Difference between revisions of "Facility location problems"

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The facility location problem deals with selecting the location of a facility (often from a list of integer possibilities) to best meet demand wether to the next line of customers. Goal here is to most efficiently serve the constraints demanded while doing so at the lowest cost.  
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The facility location problem deals with selecting the location of a facility (often from a list of integer possibilities) to best meet demand. The goal is to most efficiently serve the needs of the c
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Finding the location to build a factory that minimizes total weighted distances from suppliers and customers where weights are representative of the difficulty of transporting materials.
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constraints demanded while doing so at the lowest cost.  
 
Finding a factory location which minimizes total weighted distances from suppliers and customers where weights represent difficulty of transportation or amounts of material
 
Finding a factory location which minimizes total weighted distances from suppliers and customers where weights represent difficulty of transportation or amounts of material
  
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"''Given three points in a plane, find a fourth point such that the sum of its distances to the three given points is as small as possible.''"  
 
"''Given three points in a plane, find a fourth point such that the sum of its distances to the three given points is as small as possible.''"  
  
In 1909 Alfred Weber used a a three point version to determine the location for industry to minimize transportation costs with the weights being  This is the simplest continous facility location model.
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In 1909 Alfred Weber used a three point version to model possible industrial locations in order to minimize transportation costs with the weights being  This is the simplest continous facility location model.
  
  
[[File:FermatPoints_700.gif|frame|none|alt=Alt text|The Fermat Point, or Torricelli Point, is the solution that minimizes distances from A, B, and C the three corners of the black triangle.]]
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[[File:FermatPoints_700.gif|frame|none|alt=Alt text|The Fermat Point, or Torricelli Point, is the solution that minimizes distances from A, B, and C (the three corners of the black triangle).]]
  
 
A modern day engineering interpretation could be as follows:<br>
 
A modern day engineering interpretation could be as follows:<br>
"''Find the best location for a refining plant between three cities in such a way that te sum of the connections between the power plant and the cities in minimal.''"
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"''Find the best location for a refining plant between three cities in such a way that the sum of the connections between the plant and the cities in minimal.''"
  
  
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Binary decision variables
  
 
==Examples and Applications==
 
==Examples and Applications==
  
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===A Real World Example===
  
 
Suppose you are a manager at a company that builds  
 
Suppose you are a manager at a company that builds  
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Applications in physics, solution to Fermat-Weber problem allowing for "repulsion" or negative distances.
 
Applications in physics, solution to Fermat-Weber problem allowing for "repulsion" or negative distances.
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===Applications in Industry===
  
 
==Conclusion==
 
==Conclusion==
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[1] Dorrie, H. (1965) 100 great problems of elementary mathematics: their history and solution. New York, NY: Dover Publications.
 
[1] Dorrie, H. (1965) 100 great problems of elementary mathematics: their history and solution. New York, NY: Dover Publications.
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[2] Drezner, Z & Hamacher. H. W. (2004). Facility location: applications and theory. New York, NY: Springer.
  
 
Last, F. M. (Year Published) Book. City, State: Publisher.
 
Last, F. M. (Year Published) Book. City, State: Publisher.

Revision as of 20:39, 24 May 2015

Author: Aaron Litoff
Stewards: Dajun Yue and Fengqi You

MILP [1]


The facility location problem deals with selecting the location of a facility (often from a list of integer possibilities) to best meet demand. The goal is to most efficiently serve the needs of the c

Finding the location to build a factory that minimizes total weighted distances from suppliers and customers where weights are representative of the difficulty of transporting materials.

constraints demanded while doing so at the lowest cost. Finding a factory location which minimizes total weighted distances from suppliers and customers where weights represent difficulty of transportation or amounts of material


Contents

History

The Fermat-Weber problem was one of the first facility location problems every proposed, and was done so as early as the 17th century. This "geometric median of three points" can be thought of as a version of the facility location problem where the assumption is made that transportation costs per distance are the same for all destinations. It was put forth by the French mathematician Pierre de Fermat to the Italian physicist Evangelista Torricelli as follows:

"Given three points in a plane, find a fourth point such that the sum of its distances to the three given points is as small as possible."

In 1909 Alfred Weber used a three point version to model possible industrial locations in order to minimize transportation costs with the weights being This is the simplest continous facility location model.


Alt text
The Fermat Point, or Torricelli Point, is the solution that minimizes distances from A, B, and C (the three corners of the black triangle).

A modern day engineering interpretation could be as follows:
"Find the best location for a refining plant between three cities in such a way that the sum of the connections between the plant and the cities in minimal."


Description and Formulation

Binary decision variables

Examples and Applications

A Real World Example

Suppose you are a manager at a company that builds Warehouse needs to be built in a central location so that the transportation costs are minimized


Applications in physics, solution to Fermat-Weber problem allowing for "repulsion" or negative distances.

Applications in Industry

Conclusion

References

[1] Dorrie, H. (1965) 100 great problems of elementary mathematics: their history and solution. New York, NY: Dover Publications.

[2] Drezner, Z & Hamacher. H. W. (2004). Facility location: applications and theory. New York, NY: Springer.

Last, F. M. (Year Published) Book. City, State: Publisher.