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Operations Research Transactions >

2016 , Vol. 20 >Issue 2: 69 - 78

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2016.02.006

Approximation algorithm for the fault-tolerant facility placement problem with penalties

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  • 1. Faculty of Science, Ningbo University, Ningbo 315211, Zhejiang, China

Received date: 2015-09-14

  Online published: 2016-06-15

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Abstract

In the fault-tolerant facility placement problem with penalties, we are given a set of customers and a set of sites, and connection costs between customers and sites. We assume that the connection costs satisfy the metric principle. Each customer has its service demands. We can open an unbounded number of different facilities at each site. Each customer can be either assigned to some different opened facilities in some sites to satisfy its demands or rejected by paying a penalty. The objective is to minimize the total cost of opening facilities and connecting those non-rejected customers to different open facilities, and the reject penalties. In this paper, we formulate the fault-tolerant facility placement problem with penalties as a linear integer programming and give its dual programming. Then we propose a 4-approximation algorithm  based on rounding its linear programming and dual programming.

Key words： fault-tolerant facility placement problem; penalties; rounding; approximation algorithm

Cite this article

FANG Rui, LUO Wenchang . Approximation algorithm for the fault-tolerant facility placement problem with penalties[J]. Operations Research Transactions, 2016 , 20(2) : 69 -78 . DOI: 10.15960/j.cnki.issn.1007-6093.2016.02.006

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