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doi: 10.3934/jimo.2020044

Genetic algorithm for obstacle location-allocation problems with customer priorities

1. 

Department of Industrial Management, School of Management and Accounting, Shahid Beheshti University, G.C., Tehran, Iran

2. 

Mario J. Gabelli School of Business, Roger Williams University, 1 Old Ferry Road, Bristol, RI 02809, USA

3. 

Kar Higher Education Institute, Tehran, Iran

Corresponding author: Mostafa Zandieh

Received  August 2018 Revised  June 2019 Published  March 2020

In this paper we propose a metaheuristic approach to solve a customer priority based location-allocation problem in presence of obstacles and location-dependent supplier capacities. In many network optimization problems presence of obstacles prohibits feasibility of a regular network design. This includes a wide range of applications including disaster relief and pandemic disease containment problems in healthcare management. We focus on this application since fast and efficient allocation of suppliers to demand nodes is a critical process that impacts the results of the containment strategy. In this study, we propose an integrated mixed-integer program with location-based capacity decisions that considers customer priorities in the network design. We propose an efficient multi-stage genetic algorithm that solves the problem in continuous space. The computational findings show the best allocation strategies derived from proposed algorithms.

Citation: Ashkan Ayough, Farbod Farhadi, Mostafa Zandieh, Parisa Rastkhadiv. Genetic algorithm for obstacle location-allocation problems with customer priorities. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020044
References:
[1]

A. Ahmadi-JavidP. Seyedi and S. S. Syam, A survey of healthcare facility location, Computers and Operations Research, 79 (2017), 223-263.  doi: 10.1016/j.cor.2016.05.018.  Google Scholar

[2]

H. Alt and E. Welzl, Visibility graphs and obstacle-avoiding shortest paths, Mathematical Methods of Operations Research, 32 (1988), 145-164.  doi: 10.1007/BF01928918.  Google Scholar

[3]

Y. P. Aneja and M. Parlar, Algorithms for Weber facility location in the presence of forbidden regions and/or barriers to travel, Transportation Science, 28 (1994), 70-76.  doi: 10.1287/trsc.28.1.70.  Google Scholar

[4]

A. B. Arabani and R. Z. Farahani, Facility location dynamics: An overview of classifications and applications, Computers and Industrial Engineering, 62 (2012), 408-420.   Google Scholar

[5]

J. BrimbergP. HansenN. Mladenović and E. D. Taillard, Improvements and comparison of heuristics for solving the uncapacitated multisource Weber problem, Operations Research, 48 (2000), 444-460.  doi: 10.1287/opre.48.3.444.12431.  Google Scholar

[6]

S. E. Butt and T. M. Cavalier, An efficient algorithm for facility location in the presence of forbidden regions, European Journal of Operational Research, 90 (1996), 56-70.  doi: 10.1016/0377-2217(94)00297-5.  Google Scholar

[7]

E. DurmazN. Aras and İ. K. Altınel, Discrete approximation heuristics for the capacitated continuous locationallocation problem with probabilistic customer locations, Computers and Operations Research, 36 (2009), 2139-2148.  doi: 10.1016/j.cor.2008.08.003.  Google Scholar

[8]

D. GongM. GenW. Xu and G. Yamazaki, Hybrid evolutionary method for obstacle location-allocation problem, Computers and Industrial Engineering, 29 (1995), 525-530.   Google Scholar

[9]

D. J. GongM. GenG. Yamazaki and W. X. Xu, Hybrid evolutionary method for capacitated location-allocation problem, Computers and Industrial Engineering, 33 (1997), 577-580.  doi: 10.1016/S0360-8352(97)00197-6.  Google Scholar

[10]

S. C. Ho, An iterated tabu search heuristic for the single source capacitated facility location problem, Applied Soft Computing, 27 (2015), 169-178.  doi: 10.1016/j.asoc.2014.11.004.  Google Scholar

[11]

C. R. HouckJ. A. Joines and M. G. Kay, Comparison of genetic algorithms, random restart and two-opt switching for solving large location-allocation problems, Computers and Operations Research, 23 (1996), 587-596.  doi: 10.1016/0305-0548(95)00063-1.  Google Scholar

[12]

