orloca-package: Operations Research LOCational Analysis Models

In orloca: Operations Research LOCational Analysis Models

Operations Research LOCational Analysis Models

Description

Objects and methods to handle and solve the min-sum location problem, also known as Fermat-Weber problem.

Details

The min-sum location problem search for a point such that the weighted sum of the distances to the demand points are minimized. See "The Fermat-Weber location problem revisited" by Brimberg, Mathematical Programming, 1, pg. 71-76, 1995, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/BF01592245")}.

General global optimization algorithms are used to solve the problem, along with the adhoc Weiszfeld method, see "Sur le point pour lequel la Somme des distances de n points donnes est minimum", by E. Weiszfeld, Tohoku Mathematical Journal, First Series, 43, pg. 355-386, 1937 or "On the point for which the sum of the distances to n given points is minimum", by E. Weiszfeld and F. Plastria, Annals of Operations Research, 167, pg. 7-41, 2009, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10479-008-0352-z")}.

Package:   orloca

Type:      Package

Version:   5.3

Date:      2023-05-16

License:   GPL (>= 3)

The package provides a class (loca.p) that represents a location problem with a finite set of demand points over the plane. Also, it is possible to plot the points and the objective function. Such objective function is the total weighted distances travelled by all the customers to the service.

Non-planar location problems could be handle in future versions of the package.

For a demo, load the package with library(orloca), and use demo(orloca).

The package is ready for internationalization. The author ask for translated version of the .mo file to include in the package.

Author(s)

Manuel Munoz-Marquez <[e-mail]>

Mantainer: Manuel Munoz-Marquez <[e-mail]>

References

[1] Brimberg, J. The Fermat-Weber location problem revisited, Mathematical Programming, 1, pg. 71-76, 1995. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/BF01592245")}.

[2] Love, R. F., Morris, J. G., Wesolowsky, G. O. Facilities Location: Chapter 2: Introduction to Single-Facility Location, 1988, North-Holland. ISBN: 0-444-01031-9.

[3] Weiszfeld, E. and Plastria, F. On the point for which the sum of the distances to n given points is minimum, Annals of Operations Research, 167, pg. 7-41, 2009, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10479-008-0352-z")}.

[4] http://knuth.uca.es/orloca/

See Also

Para la version en espanol, instale el paquete orloca.es y consulte la ayuda sobre orloca.es-package. (For the spanish version, install the orloca.es package and see the help about orloca.es-package).

Examples

# A new unweighted loca.p object
o <- loca.p(x = c(-1, 1, 1, -1), y = c(-1, -1, 1, 1))

# Compute the sum of distances to point (3, 4)
distsum(o, 3, 4)

# Compute the sum of distances to point (3, 4) using lp norm
distsum(o, 3, 4, lp=2.5)

# Solve the optimization problem
distsummin(o)
# Contour plot
contour(o)

# Make a demo of the package
demo(orloca)

orloca documentation built on May 31, 2023, 8:59 p.m.