$title P-Median Problem (PMEDIAN,SEQ=408)

$onText
The pmedian problem is defined as follows: given a set I={1...n} of
locations and a transportation cost W between each pair of
locations. Select a subset S of p location minimizing the sum of the
distances between each location and the closest one in S.

There are currently 40 data files from the OR-LIB
http://people.brunel.ac.uk/~mastjjb/jeb/orlib/pmedinfo.html

These data files are the 40 test problems from Table 2 of
J.E.Beasley "A note on solving large p-median problems" European
Journal of Operational Research 21 (1985) 270-273.

 pmed15      1729                1734

J.E.Beasley "A note on solving large p-median problems" European
Journal of Operational Research 21 (1985) 270-273.

Keywords: mixed integer linear programming, mixed integer nonlinear programming,
          p-median problem, facility location problem
$offText

$if not set instance $set instance pmed15.inc
$if not exist "%instance%" $abort File of instance does not exist

$onEchoV > pm.awk
BEGIN { nr=0 }
!/^#/ {
   if (nr==0) {
     n = $1;
     printf("set n /0*%d/; Scalar p /%d/;\n", n-1,$3);
     printf("Table w(n,n) distances\n$onDelim\nn");
     for (i=0; i<n; i++) printf(",%d",i);
   } if (nr>0)
     printf("\n%d %s",nr-1,$0);
   nr++;
}
END {
   printf("\n$offDelim\n;")
}
$offEcho

$set fn %gams.scrdir%tlinst.%gams.scrext%
$call awk -f pm.awk %instance% > "%fn%"
$ifE errorLevel<>0 $abort problems with awk call

$offListing
$include "%fn%"
$onListing

Alias (n,i,j);

Scalar wMax;
wMax = smax((i,j), w(i,j));

Variable
   x(n)       'location selection'
   costs(n,n) 'costs between location i and j'
   cost(n)    'cost to serve i'
   obj        'objective';

Binary Variable x;

Equation
   defp          'select p locations'
   defcosts(i,j) 'costs between location i and j is w(i,j) or inf (=2*wMax))'
   defcost(i)    'cost to serve i is the smallest cost between i and other locations'
   defobj        'objective';

$ifThen set MIP
   Positive Variable diff(i,j);
   Binary   Variable bdiff(i,j);

   Equation defcosts2(i,j), defdiffZero(i,j);

   defcosts(i,j)..    costs(i,j) =g= 2*wMax - 2*wMax*x(j);

   defcosts2(i,j)..   cost(i)    =e= costs(i,j) - diff(i,j);

   defdiffZero(i,j).. diff(i,j)  =l= 2*wMax - 2*wMax*bdiff(i,j);

   defcost(i)..       sum(j, bdiff(i,j)) =g= 1;
$else
   defcosts(i,j)..    costs(i,j) =e= ifthen (x(j) >= 0.5, w(i,j), 2*wMax);

   defcost(i)..       cost(i)    =e= smin(j, costs(i,j));
$endIf

defp..   sum(n, x(n)) =e= p;

defobj.. obj =e= sum(n, cost(n));

Model pmedian / all /;

costs.lo(i,j) = w(i,j);
$ifThen set MIP
   solve pmedian using mip   min obj;
$else
   solve pmedian using minlp min obj;
$endIf