The Pyramidal Capacitated Vehicle Routing Problem

This paper introduces the Pyramidal Capacitated Vehicle Routing Problem (PCVRP) as a restricted version of the Capacitated Vehicle Routing Problem (CVRP). In the PCVRP each route is required to be pyramidal in a sense generalized from the Pyramidal Traveling Salesman Problem (PTSP). A pyramidal route is de ned as a route on which the vehicle rst visits customers in increasing order of customer index, and on the remaining part of the route visits customers in decreasing order of customer index. Provided that customers are indexed in nondecreasing order of distance from the depot, the shape of a pyramidal route is such that its traversal can be divided in two parts, where on the rst part of the route, customers are visited in nondecreasing distance from the depot, and on the remaining part of the route, customers are visited in nonincreasing distance from the depot. Such a route shape is indeed found in many optimal solutions to CVRP instances. An optimal solution to the PCVRP may therefore be useful in itself as a heuristic solution to the CVRP. Further, an attempt can be made to nd an even better CVRP solution by solving a TSP, possibly leading to a non-pyramidal route, for each of the routes in the PCVRP solution. This paper develops an exact branch-and-cut-and-price (BCP) algorithm for the PCVRP. At the pricing stage, elementary routes can be computed in pseudo-polynomial time in the PCVRP, unlike in the CVRP. We have therefore implemented pricing algorithms that generate only elementary routes. Computational results suggest that PCVRP solutions are highly useful for obtaining near-optimal solutions to the CVRP. Moreover, pricing of pyramidal routes may due to its eciency prove to be very useful in column generation for the CVRP.vehicle routing; pyramidal traveling salesman; branch-and-cut-and-price

A Branch-and-Cut Algorithm for the Capacitated Open Vehicle Routing Problem

In open vehicle routing problems, the vehicles are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacitated vehicle routing problem (CVRP). The algorithm is based on branch-and-cut. We show that, even though the open CVRP initially looks like a minor variation of the standard CVRP, the integer programming formulation and cutting planes need to be modified in subtle ways. Computational results are given for several standard test instances, which enables us for the first time to assess the quality of existing heuristic methods, and to compare the relative difficulty of open and closed versions of the same problem.Vehicle routing; branch-and-cut; separation

Ant Colony Optimization for the Electric Vehicle Routing Problem

Ant colony optimization (ACO) algorithms have proved to be powerful tools to solve difficult optimization problems. In this paper, ACO is applied to the electric vehicle routing problem (EVRP). New challenges arise with the consideration of electric vehicles instead of conventional vehicles because their energy level is affected by several uncertain factors. Therefore, a feasible route of an electric vehicle (EV) has to consider visit(s) to recharging station(s) during its daily operation (if needed). A look ahead strategy is incorporated into the proposed ACO for EVRP (ACO-EVRP) that estimates whether at any time EVs have within their range a recharging station. From the simulation results on several benchmark problems it is shown that the proposed ACO-EVRP approach is able to output feasible routes, in terms of energy, for a fleet of EVs

An exact approach for the vehicle routing problem with two-dimensional loading constraints

We consider a special case of the symmetric capacitated vehicle routing problem, in which a fleet of K identical vehicles must serve n customers, each with a given demand consisting in a set of rectangular two-dimensional weighted items. The vehicles have a two-dimensional loading surface and a maximum weight capacity. The aim is to find a partition of the customers into routes of minimum total cost such that, for each vehicle, the weight capacity is taken into account and a feasible two-Dimensional allocation of the items into the loading surface exists. The problem has several practical applications in freight transportation, and it is -hard in the strong sense. We propose an exact approach, based on a branch-and-cut algorithm, for the minimization of the routing cost that iteratively calls a branch-and-bound algorithm for checking the feasibility of the loadings. Heuristics are also used to improve the overall performance of the algorithm. The effectiveness of the approach is shown by means of computational results

Metaheuristics for the Vehicle Routing Problem with Loading Constraints

We consider a combination of the capacitated vehicle routing problem and a class of additional loading constraints involving a parallel machine scheduling problem. The work is motivated by a real-world transportation problem occurring to a wood-products retailer, which delivers its products to a number of customers in a specific region. We solve the problem by means of two different metaheuristics algorithms: a Tabu Search and an Ant Colony Optimization. Extensive computational results are given for both algorithms, on instances derived from the vehicle routing literature and on real-world instances

Routing in waste collection: a simulated annealing algorithm for an Argentinean case study

The management of the collection of Municipal Solid Waste is a complex task for local governments since it consumes a large portion of their budgets. Thus, the use of computer-aided tools to support decision-making can contribute to improve the efficiency of the system and reduce the associated costs, especially in developing countries, which usually suffer from a shortage of resources. In the present work, a simulated annealing algorithm is proposed to address the problem of designing the routes of waste collection vehicles. The proposed algorithm is compared to a commercial solver based on a mixed-integer programming formulation and two other metaheuristic algorithms, i.e., a state-of-the-art large neighborhood search and a genetic algorithm. The evaluation is carried out on both a well-known benchmark from the literature and real instances of the Argentinean city of Bahía Blanca. The proposed algorithm was able to solve all the instances, having a performance similar to the large neighborhood procedure, while the genetic algorithm showed the worst results. The simulated annealing algorithm was also able to improve the solutions of the solver in many instances of the real dataset.Fil: Rossit, Diego Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Toncovich, Adrián Andrés. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Fermani, Matías. Universidad Nacional del Sur. Departamento de Ingeniería; Argentin

The pickup and delivery problem with time windows and handling operations

This paper introduces the pickup and delivery problem with time windows and handling operations. In this problem, the loading compartment of a vehicle is modeled as a linear LIFO stack. When an item is picked up, it is positioned on top of the stack. When it is on top of the stack, it can be delivered without additional handling. Otherwise, items on top must be unloaded before the delivery and reloaded afterwards, which requires time. We define two rehandling policies. For both policies, rehandling is only allowed at delivery locations and there is no specific reloading order for the rehandled items. Under the first policy, only compulsory rehandling is allowed. Under the second policy, in addition to compulsory rehandling, preventive rehandling is allowed. For each policy, we propose a branch-price-and-cut algorithm with an ad hoc dominance criterion for the labeling algorithm used to generate routes. Computational results are reported on benchmark instances for the pickup and delivery problem with time windows. (C) 2016 Elsevier Ltd. All rights reserved

Introducing heterogeneous users and vehicles into models and algorithms for the dial-a-ride problem

AbstractDial-a-ride problems deal with the transportation of people between pickup and delivery locations. Given the fact that people are subject to transportation, constraints related to quality of service are usually present, such as time windows and maximum user ride time limits. In many real world applications, different types of users exist. In the field of patient and disabled people transportation, up to four different transportation modes can be distinguished. In this article we consider staff seats, patient seats, stretchers and wheelchair places. Furthermore, most companies involved in the transportation of the disabled or ill dispose of different types of vehicles. We introduce both aspects into state-of-the-art formulations and branch-and-cut algorithms for the standard dial-a-ride problem. Also a recent metaheuristic method is adapted to this new problem. In addition, a further service quality related issue is analyzed: vehicle waiting time with passengers aboard. Instances with up to 40 requests are solved to optimality. High quality solutions are obtained with the heuristic method