily accessible to operators, reducing time for order picking and improving workplace safety and ergonomics. Designing a VLM for logistics companies is a complex and time-consuming task since it requires optimizing a target objective while satisfying a large set of constraints. The current manual approach lacks automated methods and relies on experienced operators and iterative improvement processes. Our two-phase matheuristic algorithm automates VLMs layout configuration, addressing tasks from item placement to tray allocation within columns. The algorithm is versatile, considering various practical and logistic constraints, making it applicable in warehouse design decision support systems or engineering software.

In distribution logistics, the planning of vehicles’ routes and vehicles’ loads are traditionally managed separately, despite these activities are correlated. This often leads to various re-designs to make the routes and load plans compatible and applicable in practice. Moreover, the planned routes, which are static by definition, cannot always cope with unexpected events. Traffic congestion, vehicle failures, adverse meteorological conditions, and further undesired events can make the planned routes inapplicable and requirevehicles’ re-routing. This results in lower service levels, undesired delays, and higher costs for logistics companies. With the aim of overcoming the above limitations, this work proposes a novel approach based on a matheuristic algorithm that jointly solves the problem ofdelivery planninganddynamic vehicle routingto automate the delivery process in a logistics 4.0 perspective. The presented algorithm includes two different phases: the static phase, which is executed offline and in advance with respect to the delivery day, and the dynamic phase, which is executed in real-time to cope with unexpected events during the delivery. For the first phase, a matheuristic approach is defined to efficiently solve the combined vehicle routing and loading problems. Differently, for the second phase, a genetic algorithm is proposed to re-route vehicles in real-time, considering both the redefinition in real-time of the nominal trip and/or of the sequence of the customers to be visited. The algorithm is tested both on a literature benchmark and on a real dataset provided by an Italian logistics company. The obtained results show that, on the one hand, the proposed algorithm can automatically provide feasible solutions that minimise travel costs, total travelled distance, and empty space on the vehicles; on the other hand, it can ensure in real-time effective re-routing solutions in case of unexpected events occurring during delivery.Note to Practitioners—This work is motivated by the need for facilitating the operations of planning and routing deliveries in the external logistics sector. We propose an algorithm that automatically generates feasible routing and loading plans for a set of Transport Units (TUs) (i.e., the static phase), and then updates in real-time the nominal route in case of unexpected events (i.e., the dynamic phase). More specifically, the first phase of the algorithm takes as input the set of different clients, the list of products packed into bins (i.e., standard packing units) to be delivered to each client, and the set of transport units available for the deliveries, and provides as output the number and type of TUs to be used, the composition of the bins in each transport unit, and the corresponding route, while optimising the space occupation in each TU and the travel costs. The second phase, instead, takes as input the nominal routes computed in the first phase and, in case of unexpected events (e.g., accidents, slowdowns, etc.) affecting one or more routes, it re-routes the involved trucks guaranteeing the maximum efficiency in regards to travel cost, travel time, and quality of service. The adoption of this algorithm by logistic companies supports the automation of the delivery process and drastically improves the efficiency of logistic operations, with particular regard to the number of used TUs, costs, safety of goods, and customers’ satisfaction.

Last-mile delivery is one of the most discussed problems of the last decade due to the growing importance of e-commerce and the development of Industry 4.0. In particular, this problem regards the delivery of parcels from the warehouse to the final customers. In order to bring efficiency and innovation, in this paper a hybrid delivery architecture is considered, which takes advantage of the combined use of a drone and a truck to perform a sequence of pick-ups and deliveries, and the problem of optimal control of the drones' missions is addressed. The reference scenario is the smart city where the drone of the hybrid delivery architecture is in charge of three different pick-up and delivery missions: truck to point (i.e., pick-up from the truck and delivery to the customer), point to point (i.e., delivery to a customer and pick-up from the subsequent customer), and point to truck (i.e., reentry from a customer to the truck). From the control point of view, the drone is optimally guided in all the operating modes, i.e., ascent and descent from/to truck mode, free flight mode with/without payload, and descent for pick-up/delivery mode, by a receding horizon linear quadratic regulator (LQR), which is able to manage the drone in the dynamic landing on a movable vehicle and to allow the changing in real time of the landing point on the truck. Simulation results of the truck-drone delivery architecture are presented and discussed in detail, proving the effectiveness of the proposed method.

The increasing demand for freight transport requires logistic companies to improve their competitiveness by ensuring high service levels at limited costs. This paper investigates the problem of defining delivery plans with the aim to support logistic companies in reducing planning times and freight delivery costs. In delivery planning, given a set of delivery requests, both the routes and load configurations of Transport Units (TUs) are to be established. In the literature, this problem is defined as Three-dimensional Loading Capacitated Vehicle Routing Problem with Time Windows (3LCVRPTW). However, these problems are generally tackled separately and referred to as the vehicle routing problem and the container loading problem, respectively. Moreover, only a few contributions present solution approaches for real logistic systems, and these methods are mainly based on heuristics. In this work, we define a novel matheuristic algorithm for the integrated solution of the vehicle routing problem and container loading problem. The proposed method is suitable for real logistic applications and combines the advantages of exact solutions with the rapidity of heuristics. The approach aims at minimizing the total travel costs and the clients’ time windows violations in the routes’ definition, while optimizing the configuration of the cargo inside each TU. The developed matheuristic algorithm is tested both on a well-known literature benchmark and on a real dataset provided by the Italian company Elettric80. The obtained results show that the proposed method succeeds in determining in a short computational time both feasible routes and loading plans, minimizing the related costs while fulfilling logistics constraints.

In this paper, we address the problem of automating the definition of feasible pallets configurations. This issue is crucial for the competitiveness of logistic companies and is still one of the most difficult problems in internal logistics. In fact, it requires the fast solution of a three-dimensional Bin Packing Problem (3D-BPP) with additional logistic specifications that are fundamental in real applications. To this aim, we propose a matheuristics that, given a set of items, provides feasible pallets configurations that satisfy the practical requirements of items’ grouping by logistic features, load bearing, stability, height homogeneity, overhang as well as weight limits, and robotized layer picking. The proposed matheuristics combines a mixed integer linear programming (MILP) formulation of the 3D-Single Bin-Size BPP (3D-SBSBPP) and a layer building heuristics. In particular, the feasible pallets configurations are obtained by sequentially solving two MILP sub-problems: the first, given the set of items to be packed, aims at minimizing the unused space in each layer and thus the number of layers; the latter aims at minimizing the number of shipping bins given the set of layers obtained from the first problem. The approach is extensively tested and compared with existing approaches. For its validation we use both realistic data-sets drawn from the literature and real data-sets, obtained from an Italian logistics leader. The resulting outcomes show the effectiveness of the method in providing high-quality bin configurations in short computational times.Note to Practitioners—This work is motivated by the intention of facilitating the transition from Logistics 3.0 to Logistics 4.0 by providing an effective tool to automate bin packing, suitable for automated warehouses. On the one hand, the proposed technique provides stable and compact bin configurations in less than half a minute per bin on average, despite the high computational complexity of the 3D-SBSBPP. On the other hand, the approach allows to consider compatibility constraints for the items (e.g., final customer and category of the items), and the use of robotized layer picking in automated warehouses. In effect, layers composed by only one type of items (i.e., monoitem layers) can be directly picked and placed on the pallet by a robotic arm without the intervention of any operator. Consequently, the adoption of this approach in warehouses could drastically improve the efficiency of the packing process.