Facility location problem - Revision history

Wc593 at 11:35, 21 December 2020

2020-12-21T11:35:38Z

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	Authors: Liz Cantlebary, Lawrence Li (~~CHEME~~ 6800 Fall 2020)		Authors: Liz Cantlebary, Lawrence Li (ChemE 6800 Fall 2020)

	== Introduction ==		== Introduction ==

Wc593 at 10:33, 21 December 2020

2020-12-21T10:33:29Z

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	Authors: Liz Cantlebary, Lawrence Li (CHEME 6800 Fall 2020)		Authors: Liz Cantlebary, Lawrence Li (CHEME 6800 Fall 2020)

	~~Stewards: Allen Yang, Fengqi You~~

	== Introduction ==		== Introduction ==
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	The problem is solved in GAMS (General Algebraic Modeling System). ~~As an example, the code for the St. Louis factory is shown below.~~		The problem is solved in GAMS (General Algebraic Modeling System).
	~~[[File:Code.png\|center\|frame\|Formulation of the problem in GAMS code ]]~~


	If the factory is built in Denver, 300 tons/day of product go to Los Angeles and 100 tons/day go to Topeka, for a total profit of $36,300/day.		If the factory is built in Denver, 300 tons/day of product go to Los Angeles and 100 tons/day go to Topeka, for a total profit of $36,300/day.

Lawrenceli: /* Capacitated and Uncapacitated FLPs */

2020-12-12T18:27:21Z

Capacitated and Uncapacitated FLPs

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	== Applications ==		== Applications ==
	[[File:BadranElHaggarFacilityLocation.jpg\|thumb\|~~314x314px~~\|Map of optimal collection stations in Port Said, Egypt<sup>(12)</sup>.]]		[[File:BadranElHaggarFacilityLocation.jpg\|thumb\|321x321px\|Map of optimal collection stations in Port Said, Egypt<sup>(12)</sup>.]]
	Facility location problems are utilized in many industries to find the optimal placement of various facilities, including warehouses, power plants, public transportation terminals, polling locations, and cell towers, to maximize efficiency, impact, and profit. In more unique applications, extensive research has been done in applying FLPs to humanitarian efforts, such as identifying disaster management sites to maximize accessibility to healthcare and treatment<sup>(10)</sup>. A case study by researchers in Nigeria explored the application of mixed-integer FLPs in optimizing the locations of waste collection centers to provide sanitation services in crucial communities. More effective waste collection systems could combat unsanitary practices and environmental pollution, which are major concerns in many developing nations<sup>(11)</sup>. For example, Badran and El-Haggar proposed a solid waste management system for Port Said, Egypt, implementing a mixed-integer program to optimally place waste collection stations and minimize cost<sup>(12)</sup>. This program was formulated to select collection stations from a set of locations such that the sum of the fixed cost of opening collections stations, the operating costs of the collection stations, and the transportation costs from the collection stations to the composting plants is minimized.		Facility location problems are utilized in many industries to find the optimal placement of various facilities, including warehouses, power plants, public transportation terminals, polling locations, and cell towers, to maximize efficiency, impact, and profit. In more unique applications, extensive research has been done in applying FLPs to humanitarian efforts, such as identifying disaster management sites to maximize accessibility to healthcare and treatment<sup>(10)</sup>. A case study by researchers in Nigeria explored the application of mixed-integer FLPs in optimizing the locations of waste collection centers to provide sanitation services in crucial communities. More effective waste collection systems could combat unsanitary practices and environmental pollution, which are major concerns in many developing nations<sup>(11)</sup>. For example, Badran and El-Haggar proposed a solid waste management system for Port Said, Egypt, implementing a mixed-integer program to optimally place waste collection stations and minimize cost<sup>(12)</sup>. This program was formulated to select collection stations from a set of locations such that the sum of the fixed cost of opening collections stations, the operating costs of the collection stations, and the transportation costs from the collection stations to the composting plants is minimized.

