Star p-hub median problem with modular arc capacities

Cataloged from PDF version of article.We consider the hub location problem, where p hubs are chosen from a given set of nodes, each nonhub node is connected to exactly one hub and each hub is connected to a central hub. Links are installed on the arcs of the resulting network to route the traffic. The aim is to find the hub locations and the connections to minimize the link installation cost.We propose two formulations and a heuristic algorithm to solve this problem. The heuristic is based on Lagrangian relaxation and local search.We present computational results where formulations are compared and the quality of the heuristic solutions are tested. 2007 Elsevier Ltd. All rights reserved

Network hub locations problems: the state of the art

Cataloged from PDF version of article.Hubs are special facilities that serve as switching, transshipment and sorting points in many-to-many distribution systems. The hub location problem is concerned with locating hub facilities and allocating demand nodes to hubs in order to route the traffic between origin-destination pairs. In this paper we classify and survey network hub location models. We also include some recent trends on hub location and provide a synthesis of the literature. (C) 2007 Elsevier B.V. All rights reserved

Applying Minimum-Risk Criterion to Stochastic Hub Location Problems

AbstractThis paper presents a new class of two-stage stochastic hub location (HL) programming problems with minimum-risk criterion, in which uncertain demands are characterized by random vector. Meanwhile we demonstrate that the twostage programming problem is equivalent to a single-stage stochastic P-model. Under mild assumptions, we develop a deterministic binary programming problem by using standardization, which is equivalent to a binary fractional programming problem. Moreover, we show that the relaxation problem of the binary fractional programming problem is a convex programming problem. Taking advantage of branch-and-bound method, we provide a number of experiments to illustrate the efficiency of the proposed modeling idea

Solving the hub location problem in a star-star network

We consider the problem of locating hubs and assigning terminals to hubs for a telecommunication network. The hubs are directly connected to a central node and each terminal node is directly connected to a hub node. The aim is to minimize the cost of locating hubs, assigning terminals and routing the traffic between hubs and the central node. We present two formulations and show that the constraints are facet-defining inequalities in both cases. We test the formulations on a set of instances. Finally, we present a heuristic based on Lagrangian relaxation. ©2007 Wiley Periodicals, Inc

Polyhedral analysis for the uncapacitated hub location problem with modular arc capacities

We consider the problem of installing a two-level telecommunication network. Terminal nodes communicate with each other through hubs. Hubs can be installed on terminal nodes and they are interconnected by a complete network. Each terminal is connected directly to a hub node. Integer amounts of capacity units are installed on the arcs between hub pairs and terminals and their hubs. The aim is to minimize the cost of installing hubs and capacity units on arcs. We present valid and facet defining inequalities for the polyhedron associated with this problem. © 2005 Society for Industrial and Applied Mathematics

The latest arrival hub location problem for cargo delivery systems with stopovers

Cataloged from PDF version of article.In this paper, we concentrate on the service structure of ground-transportation based cargo delivery companies. The transient times that arise from nonsimultaneous arrivals at hubs (typically spent for unloading, loading, and sorting operations) can constitute a significant portion of the total delivery time for cargo delivery systems. The latest arrival hub location problem is a new minimax model that focuses on the minimization of the arrival time of the last item to arrive, taking into account journey times as well as the transient times at hubs. We first focus on a typical cargo delivery firm operating in Turkey and observe that stopovers are essential components of a ground-based cargo delivery system. The existing formulations of the hub location problem in the literature do not allow stopovers since they assume direct connections between demand centers and hubs. In this paper, we propose a generic mathematical model, which allows stopovers for the latest arrival hub location problem. We improve the model using valid inequalities and lifting. We present computational results using data from the US and Turkey. 2007 Elsevier Ltd. All rights reserved

Release Time Scheduling and Hub Location for Next-Day Delivery

Cataloged from PDF version of article.Inspired by a real-life problem faced by one of the largest ground-based cargo companies of Turkey, the current study introduces a new facet to the hub location literature. The release time scheduling and hub location problem aims to select a specified number of hubs from a fixed set of demand centers, to allocate each demand center to a hub, and to decide on the release times of trucks from each demand center in such a way that the total amount of cargo guaranteed to be delivered to every potential destination by the next day is not below a threshold and the total routing cost is minimized. The paper introduces integer programming models to solve this problem in the special cases when the cargo uniformly arrives to each demand center during the day and the more realistic pattern of when the cargo arrivals exhibit a piecewise linear form. Several classes of valid inequalities are proposed to strengthen the formulations. Extensions with multiple service levels and discrete sets for release times are also discussed. Computational results show the computational viability of the models under realistic scenarios as well as the validity of the proposed problems in answering several interesting questions from the cargo sector’s perspective

A capacitated hub location problem under hose demand uncertainty

In this study, we consider a capacitated multiple allocation hub location problem with hose demand uncertainty. Since the routing cost is a function of demand and capacity constraints are imposed on hubs, demand uncertainty has an impact on both the total cost and the feasibility of the solutions. We present a mathematical formulation of the problem and devise two different Benders decomposition algorithms. We develop an algorithm to solve the dual subproblem using complementary slackness. In our computational experiments, we test the efficiency of our approaches and we analyze the effects of uncertainty. The results show that we obtain robust solutions with significant cost savings by incorporating uncertainty into our problem. © 2017 Elsevier Lt

Quadratic stabilization of Benders decomposition

The foundational Benders decomposition, or variable decomposition, is known to have the inherent instability of cutting plane-based methods. Several techniques have been proposed to improve this method, which has become the state of the art for important problems in operations research. This paper presents a complementary improvement featuring quadratic stabilization of the Benders cutting-plane model. Inspired by the level-bundle methods of nonsmooth optimization, this algorithmic improvement is designed to reduce the number of iterations of the method. We illustrate the interest of the stabilization on two classical problems: network design problems and hub location problems. We also prove that the stabilized Benders method has the same theoretical convergence properties as the usual Benders method