$TITLE Multi Facility Location Problem - Conic Formulation (EMFL_SOCP,SEQ=273)
$ONTEXT
Euclidian multi-facility location problem using second order
cone constraints. Given a set of m existing facilities,
we compute the coordinates of n new facilities subject
to minimizing the euclidian distance between facilities.
We use quadratic cone constraints to model the euclidian
distances.
Vanderbei, R, online at
http://www.princeton.edu/~rvdb/ampl/nlmodels/facloc/emfl_socp.mod
$OFFTEXT
* Note that the number of new facilities must be new=N1*N2
$set old 200
$set N1 5
$set N2 5
$set new 25
Set m "old facilities" /m1*m%old%/
nX "number facilities in x direction" /nX1*nX%N1%/
nY "number facilities in y direction" /nY1*nY%N2%/
n "total number of new facilities" /n1*n%new%/
d "dimension" /"x-axis", "y-axis"/
;
Alias(nn,n);
Parameter
coords(m,d) "coordinates of existing facilities"
w(m,n) "weights associated with new-old facility pairs"
v(n,n) "weights associated with new-new facility pairs"
;
Positive Variable
x(n,d) "coordinates of new facilities"
s(m,n) "euclidian distance between new-old facilities"
t(n,n) "euclidian distance between new-new facilities"
;
Variable
diff_o(m,n,d)
diff_n(n,nn,d)
obj;
Equation
objective
diff_o_eq(m,n,d) "compute distance between new-old"
diff_n_eq(n,nn,d) "compute distance between new-new"
old_dist(m,n) "distance between new-old facilities"
new_dist(n,n) "distance between new-new facilities"
;
objective.. obj =E= sum( (m,n), w(m,n)*s(m,n)) +
sum( (n,nn), v(n,nn)*t(n,nn));
diff_o_eq(m,n,d).. diff_o(m,n,d) =E= x(n,d) - coords(m,d);
diff_n_eq(n,nn,d).. diff_n(n,nn,d) =E= x(n,d) - x(nn,d);
old_dist(m,n).. s(m,n) =C= sum(d, diff_o(m,n,d));
new_dist(n,nn).. t(n,nn) =C= sum(d, diff_n(n,nn,d));
Model facility /all/;
* Specify existing coordinates via uniform distribution
coords(m,d) = uniform(0,1);
* Compute weights: 0.2 for new-new facility pairs
v(n,nn)$[ord(n)