	FLPs have also been used in clustering analysis, which involves partitioning a given set of elements (e.g. data points) into different groups based on the similarity of the elements. The elements can be placed into groups by identifying the locations of center points that effectively partition the set into clusters, based on the distances from the center points to each element<sup>(13)</sup>. For example, the <math>k</math>-median clustering problem can be formulated as a FLP that selects a set of <math>k</math> cluster centers to minimize the cost between each point and its closest center. The cost in this problem is represented as the Euclidean distance between ~~two~~ points. ~~These problems are~~ commonly solved using approximation algorithms.		FLPs have also been used in clustering analysis, which involves partitioning a given set of elements (e.g. data points) into different groups based on the similarity of the elements. The elements can be placed into groups by identifying the locations of center points that effectively partition the set into clusters, based on the distances from the center points to each element<sup>(13)</sup>. For example, the <math>k</math>-median clustering problem can be formulated as a FLP that selects a set of <math>k</math> cluster centers to minimize the cost between each point and its closest center. The cost in this problem is represented as the Euclidean distance <math>d(i,j)</math> between a point <math>i</math> and a proposed cluster center <math>j</math>. The problem can be formulated as the following integer program, which selects <math>k</math> centers from a set of <math>N</math> points<sup>(13)</sup>.

			<math>\min\ \sum_{i=1}^N x_{ij}d(ij)</math>

			<math>s.t.\ \sum_{j=1}^Ny_j\leq k</math>

			<math>\quad \quad \sum_{j=1}^Nx_{ij}=1</math>

			<math>\quad \quad x_{ij}\leq y_j</math>

			<math>\quad \quad x_{ij}, y_j\in\{0,1\}</math>

			In this formulation, the binary variables <math>y_j</math> and <math>x_{ij}</math> represent whether <math>j</math> is used as a center point and whether <math>j</math> is the optimal center for <math>i</math>, respectively. The <math>k</math>-median problem is NP-hard and is commonly solved using approximation algorithms. One of the most effective algorithms to date, proposed by Byrka et al., has an approximation factor of 2.611<sup>(13)</sup>.

	== Conclusion ==		== Conclusion ==

Lawrenceli: /* References */

2020-12-10T04:32:35Z

References

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	# Adeleke, O. J.; Olukanni, D. O. (2020), [https://www.mdpi.com/2313-4321/5/2/10 Facility Location Problems: Models, Techniques, and Applications in Waste Management.] ''Recycling, 5'', 10.		# Adeleke, O. J.; Olukanni, D. O. (2020), [https://www.mdpi.com/2313-4321/5/2/10 Facility Location Problems: Models, Techniques, and Applications in Waste Management.] ''Recycling, 5'', 10.
	# Badran, M.F.; El-Haggar, S.M. (2006), [https://www.sciencedirect.com/science/article/abs/pii/S0956053X05001534 Optimization of Municipal Solid Waste Management in Port Said – Egypt.] ''Waste Management, 26'', 5, 534-545.		# Badran, M.F.; El-Haggar, S.M. (2006), [https://www.sciencedirect.com/science/article/abs/pii/S0956053X05001534 Optimization of Municipal Solid Waste Management in Port Said – Egypt.] ''Waste Management, 26'', 5, 534-545.
	# Meira, L. A. A.~~; Miyazawa~~, ~~F. K.; Pedrosa, L. L. C~~. (2017), [https://www.sciencedirect.com/science/article/abs/pii/S030439751630514X Clustering through Continuous Facility Location Problems.] ''Theoretical Computer Science, 657'', 137-145.		# Meira, L. A. A., et al. (2017), [https://www.sciencedirect.com/science/article/abs/pii/S030439751630514X Clustering through Continuous Facility Location Problems.] ''Theoretical Computer Science, 657'', 137-145.
	# Balcik, B.; Beamon, B. M. (2008), [https://www.tandfonline.com/doi/full/10.1080/13675560701561789 Facility Location in Humanitarian Relief.] ''International Journal of Logistics Research and Applications, 11'', 101-121.		# Balcik, B.; Beamon, B. M. (2008), [https://www.tandfonline.com/doi/full/10.1080/13675560701561789 Facility Location in Humanitarian Relief.] ''International Journal of Logistics Research and Applications, 11'', 101-121.
	# Eiselt, H. A.; Marianov, V. (2019), ''Contributions to Location Analysis''. Cham, Switzerland: Springer.		# Eiselt, H. A.; Marianov, V. (2019), ''Contributions to Location Analysis''. Cham, Switzerland: Springer.