J. H. JaramilloJ. Bhadury and R. Batta, On the use of genetic algorithms to solve location problems, Computers and Operations Research, 29 (2002), 761-779.  doi: 10.1016/S0305-0548(01)00021-1.  Google Scholar

[13]

J. KalcsicsS. NickelM. A. PozoJ. Puerto and A. M. Rodríguez-Chía, The multicriteria $p$-facility median location problem on networks, European Journal of Operational Research, 235 (2014), 484-493.  doi: 10.1016/j.ejor.2014.01.003.  Google Scholar

[14]

I. N. Katz and L. Cooper, Facility location in the presence of forbidden regions. I: Formulation and the case of Euclidean distance with one forbidden circle, European Journal of Operational Research, 6 (1981), 166-173.  doi: 10.1016/0377-2217(81)90203-4.  Google Scholar

[15]

K. Klamroth, A reduction result for location problems with polyhedral barriers, European Journal of Operational Research, 130 (2001), 486-497.  doi: 10.1016/S0377-2217(99)00399-9.  Google Scholar

[16]

J. Krarup and P. M. Pruzan, The simple plant location problem: Survey and synthesis, European Journal of Operational Research, 12 (1983), 36-81.  doi: 10.1016/0377-2217(83)90181-9.  Google Scholar

[17]

R. E. Kuenne and R. M. Soland, Exact and approximate solutions to the multisource Weber problem, Mathematical Programming, 3 (1972), 193-209.  doi: 10.1007/BF01584989.  Google Scholar

[18]

G. LaporteF. V. Louveaux and L. van Hamme, Exact solution to a location problem with stochastic demands, Transportation Science, 28 (1994), 95-103.  doi: 10.1287/trsc.28.2.95.  Google Scholar

[19]

G. Laporte, S. Nickel and F. S. da Gama, Location Science, Springer, Berlin, 2015. doi: 978-3-319-13111-5.  Google Scholar

[20]

R. C. Larson and G. Sadiq, Facility locations with the Manhattan metric in the presence of barriers to travel, Operations Research, 31 (1983), 652-669.  doi: 10.1287/opre.31.4.652.  Google Scholar

[21]

B. LiI. HernandezA. B. Milburn and J. E. Ramirez-Marquez, Integrating uncertain user-generated demand data when locating facilities for disaster response commodity distribution, Socio-Economic Planning Sciences, 62 (2018), 84-103.  doi: 10.1016/j.seps.2017.09.003.  Google Scholar

[22]

R. Logendran and M. P. Terrell, Uncapacitated plant location-allocation problems with price sensitive stochastic demands, Computers and Operations Research, 15 (1988), 189-198.  doi: 10.1016/0305-0548(88)90011-1.  Google Scholar

[23]

R. G. McGarvey and T. M. Cavalier, A global optimal approach to facility location in the presence of forbidden regions, Computers and Industrial Engineering, 45 (2003), 1-15.  doi: 10.1016/S0360-8352(03)00028-7.  Google Scholar

[24]

M. T. MeloS. Nickel and F. Saldanha-da-Gama, Facility location and supply chain management - a review, European journal of operational research, 196 (2009), 401-412.  doi: 10.1016/j.ejor.2008.05.007.  Google Scholar

[25]

S. M. MousaviS. T. A. NiakiE. Mehdizadeh and M. R. Tavarroth, The capacitated multi-facility locationallocation problem with probabilistic customer location and demand: Two hybrid metaheuristics algorithms, International Journal of Systems Science, 44 (2013), 1897-1912.  doi: 10.1080/00207721.2012.670301.  Google Scholar

[26]

J. A. Paul and R. Batta, Models for hospital location and capacity allocation for an area prone to natural disasters, International Journal of Operational Research, 3 (2008), 473-496.  doi: 10.1504/IJOR.2008.019170.  Google Scholar

[27]

F. Pérez-Galarce, L. J. Canales, C. Vergara and A. Candia-Véjar, An optimization model for the location of disaster refuges, Socio-Economic Planning Sciences, 59 (2017), 56-66. Google Scholar

[28]

