Hub location problems deal with finding the location of hub facilities and with the allocation of demand nodes to these located hub facilities. In this paper, we study the single allocation hub covering problem over incomplete hub networks and propose an integer programming formulation to this end. The aim of our model is to find the location of hubs, the hub links to be established between the located hubs, and the allocation of non-hub nodes to the located hub nodes such that the travel time between any origin-destination pair is within a given time bound. We present an efficient heuristic based on tabu search and test the performance of our heuristic on the CAB data set and on the Turkish network. © 2008 Elsevier Ltd. All rights reserved

We give a review of existing methods for solving the absolute and vertex restricted p-center problems on networks and propose a new integer programming formulation, a tightened version of this formulation and a new method based on successive restrictions of the new formulation. A specialization of the new method with two-element restrictions obtains the optimal p-center solution by solving a series of simple structured integer programs in recognition form. This specialization is called the double bound method. A relaxation of the proposed formulation gives the tightest known lower bound in the literature (obtained earlier by Elloumi et al., [1]). A polynomial time algorithm is presented to compute this bound. New lower and upper bounds are proposed. Problems from the OR-Library [2] and TSPLIB [3] are solved by the proposed algorithms with up to 3038 nodes. Previous computational results were restricted to networks with at most 1817 nodes. © 2013 Elsevier Ltd

We focus on a problem of locating recharging stations in one-way station based electric car sharing systems which operate under demand uncertainty. We model this problem as a mixed integer stochastic program and develop a Benders decomposition algorithm based on this formulation. We integrate a stabilization procedure to our algorithm and conduct a large-scale experimental study on our methods. To conduct the computational experiments, we develop a demand forecasting method allowing to generate many demand scenarios. The method is applied to real data from Manhattan taxi trips. We are able to solve problems with 100 to 500 scenarios, each scenario including 1000 to 5000 individual customer requests, under high and low cost values and 5 to 15 mins of accessibility restrictions, which is measured as the maximum walking time to the operating stations.

In this work, we present an algorithmic framework based on Benders decomposition for the Capacitated p-Cable Trench Problem with Covering. We show that our approach can be applied to most variants of the Cable Trench Problem (CTP) that have been considered in the literature. The proposed algorithm is augmented with a stabilization procedure to accelerate the convergence of the cut loop and with a primal heuristic to derive high-quality primal solutions. Three different variants of the CTP are considered in a computational study which compares the Benders approach with two compact integer linear programming formulations that are solved with CPLEX. The obtained results show that the proposed algorithm significantly outperforms the two compact models and that it can be used to tackle significantly larger instances than previously considered algorithms based on Lagrangean relaxation.

A p-center is a minimax solution that consists in a set of p points that minimizes the maximum distance between a demand point and a closest point belonging to that set. We present different variants of that problem. We review special polynomial cases, determine the complexity of the problems and present mixed integer linear programming formulations, exact algorithms and heuristics. Several extensions are also reviewed.

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