Lawrenceli: /* Numerical Example */

2020-12-10T04:29:55Z

Numerical Example

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	<math>D_j</math> is the amount of unmet demand in the city		<math>D_j</math> is the amount of unmet demand in the city




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	The problem is solved in GAMS (General Algebraic ~~Modelling~~ System). As an example, the code for the St. Louis factory is shown below.		The problem is solved in GAMS (General Algebraic Modeling System). As an example, the code for the St. Louis factory is shown below.
	[[File:Code.png\|center\|frame]]		[[File:Code.png\|center\|frame\|Formulation of the problem in GAMS code ]]


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	This example can also be solved approximately through the branch and bound method. The tree diagram showing the optimization is shown below.		This example can also be solved approximately through the branch and bound method. The tree diagram showing the optimization is shown below.

	[[File:Branch and bound.png\|center\|frame]]		[[File:Branch and bound.png\|center\|frame\|Branch and bound approach]]
	As shown in the tree diagram, building factories in both Denver and St. Louis would yield the highest profit of $82,200/day. Unfortunately, the company only has enough capital to build one facility. As a result of this, the only acceptable values are those in which one value is "1" and two are "0". Based on this constraint, it is clear that the company should build the factory in Seattle, as shown in the exact solution above. However, this also yields valuable information if the company hopes to expand again in the near future, because building a factories in St. Louis and Denver is more profitable than building factories in Seattle and Denver or Seattle and St. Louis. Depending on company projections, it may be a better decision to build the first factory St. Louis and aim to build an additional factory in Denver as soon as possible.		As shown in the tree diagram, building factories in both Denver and St. Louis would yield the highest profit of $82,200/day. Unfortunately, the company only has enough capital to build one facility. As a result of this, the only acceptable values are those in which one value is "1" and two are "0". Based on this constraint, it is clear that the company should build the factory in Seattle, as shown in the exact solution above. However, this also yields valuable information if the company hopes to expand again in the near future, because building a factories in St. Louis and Denver is more profitable than building factories in Seattle and Denver or Seattle and St. Louis. Depending on company projections, it may be a better decision to build the first factory St. Louis and aim to build an additional factory in Denver as soon as possible.

	== Applications ==		== Applications ==
			[[File:BadranElHaggarFacilityLocation.jpg\|thumb\|314x314px\|Map of optimal collection stations in Port Said, Egypt<sup>(12)</sup>.]]
	Facility location problems are utilized in many industries to find the optimal placement of various facilities, including warehouses, power plants, public transportation terminals, polling locations, and cell towers, to maximize efficiency, impact, and profit. In more unique applications, extensive research has been done in applying FLPs to humanitarian efforts, such as identifying disaster management sites to maximize accessibility to healthcare and treatment<sup>(10)</sup>. A case study by researchers in Nigeria explored the application of mixed-integer FLPs in optimizing the locations of waste collection centers to provide sanitation services in crucial communities. More effective waste collection systems could combat unsanitary practices and environmental pollution, which are major concerns in many developing nations<sup>(11)</sup>. For example, Badran and El-Haggar proposed a solid waste management system for Port Said, Egypt, implementing a mixed-integer program to optimally place waste collection stations and minimize cost<sup>(12)</sup>. This program was formulated to select collection stations from a set of locations such that the sum of the fixed cost of opening collections stations, the operating costs of the collection stations, and the transportation costs from the collection stations to the composting plants is minimized.		Facility location problems are utilized in many industries to find the optimal placement of various facilities, including warehouses, power plants, public transportation terminals, polling locations, and cell towers, to maximize efficiency, impact, and profit. In more unique applications, extensive research has been done in applying FLPs to humanitarian efforts, such as identifying disaster management sites to maximize accessibility to healthcare and treatment<sup>(10)</sup>. A case study by researchers in Nigeria explored the application of mixed-integer FLPs in optimizing the locations of waste collection centers to provide sanitation services in crucial communities. More effective waste collection systems could combat unsanitary practices and environmental pollution, which are major concerns in many developing nations<sup>(11)</sup>. For example, Badran and El-Haggar proposed a solid waste management system for Port Said, Egypt, implementing a mixed-integer program to optimally place waste collection stations and minimize cost<sup>(12)</sup>. This program was formulated to select collection stations from a set of locations such that the sum of the fixed cost of opening collections stations, the operating costs of the collection stations, and the transportation costs from the collection stations to the composting plants is minimized.

