Carlos Obreque

A single vehicle routing problem with fixed delivery and optional collections

The Single-Vehicle Routing Problem with Fixed Delivery and Optional Collections considers a set of delivery customers receiving goods from a depot and a set of collection customers sending goods to the same depot. All delivery customers must be visited by the vehicle, while a collection customer is visited only if the capacity of the vehicle is large enough to fit the collected load and the visit reduces collection costs that would be otherwise incurred. The goal is to minimize the transportation and collection costs. A model is proposed and solved utilizing a branch-and-cut method. Efficient new cuts are proposed. Computational experience is offered on two sets of test problems. It is proved possible to solve instances that previous methods were unable to solve. The method was tested on larger instances.

A branch and cut algorithm for the hierarchical network design problem

The Hierarchical Network Design Problem consists of locating a minimum cost bi-level network on a graph. The higher level sub-network is a path visiting two or more nodes. The lower level sub-network is a forest connecting the remaining nodes to the path. We optimally solve the problem using an ad hoc branch and cut procedure. Relaxed versions of a base model are solved using an optimization package and, if binary variables have fractional values or if some of the relaxed constraints are violated in the solution, cutting planes are added. Once no more cuts can be added, branch and bound is used. The method for finding valid cutting planes is presented. Finally, we use different available test instances to compare the procedure with the best known published optimal procedure, with good results. In none of the instances we needed to apply branch and bound, but only the cutting planes.

Scheduling operating rooms with consideration of all resources, post anesthesia beds and emergency surgeries

We propose two exact and a metaheuristic method for surgery room scheduling.We take into consideration constrained human and physical resources.The scheduling considers the availability of post-anesthesia recovery beds.We ensure adequate inter-surgery intervals for attending emergency surgeries. Surgery rooms are among the most expensive resources in hospitals and clinics. Their scheduling is difficult because, in addition to the surgical room itself, each surgery requires a particular combination of human resources, as well as different pieces of equipment and materials. Furthermore, after each surgery, a post-anesthesia bed is required for the patient to recover. Finally, in addition to planned surgeries, the scheduling must be made in such a way as to accommodate the emergency surgeries that may arrive during each day, which must be attended within a limited time. We address the surgery scheduling problem considering simultaneously, for the first time, the operating rooms, the post anesthesia recovery, the resources required by the surgery and the possible arrival of emergency surgeries. We propose an integer linear programming model that allows finding optimal solutions for small size instances, we transform it to use constraint programming, and develop a metaheuristic based on a genetic algorithm and a constructive heuristic, that solves larger size instances. Finally, we present numerical experiments.

Rapid transit network design for optimal cost and origin-destination demand capture

This paper proposes a tractable model for the design of a rapid transit system. Travel cost is minimized and traffic capture is maximized. The problem is modeled on an undirected graph and cast as an integer linear program. The idea is to build segments within broad corridors to connect some vertex sets. These segments can then be assembled into lines, at a later stage. The model is solved by branch-and-cut within the CPLEX framework. Tests conducted on data from Concepcion, Chile, confirm the effectiveness of the proposed methodology.

Lagrangean relaxation heuristics for the p-cable-trench problem

We address the p-cable-trench problem. In this problem, p facilities are located, a trench network is dug and cables are laid in the trenches, so that every customer - or demand - in the region is connected to a facility through a cable. The digging cost of the trenches, as well as the sum of the cable lengths between the customers and their assigned facilities, are minimized. We formulate an integer programming model of the problem using multicommodity flows that allows finding the solution for instances of up to 200 nodes. We also propose two Lagrangean Relaxation-based heuristics to solve larger instances of the problem. Computational experience is provided for instances of up to 300 nodes.

Optimal design of hierarchical networks with free main path extremes

We propose an optimal, two-stage procedure for the optimal design of minimum cost hierarchical spanning networks, consisting of a main path and secondary trees. The optimal location of the origin and destination nodes of the path is also found. We test our procedure and compare it with a known method.

Minimum cost path location for maximum traffic capture

A free path (with no preset extreme nodes) is located on a network, in such a way as to minimize the cost and maximize the traffic captured by the path. Traffic between a pair of nodes is captured if both nodes are visited by the path. Applications are the design of the route and locations of mailboxes for a local package delivery company, or the design of bus or subway lines, in which the shape of the route and the number of stops is determined by the solution of the optimization problem. The problem also applies to the design of an optical fiber network interconnecting WiFi antennas in a university campus. We propose two models and an exact solution method. Computational experience is presented for up to 300 nodes and 1772 arcs, as well as a practical case for the city of Concepcion, Chile.

An optimal procedure for solving the hierarchical network design problem

The hierarchical network design problem consists of finding a minimum cost bilevel network that connects all the nodes in a set, created by a loopless main path and a forest. The main path is formed by primary (higher cost) arcs, providing a path between an origin node and a destination node. The forest, built using secondary (lower cost) arcs, connects all the nodes not on the main path, to the path itself. We state and prove some properties of the problem, which allow finding good upper bounds to the solution in polynomial time when the primary costs are proportional to secondary costs. We also propose an O(n 4) procedure to improve on these bounds. In turn, these bounds are used to significantly reduce the number of nodes and arcs of the problem. Once the problem is reduced, large instances can be solved to optimality. At this stage, we use one of two linear integer optimization formulations. The first and preferred one is based on multicommodity flows, which avoids the formation of subtours. The second formulation avoids subtours by iteratively adding ad hoc constraints. We show some examples and provide computational experiments performed on networks with sizes up to 600 nodes and 14 000 arcs.

The bi-objective insular traveling salesman problem with maritime and ground transportation costs

Abstract This paper introduces and studies the bi-objective insular traveling salesman problem, where a set of rural islands must be served using a single barge following a single route. Each island presents a number of docks from which at least one dock must be selected for visiting. One distinctive feature is that the freight to be collected from each dock or node is not known in advance, since they depend on a set of selected docks at each island and on the strategy employed to allocate the island demands among the visited docks. In contrast to other similar problems found in the literature, particularly the generalized traveling salesman problem, two objective functions are aimed to be minimized: maritime and ground transportation costs. The ground transportation cost incurred at the islands is strongly related to the strategy for transporting the freight to the selected docks inside the islands, which is a distinct characteristic of the studied problem. The proposed mixed integer programming model is solved for a set of real instances from Chile using a weighted sum approach, denoting the bi-objective nature of the problem. This problem feature along with the optimal solution structure are revealed and analyzed, and the appropriateness of the proposed approach is highlighted for freight collection or distribution decision making in insular zones.