C. S. ReVelle and H. A. Eiselt, Location analysis: A synthesis and survey, European Journal of Operational Research, 165 (2005), 1-19.  doi: 10.1016/j.ejor.2003.11.032.  Google Scholar

[29]

C. S. ReVelleH. A. Eiselt and M. S. Daskin, A bibliography for some fundamental problem categories in discrete location science, European Journal of Operational Research, 184 (2008), 817-848.  doi: 10.1016/j.ejor.2006.12.044.  Google Scholar

[30]

S. Salhi and M. D. H. Gamal, A genetic algorithm based approach for the uncapacitated continuous locationallocation problem, Annals of Operations Research, 123 (2003), 203-222.  doi: 10.1023/A:1026131531250.  Google Scholar

[31]

T. SantosoS. AhmedM. Goetschalckx and A. Shapiro, A stochastic programming approach for supply chain network design under uncertainty, European Journal of Operational Research, 167 (2005), 96-115.  doi: 10.1016/j.ejor.2004.01.046.  Google Scholar

[32]

A. Schöbel, Location of Dimensional Facilities in a Continuous Space, in: Laporte G., Nickel S., Saldanha da Gama F. (eds), Location Science, Berlin: Springer, 2015. Google Scholar

[33]

S. R. ShariffN. H. Moin and M. Omar, Location allocation modeling for healthcare facility planning in Malaysia, Computers and Industrial Engineering, 62 (2012), 1000-1010.  doi: 10.1016/j.cie.2011.12.026.  Google Scholar

[34]

H. D. SheraliT. B. Carter and A. G. Hobeika, A location-allocation model and algorithm for evacuation planning under hurricane/flood conditions, Transportation Research Part B: Methodological, 25 (1991), 439-452.  doi: 10.1016/0191-2615(91)90037-J.  Google Scholar

[35]

Z. Stanimirović, A genetic algorithm approach for the capacitated single allocation p-hub median problem, Computing and Informatics, 29 (2012), 117-132.   Google Scholar

[36]

J. TaniguchiX. WangM. Gen and T. Yokota, Hybrid genetic algorithm with fuzzy logic controller for obstacle location-allocation problem, IEEJ Transactions on Electronics, Information and Systems, 124 (2004), 2027-2033.   Google Scholar

[37]

A. Verma and G. M. Gaukler, Pre-positioning disaster response facilities at safe locations: An evaluation of deterministic and stochastic modeling approaches, Computers and Operations Research, 62 (2015), 197-209.  doi: 10.1016/j.cor.2014.10.006.  Google Scholar

[38]

N. Vidyarthi and S. Jayaswal, Efficient solution of a class of locationallocation problems with stochastic demand and congestion, Computers and Operations Research, 48 (2014), 20-30.  doi: 10.1016/j.cor.2014.02.014.  Google Scholar

[39]

J. Zhou and B. D. Liu, New stochastic models for capacitated location-allocation problem, Computers and Industrial Engineering, 45 (2003), 111-125.  doi: 10.1016/S0360-8352(03)00021-4.  Google Scholar

show all references

References:
[1]

A. Ahmadi-JavidP. Seyedi and S. S. Syam, A survey of healthcare facility location, Computers and Operations Research, 79 (2017), 223-263.  doi: 10.1016/j.cor.2016.05.018.  Google Scholar

[2]

H. Alt and E. Welzl, Visibility graphs and obstacle-avoiding shortest paths, Mathematical Methods of Operations Research, 32 (1988), 145-164.  doi: 10.1007/BF01928918.  Google Scholar

[3]

Y. P. Aneja and M. Parlar, Algorithms for Weber facility location in the presence of forbidden regions and/or barriers to travel, Transportation Science, 28 (1994), 70-76.  doi: 10.1287/trsc.28.1.70.  Google Scholar

[4]

A. B. Arabani and R. Z. Farahani, Facility location dynamics: An overview of classifications and applications, Computers and Industrial Engineering, 62 (2012), 408-420.   Google Scholar

[5]

J. BrimbergP. HansenN. Mladenović and E. D. Taillard, Improvements and comparison of heuristics for solving the uncapacitated multisource Weber problem, Operations Research, 48 (2000), 444-460.  doi: 10.1287/opre.48.3.444.12431.  Google Scholar