	FLPs have also been used in clustering analysis, which involves partitioning a given set of elements (e.g. data points) into different groups based on the similarity of the elements. The elements can be placed into groups by identifying the locations of center points that effectively partition the set into clusters, based on the distances from the center points to each element<sup>(13)</sup>. For example, the <math>k</math>-median clustering problem can be formulated as a FLP that selects a set of <math>k</math> cluster centers to minimize the cost between each point and its closest center. The cost in this problem is represented as the Euclidean distance between two points. These problems are commonly solved using approximation algorithms.		FLPs have also been used in clustering analysis, which involves partitioning a given set of elements (e.g. data points) into different groups based on the similarity of the elements. The elements can be placed into groups by identifying the locations of center points that effectively partition the set into clusters, based on the distances from the center points to each element<sup>(13)</sup>. For example, the <math>k</math>-median clustering problem can be formulated as a FLP that selects a set of <math>k</math> cluster centers to minimize the cost between each point and its closest center. The cost in this problem is represented as the Euclidean distance between two points. These problems are commonly solved using approximation algorithms.

	== Conclusion ==		== Conclusion ==

Lawrenceli: /* References */

2020-12-10T04:12:42Z

References

Lawrenceli: /* Approximate and Exact Algorithms */

2020-12-10T04:02:00Z

Approximate and Exact Algorithms

Show changes

Lawrenceli: /* Applications */

2020-12-06T22:27:56Z

Applications

← Older revision		Revision as of 18:27, 6 December 2020
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	Facility location problems are utilized in many industries to find the optimal placement of various facilities, including warehouses, power plants, public transportation terminals, polling locations, and cell towers, to maximize efficiency, impact, and profit. In more unique applications, extensive research has been done in applying FLPs to humanitarian efforts, such as identifying disaster management sites to maximize accessibility to healthcare and treatment<sup>(4)</sup>. A case study by researchers in Nigeria explored the application of mixed-integer FLPs in optimizing the locations of waste collection centers to provide sanitation services in crucial communities. More effective waste collection systems could combat unsanitary practices and environmental pollution, which are major concerns in many developing nations<sup>(2)</sup>. For example, Badran and El-Haggar proposed a solid waste management system for Port Said, Egypt, implementing a mixed-integer program to optimally place waste collection stations and minimize cost<sup>(cite)</sup>. This program was formulated to select collection stations from a set of locations such that the sum of the fixed cost of opening collections stations, the operating costs of the collection stations, and the transportation costs from the collection stations to the composting plants is minimized.		Facility location problems are utilized in many industries to find the optimal placement of various facilities, including warehouses, power plants, public transportation terminals, polling locations, and cell towers, to maximize efficiency, impact, and profit. In more unique applications, extensive research has been done in applying FLPs to humanitarian efforts, such as identifying disaster management sites to maximize accessibility to healthcare and treatment<sup>(4)</sup>. A case study by researchers in Nigeria explored the application of mixed-integer FLPs in optimizing the locations of waste collection centers to provide sanitation services in crucial communities. More effective waste collection systems could combat unsanitary practices and environmental pollution, which are major concerns in many developing nations<sup>(2)</sup>. For example, Badran and El-Haggar proposed a solid waste management system for Port Said, Egypt, implementing a mixed-integer program to optimally place waste collection stations and minimize cost<sup>(cite)</sup>. This program was formulated to select collection stations from a set of locations such that the sum of the fixed cost of opening collections stations, the operating costs of the collection stations, and the transportation costs from the collection stations to the composting plants is minimized.

