Mathematical models for multicontainer loading problems

This paper deals with the problem of a distribution company that has to serve its customers by putting first the products on pallets and then loading the pallets onto trucks. We approach the problem by developing and solving integer linear models. We start with basic models, that include the essential features of the problem, such as respecting the dimensions of the truck, and not exceeding the total weight capacity and the maximum weigh capacity on each axle. Then, we add progressively new conditions to consider the weight and volume of pallet bases and to include other desirable features for the solutions to be useful in practice, such as the position of the center of gravity and the minimization of the number of pallets.The models have been tested on a large set of real instances involving up to 46 trucks and kindly provided to us by a distribution company. The results show that in most cases the optimal solution can be obtained in small running times. Moreover, when optimality cannot be proven, the gap is very small, so we obtain high quality solutions for all the instances that we tested

Axle Weights in Combined Vehicle Routing and Container Loading Problems

Overloaded axles not only lead to increased erosion on the road surface, but also to an increased braking distance and more serious accidents due to higher impact energy. Therefore, the load on axles should be already considered during the planning phase and thus before loading the truck in order to prevent overloading. Hereby, a detailed 2D or 3D planning of the vehicle loading space is required. We model the Axle Weight Constraint for trucks with and without trailers based on the Science of Statics. We include the Axle Weight Constraint into the combined Vehicle Routing and Container Loading Problem ("2L-CVRP" and "3L-CVRP"). A hybrid approach is used where an outer Adaptive Large Neighbourhood Search tackles the routing problem and an inner Deepest-Bottom-Left-Fill algorithm solves the packing problem. Moreover, to ensure feasibility, we show that the Axle Weight Constraint must be checked after each placement of an item. The impact of the Axle Weight Constraint is also evaluated.Overloaded axles not only lead to increased erosion on the road surface, but also to an increased braking distance and more serious accidents due to higher impact energy. Therefore, the load on axles should be already considered during the planning phase and thus before loading the truck in order to prevent overloading. Hereby, a detailed 2D or 3D planning of the vehicle loading space is required. We model the Axle Weight Constraint for trucks with and without trailers based on the Science of Statics. We include the Axle Weight Constraint into the combined Vehicle Routing and Container Loading Problem ("2L-CVRP" and "3L-CVRP"). A hybrid approach is used where an outer Adaptive Large Neighbourhood Search tackles the routing problem and an inner Deepest-Bottom-Left-Fill algorithm solves the packing problem. Moreover, to ensure feasibility, we show that the Axle Weight Constraint must be checked after each placement of an item. The impact of the Axle Weight Constraint is also evaluated

Multi-objective vehicle routing and loading with time window constraints:a real-life application

Motivated by a real-life application, this research considers the multi-objective vehicle routing and loading problem with time window constraints which is a variant of the Capacitated Vehicle Routing Problem with Time Windows with one/two-dimensional loading constraints. The problem consists of routing a number of vehicles to serve a set of customers and determining the best way of loading the goods ordered by the customers onto the vehicles used for transportation. The three objectives pertaining to minimisation of total travel distance, number of routes to use and total number of mixed orders in the same pallet are, more often than not, conflicting. To achieve a solution with no preferential information known in advance from the decision maker, the problem is formulated as a Mixed Integer Linear Programming (MILP) model with one objective—minimising the total cost, where the three original objectives are incorporated as parts of the total cost function. A Generalised Variable Neighbourhood Search (GVNS) algorithm is designed as the search engine to relieve the computational burden inherent to the application of the MILP model. To evaluate the effectiveness of the GVNS algorithm, a real instance case study is generated and solved by both the GVNS algorithm and the software provided by our industrial partner. The results show that the suggested approach provides solutions with better overall values than those found by the software provided by our industrial partner

THE VEHICLE ROUTING PROBLEM WITH STOCHASTIC DEMANDS IN AN URBAN AREA – A CASE STUDY

The vehicle routing problem with stochastic demands (VRPSD) is a combinatorial optimization problem. The VRPSD looks for vehicle routes to connect all customers with a depot, so that the total distance is minimized, each customer visited once by one vehicle, every route starts and ends at a depot, and the travelled distance and capacity of each vehicle are less than or equal to the given maximum value. Contrary to the classical VRP, in the VRPSD the demand in a node is known only after a vehicle arrives at the very node. This means that the vehicle routes are designed in uncertain conditions. This paper presents a heuristic and meta-heuristic approach for solving the VRPSD and discusses the real problem of municipal waste collection in the City of Niš

A unified race algorithm for offline parameter tuning

This paper proposes uRace, a unified race algorithm for efficient offline parameter tuning of deterministic algorithms. We build on the similarity between a stochastic simulation environment and offline tuning of deterministic algorithms, where the stochastic element in the latter is the unknown problem instance given to the algorithm. Inspired by techniques from the simulation optimization literature, uRace enforces fair comparisons among parameter configurations by evaluating their performance on the same training instances. It relies on rapid statistical elimination of inferior parameter configurations and an increasingly localized search of the parameter space to quickly identify good parameter settings. We empirically evaluate uRace by applying it to a parameterized algorithmic framework for loading problems at ORTEC, a global provider of software solutions for complex decision-making problems, and obtain competitive results on a set of practical problem instances from one of the world's largest multinationals in consumer packaged goods

Container Loading Problems: A State-of-the-Art Review

Container loading is a pivotal function for operating supply chains efficiently. Underperformance results in unnecessary costs (e.g. cost of additional containers to be shipped) and in an unsatisfactory customer service (e.g. violation of deadlines agreed to or set by clients). Thus, it is not surprising that container loading problems have been dealt with frequently in the operations research literature. It has been claimed though that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice.In this paper, a review of the state-of-the-art in the field of container loading will be given. We will identify factors which - from a practical point of view - need to be considered when dealing with container loading problems and we will analyze whether and how these factors are represented in methods for the solution of such problems. Modeling approaches, as well as exact and heuristic algorithms will be reviewed. This will allow for assessing the practical relevance of the research which has been carried out in the field. We will also mention several issues which have not been dealt with satisfactorily so far and give an outlook on future research opportunities

Freight Operations Modelling for Urban Delivery and Pickup with Flexible Routing: Cluster Transport Modelling Incorporating Discrete-Event Simulation and GIS

Urban pickup and delivery (PUD) activities are important for logistics operations. Real operations for general freight involve a high degree of complexity due to daily variability. Discrete-event simulation (DES) is a method that can mimic real operations and include stochastic parameters. However, realistic vehicle routing is difficult to build in DES models. The objective is to create a DES model for realistic freight routing, which considers the driver’s routing decisions. Realistic models need to predict the delivery route (including time and distance) for variable consignment address and backhaul pickup. Geographic information systems (GIS) and DES were combined to develop freight PUD models. GIS was used to process geographical data. Two DES models were developed and compared. The first was a simple suburb model, and the second an intersection-based model. Real industrial data were applied including one-year consignment data and global positioning system (GPS) data. A case study of one delivery tour is shown, with results validated with actual GPS data. The DES results were also compared with conventional GIS models. The result shows the intersection-based model is adequate to mimic actual PUD routing. This work provides a method for combining GIS and DES to build freight operation models for urban PUD. This has the potential to help industry logistics practitioners better understand their current operations and experiment with different scenarios

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