This study investigates the capacitated planar multi-facility location-allocation problem by considering various capacity constraints. The problem is also known as the capacitated multi-source Weber problem, where the number of facilities to be located is specified and each of which has a capacity constraint. An efficient greedy randomised adaptive search procedure (GRASP) is proposed to deal with the problem. A scheme that applies the furthest distance rule (FDR) and self-adjusted threshold parameters to generate initial facility locations that are situated sparsely within GRASP framework is also presented. The construction of the restricted candidate list (RCL) within GRASP is also guided by applying a concept of restricted regions that prevents new facility locations to be sited too close to the previous selected facility locations. The performance of the proposed GRASP heuristics is tested using benchmark data sets from literature. The computational experiments show that the proposed methods provide encouraging solutions when compared to recently published papers. Some future research avenues on the subject are also briefly highlighted.
REFERENCES
1.
J.
Brimberg
, P.
Hansen
, N.
Mladenović
, and S.
Salhi
, A Survey of Solution Methods for the Continuous Location-Allocation Problem
, International Journal of Operations Research
5
, 1
–12
(2008
).2.
J.
Brimberg
, Z.
Drezner
, N.
Mladenović
, and S.
Salhi
, A New Local Search for Continuous Location Problems
. European Journal of Operational Research
232
, 256
–265
(2014
).3.
L.
Cooper
, The Transportation-Location Problem
, Operations Research
20
, 94
–108
(1972
).4.
L.
Cooper
, Heuristic Methods for Location-Allocation Problems
, SIAM Review
6
, 37
–53
(1964
).5.
L.
Cooper
, An Efficient Heuristic Algorithm for the Transportation-Location Problem
, Journal of Regional Science
16
, 309
–3015
(1976
).6.
L.
Cooper
, The Fixed Charge Problem – I: A New Heuristic Method
, Computers and Mathematics with Applications
1
, 89
–95
(1975
).7.
H. D.
Sherali
, S.
Ramachandran
, and S.
Kim
, 1994. A Localization and Reformulation Discrete Programming Approach for the Rectilinear Distance Location-Allocation Problem
, Discrete Applied Mathematics
49
, 357
–378
(1994
).8.
D.
Gong
, M.
Gen
, G.
Yamazaki
, and W.
Xu
, Hybrid Evolutionary Method for Capacitated Location-Allocation Problem
, Computers and Industrial Engineering
33
, 577
–580
(1997
).9.
H. D.
Sherali
, I.
Al-Loughani
, and S.
Subramanian
, Global Optimization Procedures for the Capacitated Euclidean and lp Distance Multifacility Location-Allocation Problem
, Operations Research
50
, 433
–448
(2002
).10.
N.
Aras
, I. K.
Altınel
, and M.
Orbay
, New Heuristic Methods for the Capacitated Multi-Facility Weber Problem
, Naval Research Logistics
54
, 21
–32
(2007
).11.
P.
Hansen
, N.
Mladenović
, and E. D.
Taillard
, Heuristic of the Multisource Weber Problem as a p-Median Problem
, Operation Research Letters
22
, 55
–62
(1998
).12.
M. D. H.
Gamal
and S.
Salhi
, A Cellular Heuristic for the Multisource Weber Problem
, Computers and Operations Research
30
, 1609
–1624
(2003
).13.
N.
Aras
, S.
Yumusak
, and I. K.
Altınel
, I. K., “Solving the Capacitated Multi-Facility Weber Problem by Simulated Annealing, Threshold Accepting and Genetic Algorithms”, in Metaheuristics: Progress in Complex Systems Optimization
, edited by K. F.
Doerner
, M.
Gendreau
, P.
Greistorfer
, W. J.
Gutjahr
, R. F.
Hartl
, and M.
Reimann
(Springer
, New York
, 2007
), pp. 91
–112
.14.
N.
Aras
, M.
Orbay
, and I. K.