	FLPs have also been used in clustering analysis, which involves partitioning a given set of elements (e.g. data points) into different groups based on the similarity of the elements. The elements can be placed into groups by identifying the locations of center points that effectively partition the set into clusters, based on the distances from the center points to each element<sup>(9)</sup>. For example, the <math>k</math>-median clustering problem can be formulated as a FLP that selects a set of <math>k</math> cluster centers to minimize the cost between each point and its closest center<sup>(cite)</sup>. The cost in this problem is represented as the Euclidean distance between two points.		FLPs have also been used in clustering analysis, which involves partitioning a given set of elements (e.g. data points) into different groups based on the similarity of the elements. The elements can be placed into groups by identifying the locations of center points that effectively partition the set into clusters, based on the distances from the center points to each element<sup>(9)</sup>. For example, the <math>k</math>-median clustering problem can be formulated as a FLP that selects a set of <math>k</math> cluster centers to minimize the cost between each point and its closest center<sup>(cite)</sup>. The cost in this problem is represented as the Euclidean distance between two points. These problems are commonly solved using approximation algorithms.

	== Conclusion ==		== Conclusion ==

Lawrenceli: /* Conclusion */

2020-12-06T22:23:05Z

Conclusion

← Older revision		Revision as of 18:23, 6 December 2020
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	== Conclusion ==		== Conclusion ==
	The facility location ~~problems~~ is an important application of computational optimization. The uses of this optimization technique are far-reaching, and can be used to determine anything from where a family should live based on the location of their workplaces and school to where a Fortune 500 company should put a new manufacturing plant or distribution facility to maximize their return on investment.		The facility location problem is an important application of computational optimization. The uses of this optimization technique are far-reaching, and can be used to determine anything from where a family should live based on the location of their workplaces and school to where a Fortune 500 company should put a new manufacturing plant or distribution facility to maximize their return on investment.

	== References ==		== References ==

Lawrenceli: /* Applications */

2020-12-06T22:20:43Z

Applications

← Older revision		Revision as of 18:20, 6 December 2020
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	Facility location problems are utilized in many industries to find the optimal placement of various facilities, including warehouses, power plants, public transportation terminals, polling locations, and cell towers, to maximize efficiency, impact, and profit. In more unique applications, extensive research has been done in applying FLPs to humanitarian efforts, such as identifying disaster management sites to maximize accessibility to healthcare and treatment<sup>(4)</sup>. A case study by researchers in Nigeria explored the application of mixed-integer FLPs in optimizing the locations of waste collection centers to provide sanitation services in crucial communities. More effective waste collection systems could combat unsanitary practices and environmental pollution, which are major concerns in many developing nations<sup>(2)</sup>. For example, Badran and El-Haggar proposed a solid waste management system for Port Said, Egypt, implementing a mixed-integer program to optimally place waste collection stations and minimize cost<sup>(cite)</sup>. This program was formulated to select collection stations from a set of locations such that the sum of the fixed cost of opening collections stations, the operating costs of the collection stations, and the transportation costs from the collection stations to the composting plants is minimized.		Facility location problems are utilized in many industries to find the optimal placement of various facilities, including warehouses, power plants, public transportation terminals, polling locations, and cell towers, to maximize efficiency, impact, and profit. In more unique applications, extensive research has been done in applying FLPs to humanitarian efforts, such as identifying disaster management sites to maximize accessibility to healthcare and treatment<sup>(4)</sup>. A case study by researchers in Nigeria explored the application of mixed-integer FLPs in optimizing the locations of waste collection centers to provide sanitation services in crucial communities. More effective waste collection systems could combat unsanitary practices and environmental pollution, which are major concerns in many developing nations<sup>(2)</sup>. For example, Badran and El-Haggar proposed a solid waste management system for Port Said, Egypt, implementing a mixed-integer program to optimally place waste collection stations and minimize cost<sup>(cite)</sup>. This program was formulated to select collection stations from a set of locations such that the sum of the fixed cost of opening collections stations, the operating costs of the collection stations, and the transportation costs from the collection stations to the composting plants is minimized.