[6]

S. E. Butt and T. M. Cavalier, An efficient algorithm for facility location in the presence of forbidden regions, European Journal of Operational Research, 90 (1996), 56-70.  doi: 10.1016/0377-2217(94)00297-5.  Google Scholar

[7]

E. DurmazN. Aras and İ. K. Altınel, Discrete approximation heuristics for the capacitated continuous locationallocation problem with probabilistic customer locations, Computers and Operations Research, 36 (2009), 2139-2148.  doi: 10.1016/j.cor.2008.08.003.  Google Scholar

[8]

D. GongM. GenW. Xu and G. Yamazaki, Hybrid evolutionary method for obstacle location-allocation problem, Computers and Industrial Engineering, 29 (1995), 525-530.   Google Scholar

[9]

D. J. GongM. GenG. Yamazaki and W. X. Xu, Hybrid evolutionary method for capacitated location-allocation problem, Computers and Industrial Engineering, 33 (1997), 577-580.  doi: 10.1016/S0360-8352(97)00197-6.  Google Scholar

[10]

S. C. Ho, An iterated tabu search heuristic for the single source capacitated facility location problem, Applied Soft Computing, 27 (2015), 169-178.  doi: 10.1016/j.asoc.2014.11.004.  Google Scholar

[11]

C. R. HouckJ. A. Joines and M. G. Kay, Comparison of genetic algorithms, random restart and two-opt switching for solving large location-allocation problems, Computers and Operations Research, 23 (1996), 587-596.  doi: 10.1016/0305-0548(95)00063-1.  Google Scholar

[12]

J. H. JaramilloJ. Bhadury and R. Batta, On the use of genetic algorithms to solve location problems, Computers and Operations Research, 29 (2002), 761-779.  doi: 10.1016/S0305-0548(01)00021-1.  Google Scholar

[13]

J. KalcsicsS. NickelM. A. PozoJ. Puerto and A. M. Rodríguez-Chía, The multicriteria $p$-facility median location problem on networks, European Journal of Operational Research, 235 (2014), 484-493.  doi: 10.1016/j.ejor.2014.01.003.  Google Scholar

[14]

I. N. Katz and L. Cooper, Facility location in the presence of forbidden regions. I: Formulation and the case of Euclidean distance with one forbidden circle, European Journal of Operational Research, 6 (1981), 166-173.  doi: 10.1016/0377-2217(81)90203-4.  Google Scholar

[15]

K. Klamroth, A reduction result for location problems with polyhedral barriers, European Journal of Operational Research, 130 (2001), 486-497.  doi: 10.1016/S0377-2217(99)00399-9.  Google Scholar

[16]

J. Krarup and P. M. Pruzan, The simple plant location problem: Survey and synthesis, European Journal of Operational Research, 12 (1983), 36-81.  doi: 10.1016/0377-2217(83)90181-9.  Google Scholar

[17]

R. E. Kuenne and R. M. Soland, Exact and approximate solutions to the multisource Weber problem, Mathematical Programming, 3 (1972), 193-209.  doi: 10.1007/BF01584989.  Google Scholar

[18]

G. LaporteF. V. Louveaux and L. van Hamme, Exact solution to a location problem with stochastic demands, Transportation Science, 28 (1994), 95-103.  doi: 10.1287/trsc.28.2.95.  Google Scholar

[19]

G. Laporte, S. Nickel and F. S. da Gama, Location Science, Springer, Berlin, 2015. doi: 978-3-319-13111-5.  Google Scholar

[20]

R. C. Larson and G. Sadiq, Facility locations with the Manhattan metric in the presence of barriers to travel, Operations Research, 31 (1983), 652-669.  doi: 10.1287/opre.31.4.652.  Google Scholar

[21]

B. LiI. HernandezA. B. Milburn and J. E. Ramirez-Marquez, Integrating uncertain user-generated demand data when locating facilities for disaster response commodity distribution, Socio-Economic Planning Sciences, 62 (2018), 84-103.  doi: 10.1016/j.seps.2017.09.003.  Google Scholar

[22]