Altinel
, Efficient Heuristics for the Rectilinear Distance Capacitated Multi-Facility Weber Problem
, Journal of the Operational Research Society
59
, 64
–79
(2008
).15.
M. Z.
Zainuddin
and S.
Salhi
, A Perturbation-Based Heuristic for the Capacitated Multisource Weber Problem
, European Journal of Operational Research
179
, 1194
–1207
(2007
).16.
M.
Luis
, S.
Salhi
, and G.
Nagy
, Region-Rejection Based Heuristics for the Capacitated Multi-Source Weber Problem
, Computers and Operations Research
36
, 2007
–2017
(2009
).17.
N.
Mohammadi
, M. R.
Malek
, and A. A.
Alesheikh
, A New GA Based Solution for Capacitated Multi Source Weber Problem
, International Journal of Computational Intelligence Systems
3
, 514
–521
(2010
).18.
M.
Luis
, S.
Salhi
, and G.
Nagy
, A Guided Reactive GRASP for the Capacitated Multi-Source Weber Problem
, Computers and Operations Research
38
, 1014
–1024
(2011
).19.
M. H.
Akyüz
, I. K.
Altınel
, and T.
Öncan
, Location and Allocation based Branch and Bound Algorithms for the Capacitated Multi-Facility Weber Problem
, Annals of Operations Research
222
, 45
–71
(2014
).20.
M.
Luis
, M. F.
Ramli
, and R. Surya
Saputra
, “Efficient GRASP based Heuristics for the Capacitated Continuous Location-Allocation Problem”, in International of Mathematics, Engineering and Industrial Applications 2014
, AIP Conference Proceedings
1660
, edited by M. F.
Ramli
, et al., (American Institute of Physics
, Melville, NY
, 2015
).21.
M. H.
Akyüz
, T.
Öncan
, and I. K.
Altınel
, Beam search heuristics for the single and multi-commodity capacitated Multi-facility Weber Problems
, Computers and Operations Research
40
, 3056
–3068
(2013
).22.
A.
Jamalian
, and M.
Salahi
, Robust solutions to multi-facility Weber location problem under interval and ellipsoidal uncertainty
, Applied Mathematics and Computation
242
, 179
–186
(2014
).23.
J. P.
Hart
and A. W.
Shogan
, Semi-greedy Heuristics: An Empirical Study
. Operations Research Letters
6
, 107
–114
(1987
).24.
T. A.
Feo
and M. G. C.
Resende
, A Probabilistic Heuristic for a Computationally Difficult Set Covering Problem
. Operations Research Letters
8
, 67
–71
(1989
).25.
T. A.
Feo
and M. G. C.
Resende
, Greedy Randomized Adaptive Search Procedures
, Journal of Global Optimization
6
, 109
–133
(1995
).26.
L. S.
Pitsoulis
and M. G. C.
Resende
, “Greedy Randomized Adaptive Search Procedures”, in Handbook of Applied Optimization
edited by P. M.
Pardalos
and M. G. C.
Resende
(Oxford University Press
, Oxford
, 2002
), pp. 168
–181
.27.
M. G. C.
Resende
and C. C.
Ribeiro
, “Greedy Randomized Adaptive Search Procedures: Advances, Hybridizations, and Applications”, in Handbook of Metaheuristics of International Series in Operations Research & Management Science
, edited by M.
Gendreau
and J. Y.
Potvin
(Springer
, New York
, 2010
), pp. 283
–319
.28.
M. D. H.
Gamal
and S.
Salhi
, Constructive Heuristics for the Uncapacitated Location–Allocation Problem
. Journal of the Operational Research Society
51
, 1233
–1240
(2001
).29.
J.
Brimberg
, P.
Hansen
, N.
Mladenović
, and E. D.
Taillard
, Improvements and Comparison of Heuristics for Solving the Uncapacitated Multisource Weber Problem
. Operations Research
48
, 444
–460
(2000
).
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