Difference: FacilityLocationProblem (1 vs. 3)
Revision 32018-11-23 - TWikiAdminUser
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Revision 22008-04-22 - TWikiAdminUser
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Now the following master-slave constraint ensures that facility  only serves customers if it is used:
%BEGINLATEX{label="eq:facility"}% | ||||||||
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| < < | \sum_{c \in {\cal C}} y_{fc} \leq |{\cal C}| z_f, f \in {\cal F} | |||||||
| > > | \[ \sum_{c \in {\cal C}} y_{fc} \leq |{\cal C}| z_f, f \in {\cal F} \] | |||||||
| %ENDLATEX% The decision variables, objective function and constraints vary depending on the problem, but similar master-slave constraints are always present in facility location problems. | ||||||||
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We will not delve into it here, but a "tighter" formulation would use the following constraints instead of (?? REFLATEX{eq:facility} not defined in eqn list ??):
![\[ y_{fc} \leq z_f, f \in {\cal F}, c \in {\cal C} \]](/pub/OpsRes/FacilityLocationProblem/latex20a9aeb14e1f6da01d742f1f094c5aad.png) | ||||||||
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| > > | Facility Location Case StudiesResults from OpsRes web retrieved at 11:24 (GMT)<--/twikiTopRow--> \usepackage{amsmath} Case Study: Submitted: Operations Research Topics: Application Areas: Contents Problem Description Problem Description Return... <--/twikiSummary--> <--/twikiBottomRow--> <--/patternSearchResult--> <--/twikiTopRow--> \usepackage{amsmath} Case Study: Submitted: Operations Research Topics: Application Areas: Contents Problem Description Problem Description Return... <--/twikiSummary--> <--/twikiBottomRow--> <--/patternSearchResult--> <--/twikiTopRow--> \usepackage{amsmath} Case Study: Submitted: Operations Research Topics: Application Areas: Contents Problem Description Problem Description Return... <--/twikiSummary--> <--/twikiBottomRow--> <--/patternSearchResult--> Number of topics: 3 <--/patternSearchResultCount--> | |||||||
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Revision 12008-04-22 - TWikiAdminUser
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Facility Location ProblemsFacility location problems are a classical example of the use of master-slave constraints. The following definition of the general facility location problem is from J. E. Beasley's OR-Notes .
The general facility location problem is: given a set of facility locations and a set of customers who are served from the facilities then:Given the set of facilities  and the set of customers  , we can define binary (0-1) variables:
only serves customers if it is used:
Latex rendering error!! dvi file was not created. | |||||||||||||||||
= 1 if facility 
= 1 if facility 
, 0 otherwise.
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