R. Logendran and M. P. Terrell, Uncapacitated plant location-allocation problems with price sensitive stochastic demands, Computers and Operations Research, 15 (1988), 189-198.  doi: 10.1016/0305-0548(88)90011-1.  Google Scholar

[23]

R. G. McGarvey and T. M. Cavalier, A global optimal approach to facility location in the presence of forbidden regions, Computers and Industrial Engineering, 45 (2003), 1-15.  doi: 10.1016/S0360-8352(03)00028-7.  Google Scholar

[24]

M. T. MeloS. Nickel and F. Saldanha-da-Gama, Facility location and supply chain management - a review, European journal of operational research, 196 (2009), 401-412.  doi: 10.1016/j.ejor.2008.05.007.  Google Scholar

[25]

S. M. MousaviS. T. A. NiakiE. Mehdizadeh and M. R. Tavarroth, The capacitated multi-facility locationallocation problem with probabilistic customer location and demand: Two hybrid metaheuristics algorithms, International Journal of Systems Science, 44 (2013), 1897-1912.  doi: 10.1080/00207721.2012.670301.  Google Scholar

[26]

J. A. Paul and R. Batta, Models for hospital location and capacity allocation for an area prone to natural disasters, International Journal of Operational Research, 3 (2008), 473-496.  doi: 10.1504/IJOR.2008.019170.  Google Scholar

[27]

F. Pérez-Galarce, L. J. Canales, C. Vergara and A. Candia-Véjar, An optimization model for the location of disaster refuges, Socio-Economic Planning Sciences, 59 (2017), 56-66. Google Scholar

[28]

C. S. ReVelle and H. A. Eiselt, Location analysis: A synthesis and survey, European Journal of Operational Research, 165 (2005), 1-19.  doi: 10.1016/j.ejor.2003.11.032.  Google Scholar

[29]

C. S. ReVelleH. A. Eiselt and M. S. Daskin, A bibliography for some fundamental problem categories in discrete location science, European Journal of Operational Research, 184 (2008), 817-848.  doi: 10.1016/j.ejor.2006.12.044.  Google Scholar

[30]

S. Salhi and M. D. H. Gamal, A genetic algorithm based approach for the uncapacitated continuous locationallocation problem, Annals of Operations Research, 123 (2003), 203-222.  doi: 10.1023/A:1026131531250.  Google Scholar

[31]

T. SantosoS. AhmedM. Goetschalckx and A. Shapiro, A stochastic programming approach for supply chain network design under uncertainty, European Journal of Operational Research, 167 (2005), 96-115.  doi: 10.1016/j.ejor.2004.01.046.  Google Scholar

[32]

A. Schöbel, Location of Dimensional Facilities in a Continuous Space, in: Laporte G., Nickel S., Saldanha da Gama F. (eds), Location Science, Berlin: Springer, 2015. Google Scholar

[33]

S. R. ShariffN. H. Moin and M. Omar, Location allocation modeling for healthcare facility planning in Malaysia, Computers and Industrial Engineering, 62 (2012), 1000-1010.  doi: 10.1016/j.cie.2011.12.026.  Google Scholar

[34]

H. D. SheraliT. B. Carter and A. G. Hobeika, A location-allocation model and algorithm for evacuation planning under hurricane/flood conditions, Transportation Research Part B: Methodological, 25 (1991), 439-452.  doi: 10.1016/0191-2615(91)90037-J.  Google Scholar

[35]

Z. Stanimirović, A genetic algorithm approach for the capacitated single allocation p-hub median problem, Computing and Informatics, 29 (2012), 117-132.   Google Scholar

[36]

J. TaniguchiX. WangM. Gen and T. Yokota, Hybrid genetic algorithm with fuzzy logic controller for obstacle location-allocation problem, IEEJ Transactions on Electronics, Information and Systems, 124 (2004), 2027-2033.   Google Scholar

[37]

A. Verma and G. M. Gaukler, Pre-positioning disaster response facilities at safe locations: An evaluation of deterministic and stochastic modeling approaches, Computers and Operations Research, 62 (2015), 197-209.  doi: 10.1016/j.cor.2014.10.006.  Google Scholar

[38]

N. Vidyarthi and S. Jayaswal, Efficient solution of a class of locationallocation problems with stochastic demand and congestion, Computers and Operations Research, 48 (2014), 20-30.  doi: 10.1016/j.cor.2014.02.014.  Google Scholar

