35,515 research outputs found

    Tight Analysis of a Multiple-Swap Heuristic for Budgeted Red-Blue Median

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    Budgeted Red-Blue Median is a generalization of classic kk-Median in that there are two sets of facilities, say R\mathcal{R} and B\mathcal{B}, that can be used to serve clients located in some metric space. The goal is to open krk_r facilities in R\mathcal{R} and kbk_b facilities in B\mathcal{B} for some given bounds kr,kbk_r, k_b and connect each client to their nearest open facility in a way that minimizes the total connection cost. We extend work by Hajiaghayi, Khandekar, and Kortsarz [2012] and show that a multiple-swap local search heuristic can be used to obtain a (5+ϵ)(5+\epsilon)-approximation for Budgeted Red-Blue Median for any constant ϵ>0\epsilon > 0. This is an improvement over their single swap analysis and beats the previous best approximation guarantee of 8 by Swamy [2014]. We also present a matching lower bound showing that for every p1p \geq 1, there are instances of Budgeted Red-Blue Median with local optimum solutions for the pp-swap heuristic whose cost is 5+Ω(1p)5 + \Omega\left(\frac{1}{p}\right) times the optimum solution cost. Thus, our analysis is tight up to the lower order terms. In particular, for any ϵ>0\epsilon > 0 we show the single-swap heuristic admits local optima whose cost can be as bad as 7ϵ7-\epsilon times the optimum solution cost

    A regret model applied to the facility location problem with limited capacity facilities

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    This article addresses issues related to location and allocation problems. Herein, we intend to demonstrate the influence of congestion, through the random number generation, of such systems in final solutions. An algorithm is presented which, in addition to the GRASP, incorporates the Regret with the pminmax method to evaluate the heuristic solution obtained with regard to its robustness for different scenarios. Taking as our point of departure the Facility Location Problem proposed by Balinski [27], an alternative perspective is added associating regret values to particular solutions.N/

    A regret model applied to the maximum coverage location problem with queue discipline

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    This article discusses issues related to the location and allocation problems where is intended to demonstrate, through the random number generation, the influence of congestion of such systems in the final solutions. It is presented an algorithm that, in addition to the GRASP, incorporates the Regret with the pminmax method to evaluate the heuristic solution obtained in regard to its robustness for different scenarios. To the well know Maximum Coverage Location Problem from Church and Revelle [1] an alternative perspective is added in which the choice behavior of the server does not only depend on the elapsed time from the demand point looking to the center, but also includes the waiting time for service conditioned by a waiting queue.N/

    The Incremental Cooperative Design of Preventive Healthcare Networks

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    This document is the Accepted Manuscript version of the following article: Soheil Davari, 'The incremental cooperative design of preventive healthcare networks', Annals of Operations Research, first published online 27 June 2017. Under embargo. Embargo end date: 27 June 2018. The final publication is available at Springer via http://dx.doi.org/10.1007/s10479-017-2569-1.In the Preventive Healthcare Network Design Problem (PHNDP), one seeks to locate facilities in a way that the uptake of services is maximised given certain constraints such as congestion considerations. We introduce the incremental and cooperative version of the problem, IC-PHNDP for short, in which facilities are added incrementally to the network (one at a time), contributing to the service levels. We first develop a general non-linear model of this problem and then present a method to make it linear. As the problem is of a combinatorial nature, an efficient Variable Neighbourhood Search (VNS) algorithm is proposed to solve it. In order to gain insight into the problem, the computational studies were performed with randomly generated instances of different settings. Results clearly show that VNS performs well in solving IC-PHNDP with errors not more than 1.54%.Peer reviewe

    A regret model applied to the maximum capture location problem

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    This article addresses issues related to location and allocation problems. Herein, we intend to demonstrate the influence of congestion, through the random number generation, of such systems in final solutions. An algorithm is presented which, in addition to the GRASP, incorporates the Regret with the pminmax method to evaluate the heuristic solution obtained with regard to its robustness for different scenarios. Taking as our point of departure the Maximum Capture Location Problem proposed by Church and Revelle [1, 26], an alternative perspective is added in which the choice behavior of the server does not depend only on the elapsed time from the demand point looking to the center, but includes also the service waiting time.N/

    Lotsize optimization leading to a pp-median problem with cardinalities

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    We consider the problem of approximating the branch and size dependent demand of a fashion discounter with many branches by a distributing process being based on the branch delivery restricted to integral multiples of lots from a small set of available lot-types. We propose a formalized model which arises from a practical cooperation with an industry partner. Besides an integer linear programming formulation and a primal heuristic for this problem we also consider a more abstract version which we relate to several other classical optimization problems like the p-median problem, the facility location problem or the matching problem.Comment: 14 page
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