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easily shown to be monotonic in the number p of facilities. The same holds for the
aggregation of the facility-facility cover c
jk
.x
j
;x
k
/ to C
F
.
x
/: Hence, in order to
find the highest p
for which such covers remain within a given interval, one only
needs to solve sequentially the problem for different values of p: The design of more
direct and efficient procedures is definitely a promising research line.
Acknowledgements
Research partially supported by research grants and projects ICT COST
Action TD1207 (EU), MTM2012-36163 (Ministerio de Ciencia e Innovación, Spain), P11-FQM-
7603, FQM329 (Junta de Andalucía, Spain), all with EU ERDF funds.
References
Alonso I, Carrizosa E, Conde E (1998) Maximin location: discretization not always works. TOP
6:313-319
Avella P, Boccia M (2007) A cutting plane algorithm for the capacitated facility location problem.
Comput Optim Appl 43:39-65
Avella P, Sassano A, Vasil'ev I (2006) Computational study of large-scale p-median problems.
Math Program 109:89-114
Berman O, Huang R (2008) The minimum weighted covering location problem with distance
constraints. Comput Oper Res 35:356-372
Berman O, Krass D (2002) The generalized maximal covering location problem. Comput Oper
Res 29:563-581
Berman O, Wang J (2011) The minmax regret gradual covering location problem on a network
with incomplete information of demand weights. Eur J Oper Res 208:233-238
Berman O, Drezner Z, Wesolowsky GO (1996) Minimum covering criterion for obnoxious facility
location on a network. Networks 28:1-5
Berman O, Krass D, Drezner Z (2003) The gradual covering decay location problem on a network.
Eur J Oper Res 151:474-480
Berman O, Drezner Z, Krass D (2009a) Cooperative cover location problems: the planar case. IIE
Trans 42:232-246
Berman O, Drezner Z, Wesolowsky GO (2009b) The maximal covering problem with some
negative weights. Geogr Anal 41:30-42
Berman O, Kalcsics J, Krass D, Nickel S (2009c) The ordered gradual covering location problem
on a network. Discrete Appl Math 157:3689-3707
Berman O, Drezner Z, Krass D (2010) Generalized coverage: new developments in covering
location models. Comput Oper Res 37:1675-1687
Blanquero R, Carrizosa E (2002) A DC biobjective location model. J Global Optim 23:139-154
Blanquero R, Carrizosa E (2008) Continuous location problems and big triangle small triangle:
constructing better bounds. J Global Optim 45:389-402
Blanquero R, Carrizosa E (2013) Solving the median problem with continuous demand on a
network. Comput Optim Appl 56:723-734
Bowman A, Foster P (1993) Density based exploration of bivariate data. Stat Comput 3:171-177
Carrizosa E, Plastria F (1998) Locating an undesirable facility by generalized cutting planes. Math
Oper Res 23:680-694
Carrizosa E, Plastria F (1999) Location of semi-obnoxious facilities. Stud Locat Anal 12:1-27
Carrizosa E, Conde E, Muñoz-Márquez M, Puerto J (1995) The generalized Weber problem with
expected distances. RAIRO-Rech Oper 29:35-57
Carrizosa E, Muñoz-Márquez M, Puerto J (1998a) Location and shape of a rectangular facility in
<
n
convexity properties. Math Program 83:277-290