[39]

J. Zhou and B. D. Liu, New stochastic models for capacitated location-allocation problem, Computers and Industrial Engineering, 45 (2003), 111-125.  doi: 10.1016/S0360-8352(03)00021-4.  Google Scholar

Figure 1.  Obstacle and the marginal area
Figure 2.  Alternative connecting paths around an obstacle
Figure 3.  Visibility graph method around the obstacles
Figure 4.  Type two chromosome crossover
Figure 5.  Supplier and demand network in the sample
Figure 6.  Convergence of GCOLAP1 and GCOLAP2 on the sample
Table 1.  Sample instance from randomly generated instances
Parameter Value
Number of customers 17
Number of distribution centers 3
Number of forbidden areas 1
The radius of margin 15
The coordinates of margin center (50, 30)
Number of corners of each of regions 5
Parameter Value
Number of customers 17
Number of distribution centers 3
Number of forbidden areas 1
The radius of margin 15
The coordinates of margin center (50, 30)
Number of corners of each of regions 5
Table 2.  Summary of computational results on randomly generated instances
Objective Function
Instance m n R-SCOLAP SCOLAP GCOLAP1 GCOLAP2 MIP gap GA gap
1 2 8 0.0435 19.41 25.44 26.96 0 0.31
2 2 10 0.0443 30.56 36.57 34.21 0 0.2
3 2 12 0.0424 33.26 39.18 47.41 0 0.18
4 2 15 0.0493 65.52 80.89 77.46 0 0.23
5 3 17 0.0443 65.5 87.34 105.68 0 0.33
6 3 20 0.0542 138.12 177.07 139.72 0.00009 0.28
7 3 25 0.0677 163.25 209.29 214.77 0.0001 0.28
8 3 30 0.0723 273.86 329.96 277.23 0.00254 0.2
9 4 35 0.0738 - 249.24 501.61 - -
10 4 40 0.0881 - 387.83 500.64 - -
11 4 44 0.0733 - 618.62 645.86 - -
12 5 47 0.077 - 721.32 941.63 - -
13 5 50 0.138 - 835.72 1122.76 - -
14 5 55 0.0971 - 854.85 1025.11 - -
15 6 60 0.1343 - 1542.82 1825.43 - -
16 6 65 0.1067 - 1382.88 1738.93 - -
17 7 70 0.1536 - 1699.78 2836.1 - -
18 7 74 0.1206 - 2021.15 2590.2 - -
19 8 78 0.1088 - 2145.16 3079.13 - -
20 8 82 0.1156 - 3210.13 3450.84 - -
Objective Function
Instance m n R-SCOLAP SCOLAP GCOLAP1 GCOLAP2 MIP gap GA gap
1 2 8 0.0435 19.41 25.44 26.96 0 0.31
2 2 10 0.0443 30.56 36.57 34.21 0 0.2
3 2 12 0.0424 33.26 39.18 47.41 0 0.18
4 2 15 0.0493 65.52 80.89 77.46 0 0.23
5 3 17 0.0443 65.5 87.34 105.68 0 0.33
6 3 20 0.0542 138.12 177.07 139.72 0.00009 0.28
7 3 25 0.0677 163.25 209.29 214.77 0.0001 0.28
8 3 30 0.0723 273.86 329.96 277.23 0.00254 0.2
9 4 35 0.0738 - 249.24 501.61 - -
10 4 40 0.0881 - 387.83 500.64 - -
11 4 44 0.0733 - 618.62 645.86 - -
12 5 47 0.077 - 721.32 941.63 - -
13 5 50 0.138 - 835.72 1122.76 - -
14 5 55 0.0971 - 854.85 1025.11 - -
15 6 60 0.1343 - 1542.82 1825.43 - -
16 6 65 0.1067 - 1382.88 1738.93 - -
17 7 70 0.1536 - 1699.78 2836.1 - -
18 7 74 0.1206 - 2021.15 2590.2 - -
19 8 78 0.1088 - 2145.16 3079.13 - -
20 8 82 0.1156 - 3210.13 3450.84 - -
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