TY - JOUR

T1 - Approximation algorithms for hard capacitated k-facility location problems

AU - Aardal, Karen

AU - van den Berg, Pieter L.

AU - Gijswijt, Dion

AU - Li, Shanfei

PY - 2015

Y1 - 2015

N2 - We study the capacitated k-facility location problem, in which we are given a set of clients with demands, a set of facilities with capacities and a positive integer k. It costs fi to open facility i, and cij for facility i to serve one unit of demand from client j. The objective is to open at most k facilities serving all the demands and satisfying the capacity constraints while minimizing the sum of service and opening costs. In this paper, we give the first fully polynomial time approximation scheme (FPTAS) for the single-sink (single-client) capacitated k-facility location problem. Then, we show that the capacitated k-facility location problem with uniform capacities is solvable in polynomial time if the number of clients is fixed by reducing it to a collection of transportation problems. Third, we analyze the structure of extreme point solutions, and examine the efficiency of this structure in designing approximation algorithms for capacitated k-facility location problems. Finally, we extend our results to obtain an improved approximation algorithm for the capacitated facility location problem with uniform opening costs.

AB - We study the capacitated k-facility location problem, in which we are given a set of clients with demands, a set of facilities with capacities and a positive integer k. It costs fi to open facility i, and cij for facility i to serve one unit of demand from client j. The objective is to open at most k facilities serving all the demands and satisfying the capacity constraints while minimizing the sum of service and opening costs. In this paper, we give the first fully polynomial time approximation scheme (FPTAS) for the single-sink (single-client) capacitated k-facility location problem. Then, we show that the capacitated k-facility location problem with uniform capacities is solvable in polynomial time if the number of clients is fixed by reducing it to a collection of transportation problems. Third, we analyze the structure of extreme point solutions, and examine the efficiency of this structure in designing approximation algorithms for capacitated k-facility location problems. Finally, we extend our results to obtain an improved approximation algorithm for the capacitated facility location problem with uniform opening costs.

U2 - 10.1016/j.ejor.2014.10.011

DO - 10.1016/j.ejor.2014.10.011

M3 - Article

VL - 242

SP - 358

EP - 368

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 2

ER -