	FLPs have also been used in clustering analysis, which involves partitioning a given set of elements (e.g. data points) into different groups based on the similarity of the elements. The elements can be placed into groups by identifying the locations of center points that effectively partition the set into clusters, based on the distances from the center points to each element<sup>(9)</sup>. For example, the k-median clustering problem can be formulated as a FLP that selects a set of k cluster centers to minimize the cost between each point and its closest center. The cost in this problem is represented as the Euclidean distance between two points.		FLPs have also been used in clustering analysis, which involves partitioning a given set of elements (e.g. data points) into different groups based on the similarity of the elements. The elements can be placed into groups by identifying the locations of center points that effectively partition the set into clusters, based on the distances from the center points to each element<sup>(9)</sup>. For example, the <math>k</math>-median clustering problem can be formulated as a FLP that selects a set of <math>k</math> cluster centers to minimize the cost between each point and its closest center<sup>(cite)</sup>. The cost in this problem is represented as the Euclidean distance between two points.

	== Conclusion ==		== Conclusion ==

← Older revision		Revision as of 00:12, 10 December 2020
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	# Drezner, Z; Hamacher. H. W. (2004), ''Facility Location Applications and Theory''. New York, NY: Springer.		# Drezner, Z; Hamacher. H. W. (2004), ''Facility Location Applications and Theory''. New York, NY: Springer.
	# Francis, R. L.; Mirchandani, P. B. (1990), ''Discrete Location Theory''. New York, NY: Wiley.		# Francis, R. L.; Mirchandani, P. B. (1990), ''Discrete Location Theory''. New York, NY: Wiley.
	# Hansen, P., et al. (1985), The Minisum and Minimax Location Problems Revisited. ''Operations Research, 33'', 6, 1251-1265.		# Hansen, P., et al. (1985), [https://pubsonline.informs.org/doi/abs/10.1287/opre.33.6.1251 The Minisum and Minimax Location Problems Revisited.] ''Operations Research, 33'', 6, 1251-1265.
	# Vygen, J. (2005), ''Approximation Algorithms for Facility Location Problems''. Research Institute for Discrete Mathematics, University of Bonn.		# Vygen, J. (2005), ''Approximation Algorithms for Facility Location Problems''. Research Institute for Discrete Mathematics, University of Bonn.
	# Jain, K., et al. (2003), A Greedy Facility Location Algorithm Analyzed Using Dual Fitting with Factor-Revealing LP. ''Journal of the ACM, 50'', 6, 795-824.		# Jain, K., et al. (2003), [https://dl.acm.org/doi/10.1145/950620.950621 A Greedy Facility Location Algorithm Analyzed Using Dual Fitting with Factor-Revealing LP.] ''Journal of the ACM, 50'', 6, 795-824.
	# Alenezy, E. J. (2020), Solving Capacitated Facility Location Problem Using Lagrangian Decomposition and Volume Algorithm. ''Advances in Operations Research,'' ''2020'', 5239176, 2020.		# Alenezy, E. J. (2020), [https://www.hindawi.com/journals/aor/2020/5239176/ Solving Capacitated Facility Location Problem Using Lagrangian Decomposition and Volume Algorithm.] ''Advances in Operations Research,'' ''2020'', 5239176, 2020.
