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The Capacitated 
Facility Location Problem

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Capacitated Facility Location Problem (CFLP) is generalization of the Simple Plant Location Problem. In contrast to that we now suppose each facility can product limited quantity of produce. It is importance and quite prevalent assumption. And although mathematical models of those problems not  very differ, but solving methods for CFLP are more difficult. The most efficient  methods for CFPL are Lagrangen relaxation methods and the matrix column generation method.

Now we discrabe the mathematical model as integer programming problem. Let a set I = {1,..., I} give potential facility locations by production some uniform product. The number ci ³ 0 is the opening cost of facility at location  iI Vi0 is the utmost value of prodaction at this location.

A set J ={1,Е,J} assign clients that require service. For each pair (ijgij0 is the production and transportation costs and  pij0 is a value of product from fasility i needed to client j.

 Let us define the following notations:

Then the Capacitated Facility Location Problem may be written 


xij,  yi {0, 1},  iI ,   jJ.  


  1. V. Beresnev, E. Gimadi, and V. Dement'ev Extremal Standartization Problems. Novosibirsk: Nauka, 1978. (in Russian)

  1. Diaz J.A., Fernandez E. Column generation for the single source capacitated plant location problem. Technical report DR 2000/17, UPC Barcelona, 2000.

  1. Sridharan R. The capacitated plant location problem. European Journal of Operational Research. v. 87 (1995), p. 203Ц213.

  1. Holmberg K., Ronnqvist M., Yuan D. An exact algorithm for the capacitated facility location problems with single sourcing. European Journal of Operational Research. v113 (1999), p. 544Ц559.

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