In this paper we introduce a new facility location model, called backup multifacility location problem by considering the ideal radius for each customer. In this problem the location of clients are given in the plane. A radius is assigned to each client. We should find the location of new facilities, which some of them may fail with a given probability, such that the sum of weighted distances f...

This paper considers the Tchebychev distance for a facility location problem with a probabilistic line barrier in the plane. In particular, we develop a mixed-integer nonlinear programming (MINLP) model for this problem that minimizes the total Tchebychev distance between a new facility and the existing facilities. A numerical example is solved to show the validity of the developed model. Becau...

In this paper we propose the Online Connected Facility Location problem (OCFL), which is an online version of the Connected Facility Location problem (CFL). The CFL is a combination of the Uncapacitated Facility Location problem (FL) and the Steiner Tree problem (ST). We give a randomized O(log n)-competitive algorithm for the OCFL via the sample-and-augment framework of Gupta, Kumar, Pál, and ...

The traditional, uncapacitated facility location problem (UFLP) seeks to determine a set of warehouses to open such that all retail stores are serviced by a warehouse and the sum of the fixed costs of opening and operating the warehouses and the variable costs of supplying the retail stores from the opened warehouses is minimized. In this paper, we discuss the partial coverage uncapacitated fac...

In this paper we study the facility leasing problem with penalties. We present a primaldual algorithm which is a 3-approximation, based on the algorithm by Nagarajan and Williamson for the facility leasing problem [NW13] and on the algorithm by Charikar et al. for the facility location problem with penalties [CKMN01].

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In this paper we present a 1.52-approximation algorithm for the metric uncapacitated facility location problem, and a 2-approximation algorithm for the metric capacitated facility location problem with soft capacities. Both these algorithms improve the best previously known approximation factor for the corresponding problem, and our soft-capacitated facility location algorithm achieves the inte...