Gilberto de Miranda

Benders Decomposition for Hub Location Problems with Economies of Scale

When considering hub-and-spoke networks with multiple allocation, the classical models of the literature compute solutions with large discount factors for small flows on interhub connections. Addressing the economies of scale issue, a tighter formulation for this problem is presented, bringing forward a special structure. A specialized version of Benders decomposition is then developed to solve large instances in reasonable time.

Multiple allocation hub-and-spoke network design under hub congestion

The multiple allocation hub-and-spoke network design under hub congestion problem is addressed in this paper. A non-linear mixed integer programming formulation is proposed, modeling the congestion as a convex cost function. A generalized Benders decomposition algorithm has been deployed and has successfully solved standard data set instances up to 81 nodes. The proposed algorithm has also outperformed a commercial leading edge non-linear integer programming package. The main contribution of this work is to establish a compromise between the transportation cost savings induced by the economies of scale exploitation and the costs associated with the congestion effects.

An improved Benders decomposition algorithm for the tree of hubs location problem

The tree of hubs location problem is a particularly hard variant of the so called hub location problems. When solving this problem by a Benders decomposition approach, it is necessary to deal with both optimality and feasibility cuts. While modern implementations of the Benders decomposition method rely on Pareto-optimal optimality cuts or on rendering feasibility cuts based on minimal infeasible subsystems, a new cut selection scheme is devised here under the guiding principle of extracting useful information even when facing infeasible subproblems. The proposed algorithm outperforms two other modern variants of the method and it is capable of optimally solving instances five times larger than the ones previously reported on the literature.

Single allocation hub location problem under congestion

Highlights? Hub-and-spoke systems with single assignment are sensitive to congestion. ? An effective Benders approach is devised. ? Two congestion perspectives are assessed: The network user and the network owner. ? The two addressed congestion perspectives yield to very different networks. ? During the design phase, these two distinct optimal networks have to be considered. The single allocation hub location problem under congestion is addressed in this article. This mixed integer non-linear programming problem is referential in discrete location research having many real applications. Two different network design perspectives are proposed: the network owner and the network user. These perspectives can be translated into mathematical programming problems that are very hard to solve due to their inherently high combinatorial nature combined to the nonlinearities associated to congestion. A very efficient and effective generalized Benders decomposition algorithm is then deployed, enabling the solution of large scale instances in reasonable time.

A performance guarantee heuristic for electronic components placement problems including thermal effects

In this work, Benders decomposition algorithm is used to deal with a computer motherboard design problem. Amongst all the possible formulations for the component placement problem, the chosen one creates an instance of the extensively studied Quadratic Assignment Problem (QAP). This problem arises as a great challenge for engineers and computer scientists. The QAP inherent combinatorial structure makes the most efficient optimization algorithms to exhibit low performance for real size instances. It is also considered here the important addition of linear costs. This approach is directly responsible for the performance gain presented by our decomposition method. Coupled with the placement problem, it is under investigation the maximum temperature rising on the board surface. In order to solve the Energy Conduction Equation the Finite Volume Method is implemented, becoming possible to derive a secondary quality solution criterion. A set of test instances is then solved and the corresponding results are reported.

A hybrid Outer-Approximation/Benders Decomposition algorithm for the single allocation hub location problem under congestion

Abstract An efficient procedure that concurrently generates Outer-Approximation and Benders cuts is devised to tackle the single allocation hub location problem under congestion, an MINLP. The proposed method is able to optimally solve large instances (up to 200 nodes) in reasonable time. The combination of both cuts is an algorithmic novelty.

The Hub Line Location Problem

This paper presents the hub line location problem in which the location of a set of hub facilities connected by means of a path or line is considered. Potential applications arise in the design of public transportation and rapid transit systems, where network design costs greatly dominate routing costs and thus full interconnection of hub facilities is unrealistic. Given that service time is the predominant objective in these applications, the problem considers the minimization of the total weighted travel time between origin/destination nodes while taking into account the time spent to access and exit the hub line. An exact algorithm based on a Benders decomposition of a strong path-based formulation is proposed. The standard decomposition method is enhanced through the incorporation of several features such as a multicut strategy, an efficient algorithm to solve the subproblem and to obtain stronger optimality cuts, and a Benders branch-and-cut scheme that requires the solution of only one master problem. Computational results obtained on benchmark instances with up to 100 nodes confirm the efficiency of the proposed algorithm, which is considerably faster and able to solve larger instances than a general purpose solver.

Addressing congestion on single allocation hub-and-spoke networks

When considering hub-and-spoke networks with single allocation, the absence of alternative routes makes this kind of systems specially vulnerable to congestion effects. In order to improve the design of such networks, congestion costs must be addressed. This article deploys two different techniques for addressing congestion on single allocation hub-and-spoke networks: the Generalized Benders Decomposition and the Outer Approximation method. Both methods are able to solve large scale instances. Computational experiments show how the adoption of advanced solution strategies, such as Pareto-optimal cut generation on the Master Problem branch-and-bound tree, may be decisive. They also demonstrate that the solution effort is not only associated with the size of the instances, but also with their combination of the installation and congestion costs.

A Cut-and-Branch algorithm for the Multicommodity Traveling Salesman Problem

This paper presents a Cut-and-Branch algorithm for the Multicommodity Traveling Salesman Problem (MTSP), a useful variant of the Traveling Salesman Problem (TSP). The MTSP presents a more general cost structure, allowing for solutions that consider the quality of service to the customers, delivery priorities and delivery risk, among other possible objectives. In the MTSP the salesman pays the traditional TSP fixed cost for each arc visited, plus a variable cost for each of the commodities being transported across the network. We present a strong mathematical formulation for this relevant problem. We implement a Cut-and-Branch algorithm for the MTSP which is able to find optimal solutions faster than stand-alone CPLEX codes.

Hub Location and Network Design with Fixed and Variable Costs

Transportation hub networks are important for many large-scale logistics and supply chain systems. Basic hub location models rely on some key assumptions about the transportation cost that limits their practicality We present a new model for hub location and network design that uses fixed and variable transportation costs on all arcs, fixed costs for hubs, and also allows direct arcs. This approach allows the costs for the network components to drive the design of the network. We provide the basic model formulation and some illustrative results to show the types of optimal networks that are generated. The results document the wide range of network features that can be generated from the general cost structure in the model.