	# Held, M.; Karp, R. M. (1970), The Traveling-Salesman Problem and Minimum Spanning Trees. ''Operations Research, 18,'' 6, 1138-1162.		# Held, M.; Karp, R. M. (1970), [https://pubsonline.informs.org/doi/abs/10.1287/opre.18.6.1138 The Traveling-Salesman Problem and Minimum Spanning Trees.] ''Operations Research, 18,'' 6, 1138-1162.
	# Barahona, F.; Anbil, R. (2000), The Volume Algorithm: Producing Primal solutions with a Subgradient Method. ''Mathematical Programming, 87,'' 3, 385–399.		# Barahona, F.; Anbil, R. (2000), [https://link.springer.com/article/10.1007%2Fs101070050002 The Volume Algorithm: Producing Primal solutions with a Subgradient Method.] ''Mathematical Programming, 87,'' 3, 385–399.
	# Ceselli, A. (2003), Two Exact Algorithms for the Capacitated p-Median Problem. ''Quarterly Journal of the Belgian, French and Italian Operations Research Societies, 4'', 1, 319-340.		# Ceselli, A. (2003), [https://link.springer.com/article/10.1007/s10288-003-0023-5 Two Exact Algorithms for the Capacitated p-Median Problem.] ''Quarterly Journal of the Belgian, French and Italian Operations Research Societies, 4'', 1, 319-340.
	# Daskin, M. S.; Dean, L. K. (2004), Location of Health Care Facilities. ''Handbook of OR/MS in Health Care: A Handbook of Methods and Applications'', 43-76.		# Daskin, M. S.; Dean, L. K. (2004), [https://link.springer.com/chapter/10.1007/1-4020-8066-2_3 Location of Health Care Facilities.] ''Handbook of OR/MS in Health Care: A Handbook of Methods and Applications'', 43-76.
	# Adeleke, O. J.; Olukanni, D. O. (2020), Facility Location Problems: Models, Techniques, and Applications in Waste Management. ''Recycling, 5'', 10.		# Adeleke, O. J.; Olukanni, D. O. (2020), [https://www.mdpi.com/2313-4321/5/2/10 Facility Location Problems: Models, Techniques, and Applications in Waste Management.] ''Recycling, 5'', 10.
	# Badran, M.F.; El-Haggar, S.M. (2006), Optimization of Municipal Solid Waste Management in Port Said – Egypt, ''Waste Management, 26'', 5, 534-545.		# Badran, M.F.; El-Haggar, S.M. (2006), [https://www.sciencedirect.com/science/article/abs/pii/S0956053X05001534 Optimization of Municipal Solid Waste Management in Port Said – Egypt.] ''Waste Management, 26'', 5, 534-545.
	# Meira, L. A. A.; Miyazawa, F. K.; Pedrosa, L. L. C. (2017), Clustering through Continuous Facility Location Problems. ''Theoretical Computer Science, 657'', 137-145.		# Meira, L. A. A.; Miyazawa, F. K.; Pedrosa, L. L. C. (2017), [https://www.sciencedirect.com/science/article/abs/pii/S030439751630514X Clustering through Continuous Facility Location Problems.] ''Theoretical Computer Science, 657'', 137-145.
	# Balcik, B.; Beamon, B. M. (2008), Facility Location in Humanitarian Relief. ''International Journal of Logistics Research and Applications, 11'', 101-121.		# Balcik, B.; Beamon, B. M. (2008), [https://www.tandfonline.com/doi/full/10.1080/13675560701561789 Facility Location in Humanitarian Relief.] ''International Journal of Logistics Research and Applications, 11'', 101-121.
	# Eiselt, H. A.; Marianov, V. (2019), ''Contributions to Location Analysis''. Cham, Switzerland: Springer.		# Eiselt, H. A.; Marianov, V. (2019), ''Contributions to Location Analysis''. Cham, Switzerland: Springer.