Difference: FacilityLocationProblem (1 vs. 2)

Revision 22008-04-22 - TWikiAdminUser

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META TOPICPARENT	name="MasterSlaveConstraints"

Facility Location Problems

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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}

>
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\[ \sum_{c \in {\cal C}} y_{fc} \leq |{\cal C}| z_f, f \in {\cal F} \]

%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.

Line: 26 to 26

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 ??):

$y_{fc} \leq z_f, f \in {\cal F}, c \in {\cal C}$

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Facility Location Case Studies

Results from OpsRes web retrieved at 15:25 (GMT)

CokeSupplyChain

r20 - 2018-11-23 - 01:32 TWikiAdminUser

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\usepackage{amsmath} Case Study: Submitted: Operations Research Topics: Application Areas: Contents Problem Description Problem Description Return...

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CosmicComputersProblem

r26 - 2018-11-23 - 01:32 TWikiAdminUser

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\usepackage{amsmath} Case Study: Submitted: Operations Research Topics: Application Areas: Contents Problem Description Problem Description Return...

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CosmicComputersSolverStudio

r5 - 2019-08-12 - 13:27 TWikiAdminUser

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Number of topics: 3

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-- TWikiAdminGroup - 22 Apr 2008

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Revision 12008-04-22 - TWikiAdminUser

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META TOPICPARENT	name="MasterSlaveConstraints"

Facility Location Problems

Facility 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:

which facilities should be used;

which customers should be served from which facilities so as to minimise the total cost of serving all the customers.

Given the set of facilities ${\cal F}$ and the set of customers ${\cal C}$ , we can define binary (0-1) variables:

= 1 if facility is used, 0 otherwise;
$y_{fc}$ = 1 if facility serves customer , 0 otherwise.

Now the following master-slave constraint ensures that facility only serves customers if it is used:

$\sum_{c \in {\cal C}} y_{fc} \leq |{\cal C}| z_f, f \in {\cal F}$

(1)

The decision variables, objective function and constraints vary depending on the problem, but similar master-slave constraints are always present in facility location problems.

We will not delve into it here, but a "tighter" formulation would use the following constraints instead of (1):

$y_{fc} \leq z_f, f \in {\cal F}, c \in {\cal C}$

-- TWikiAdminGroup - 22 Apr 2008

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