Juan-José Salazar-González

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 NP-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.

A branch-and-cut algorithm for a traveling salesman problem with pickup and delivery

We study a generalization of the well-known traveling salesman problem (TSP) where each customer provides or requires a given non-zero amount of product, and the vehicle in a depot has a given capacity. Each customer and the depot must be visited exactly once by the vehicle supplying the demand while minimizing the total travel distance. We assume that the product collected from pickup customers can be delivered to delivery customers. We introduce a 0-1 integer linear model for this problem and describe a branch-and-cut procedure for finding an optimal solution. The model and the algorithm are adapted to solve instances of TSP with pickup and delivery. Some computational results are presented to analyze the performance of our proposal.

A Branch-and-Cut Algorithm for the Undirected Traveling Purchaser Problem

The purpose of this paper is to present a branch-and-cut algorithm for the undirectedTraveling Purchaser Problem which consists of determining a minimum-cost route through a subset of markets, where the cost is the sum of travel and purchase costs. The problem is formulated as an integer linear program, and several families of valid inequalities are derived to strengthen the linear relaxation. The polyhedral structure of the formulation is analyzed and several classes of valid inequalities are proved to be facet defining. A branch-and-cut procedure is developed and tested over four classes of randomly generated instances. Results show that the proposed algorithm outperforms all previous approaches and can optimally solve instances containing up to 200 markets.

A hybrid GRASP/VND heuristic for the one-commodity pickup-and-delivery traveling salesman problem

We address in this paper the one-commodity pickup-and-delivery traveling salesman problem, which is characterized by a set of customers, each of them supplying (pickup customer) or demanding (delivery customer) a given amount of a single product. The objective is to design a minimum cost Hamiltonian route for a capacitated vehicle in order to transport the product from the pickup to the delivery customers. The vehicle starts the route from a depot, and its initial load also has to be determined. We propose a hybrid algorithm that combines the GRASP and VND metaheuristics. Our heuristic is compared with other approximate algorithms described in Hernandez-Perez and Salazar-Gonzalez [Heuristics for the one-commodity pickup-and-delivery traveling salesman problem. Transportation Science 2004;38:245-55]. Computational experiments on benchmark instances reveal that our hybrid method yields better results than the previously proposed approaches.

Solving a capacitated hub location problem

In this paper we address a problem consisting of determining the routes and the hubs to be used in order to send, at minimum cost, a set of commodities from sources to destinations in a given capacitated network. The capacities and costs of the arcs and hubs are given, and the arcs connecting the hubs are not assumed to create a complete graph. We present a mixed integer linear programming formulation and describe two branch-and-cut algorithms based on decomposition techniques. We evaluate and compare these algorithms on instances with up to 25 commodities and 10 potential hubs. One of the contributions of this paper is to show that a Double Benders’ Decomposition approach outperforms the standard Benders’ Decomposition, which has been widely used in recent articles on similar problems. For larger instances we propose a heuristic approach based on a linear programming relaxation of the mixed integer model. The heuristic turns out to be very effective and the results of our computational experiments show that near-optimal solutions can be derived rapidly. 2006 Elsevier B.V. All rights reserved.

The Generalized Traveling Salesman and Orienteering Problems

Routing and Scheduling problems often require the determination of optimal sequences subject to a given set of constraints. The best known problem of this type is the classical Traveling Salesman Problem (TSP), calling for a minimum cost Hamiltonian cycle on a given graph.

Exact algorithms for the job sequencing and tool switching problem

The job Sequencing and tool Switching Problem (SSP) involves optimally sequencing jobs and assigning tools to a capacitated magazine in order to minimize the number of tool switches. This article analyzes two integer linear programming formulations for the SSP. A branch-and-cut algorithm and a branch-and-bound algorithm are proposed and compared. Computational results indicate that instances involving up to 25 jobs can be solved optimally using the branch-and-bound approach.

The multi-commodity one-to-one pickup-and-delivery traveling salesman problem

This paper concerns a generalization of the traveling salesman problem (TSP) called multi-commodity one-to-one pickup-and-delivery traveling salesman problem (m-PDTSP) in which cities correspond to customers providing or requiring known amounts of m different commodities, and the vehicle has a given upper-limit capacity. Each commodity has exactly one origin and one destination, and the vehicle must visit each customer exactly once. The problem can also be defined as the capacitated version of the classical TSP with precedence constraints. This paper presents two mixed integer linear programming models, and describes a decomposition technique for each model to find the optimal solution. Computational experiments on instances from the literature and randomly generated compare the techniques and show the effectiveness of our implementation.

Solving school bus routing using the multiple vehicle traveling purchaser problem

School bus routing problems, combining bus stop selection and bus route generation, look simultaneously for a set of bus stops to pick up students from among a group of potential locations, and for bus routes to visit the selected stops and carry the students to their school. These problems, classified as Location-Routing problems, are of interest in densely populated urban areas.This article introduces a generalization of the vehicle routing problem called the multi-vehicle traveling purchaser problem, modeling a family of routing problems combining stop selection and bus route generation. It discusses a Mixed Integer Programming formulation extending previous studies on the classical single vehicle traveling purchaser problem. The proposed model is based on a single commodity flow formulation combining continuous variables with binary variables by means of coupling constraints. Additional valid inequalities are proposed with the purpose of strengthening its Linear Programming relaxation. These valid inequalities are obtained by projecting out the flow variables.We develop a branch-and-cut algorithm that makes use of the proposed model and valid inequalities. This cutting plane algorithm is implemented and tested on a large family of symmetric and asymmetric instances derived from randomly generated problems, showing the usefulness of the proposed valid inequalities.

A heuristic approach for the Travelling Purchaser Problem

Abstract The Travelling Purchaser Problem (TPP) is a known generalization of the Travelling Salesman Problem, and is defined as follows. Let us consider a set of products and a set of markets. Each market is provided with a limited amount of each product at a known price. The TPP consists in selecting a subset of markets such that a given demand of each product can be purchased, minimizing the routing cost and the purchasing cost. This problem arises in several applications, mainly in routing and scheduling contexts, and it is NP -hard in the strong sense. A new heuristic approach based on a local-search scheme, exploring a new neighbourhood structure, is proposed. The key idea is to perform a k-exchange of markets instead of the classical 1-exchanges. A neighbour of a given TPP solution is another TPP solution obtained by removing a path of consecutive markets, and by inserting other markets so as to restore the feasibility. This proposal is evaluated on a broad class of instances from literature, where the routing costs are Euclidean distances. Computational results show that our proposal is favourably compared to previous heuristic algorithms in literature.