An incremental algorithm for uncapacitated facility location problem

We study the incremental facility location problem, wherein we are given an instance of the uncapacitated facility location problem (UFLP) and seek an incremental sequence of opening facilities and an incremental sequence of serving customers along with their fixed assignments to facilities open in the partial sequence. We say that a sequence has a competitive ratio of k, if the cost of serving the first ℓ customers in the sequence is at most k times the optimal solution for serving any ℓ customers for all possible values of ℓ. We provide an incremental framework that computes a sequence with a competitive ratio of at most eight and a worst-case instance that provides a lower bound of three for any incremental sequence. We also present the results of our computational experiments carried out on a set of benchmark instances for the UFLP. The problem has applications in multistage network planning

Robust Fault Tolerant uncapacitated facility location

In the uncapacitated facility location problem, given a graph, a set of demands and opening costs, it is required to find a set of facilities R, so as to minimize the sum of the cost of opening the facilities in R and the cost of assigning all node demands to open facilities. This paper concerns the robust fault-tolerant version of the uncapacitated facility location problem (RFTFL). In this problem, one or more facilities might fail, and each demand should be supplied by the closest open facility that did not fail. It is required to find a set of facilities R, so as to minimize the sum of the cost of opening the facilities in R and the cost of assigning all node demands to open facilities that did not fail, after the failure of up to \alpha facilities. We present a polynomial time algorithm that yields a 6.5-approximation for this problem with at most one failure and a 1.5 + 7.5\alpha-approximation for the problem with at most \alpha > 1 failures. We also show that the RFTFL problem is NP-hard even on trees, and even in the case of a single failure

An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem

We obtain a 1.5-approximation algorithm for the metric uncapacitated facility location problem (UFL), which improves on the previously best known 1.52-approximation algorithm by Mahdian, Ye and Zhang. Note, that the approximability lower bound by Guha and Khuller is 1.463. An algorithm is a {\em ($\lambda_f$,$\lambda_c$)-approximation algorithm} if the solution it produces has total cost at most $\lambda_f \cdot F^* + \lambda_c \cdot C^*$, where $F^*$ and $C^*$ are the facility and the connection cost of an optimal solution. Our new algorithm, which is a modification of the $(1+2/e)$-approximation algorithm of Chudak and Shmoys, is a (1.6774,1.3738)-approximation algorithm for the UFL problem and is the first one that touches the approximability limit curve $(\gamma_f, 1+2e^{-\gamma_f})$ established by Jain, Mahdian and Saberi. As a consequence, we obtain the first optimal approximation algorithm for instances dominated by connection costs. When combined with a (1.11,1.7764)-approximation algorithm proposed by Jain et al., and later analyzed by Mahdian et al., we obtain the overall approximation guarantee of 1.5 for the metric UFL problem. We also describe how to use our algorithm to improve the approximation ratio for the 3-level version of UFL.Comment: A journal versio

Comparison of Formulations for the Two-Level Uncapacitated Facility Location Problem with Single Assignment Constraints

International audienceWe consider the two-level uncapacitated facility location problem with single assignment constraints (TUFLP-S), an extension of the uncapacitated facility location problem. We present six mixed-integer programming models for the TUFLP-S based on reformulation techniques and on the relaxation of the integrality of some of the variables associated with location decisions. We compare the models by carrying out extensive computational experiments on large, hard, artificial instances, as well as on instances derived from an industrial application in freight transportation

An iterated local search algorithm for the facility location problem

Desenvolupar un Iterated Local Search amb tècniques d'aleatorització esbiaixada per solucionar el Uncapacitated Facility Location Problem

Return on Investment Analysis for Facility Location

We consider how the optimal decision can be made if the optimality criterion of maximizing profit changes to that of maximizing return on investment for the general uncapacitated facility location problem. We show that the inherent structure of the proposed model can be exploited to make a significant computational reduction

HYBRID FIREFLY ALGORITHM (FA) DENGAN TABU SEARCH (TS) UNTUK MENYELESAIKAN UNCAPACITATED FACILITY LOCATION PROBLEM (UFLP)

Penulisan skripsi ini bertujuan untuk menyelesaikan permasalahan Uncapacitated Facility Location Problem (UFLP) dengan menggunakan Hybrid Firefly Algorithm (FA) dengan Tabu Search (TS). Uncapacitated Facility Location Problem (UFLP) adalah suatu permasalahan penempatan fasilitas yang dibangun disebuah lokasi untuk melayani seluruh konsumen, dengan meminimalkan biaya pembangunan dan biaya pelayanan konsumen dengan kapasitas konsumen yang tidak terbatas. Firefly Algorithm terdapat proses pencarian solusi dipersekitaran solusi terbaik yang disebut local search, oleh karena itu memungkinkan solusi dapat terjebak pada minimum lokal. Tabu Search dapat digunakan untuk mencari solusi Uncapacitated Facility Location Problem yang sudah diproses dengan Firefly Algorithm agar mendapatkan hasil yang lebih baik. Program Hybrid Firefly Algorithm (FA) dengan Tabu Search (TS) untuk menyelesaikan UFLP dibuat dengan menggunakan Borland C++ yang diimplementasikan pada dua contoh kasus yaitu data kecil dengan 15 customer dan 10 lokasi serta data besar dengan 50 customer dan 50 lokasi. Dari hasil running program diperoleh total biaya minimum untuk data berukuran kecil yaitu 143757 dan untuk data berukuran besar yaitu 835857. Semakin besar jumlah firefly, nilai alfa dan maksimum iterasi maka solusi yang diperoleh cenderung lebih baik

Integrating facility location and production planning decisions

We consider a metric uncapacitated facility location problem where we must assign each customer to a facility and meet the demand of the customer in future time periods through production and inventory decisions at the facility. We show that the problem, in general, is as hard to approximate as the set cover problem. We therefore focus on developing approximation algorithms for special cases of the problem. These special cases come in two forms: (i) specialize the production and inventory cost structure and (ii) specialize the demand pattern of the customers. In the former, we offer reductions to variants of the metric uncapacitated facility location problem that have been previously studied. The latter gives rise to a class of metric uncapacitated facility location problems where the facility cost function is concave in the amount of demand assigned to the facility. We develop a modified greedy algorithm together with the idea of cost-scaling to provide an algorithm for this class of problems with an approximation guarantee of 1.52. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/64912/1/20315_ftp.pd