MODEL:
 ! Capacitated Plant Location Problem;
 ! Keywords: Capacitated plant location, Fixed charge, P median, Plant Location, Transportation problem ;
SETS:
    PLANT : FCOST, CAP, OPEN;
    CUSTOMER : DEM;
    ARCS( PLANT, CUSTOMER)  : COST, VOL;
 ENDSETS
 DATA:
  ! There is a set of candidate plants;
       PLANT = P1  P2  P3;
  ! Fixed cost of opening a plant at each origin;
       FCOST = 91, 70, 24;
  ! Capacities at each origin;
       CAP =   39, 35, 31;

  ! There is a set of customers to be served;
    CUSTOMER = C1  C2  C3  C4;
  ! Demands at each destination;
       DEM =   15, 17, 22, 12;
  ! The cost/unit shipment matrix from Plant to Customer;
       COST =   6,  2,  6,  7,
                4,  9,  5,  3,
                8,  8,  1,  5;
   NPOPEN = 2; !Max plants allowed open;
 ENDDATA

! Variables:
    OPEN( I) = 1 is PLANT I is used (or open), else 0,
                 i.e., it is a binary variable,
    VOL( I, J) = amount shipped from PLANT I to CUSTOMER J;

 ! Minimize sum of Fixed + Shipping costs;
    [TTL_COST] MIN = FCTOT + SCTOT;
       SCTOT = @SUM( ARCS( I, J): COST( I, J) * VOL( I, J));
       FCTOT = @SUM( PLANT( I) : FCOST( I)  * OPEN( I) );

 ! Must satisfy demand at Customer J;
    @FOR( CUSTOMER( J): [DEMAND]
     @SUM( PLANT( I): VOL( I, J)) >= DEM( J)
    );

 ! Cannot ship more than installed capacity from PLANT I;
    @FOR( PLANT( I): [SUPPLY]
     @SUM( CUSTOMER( J): VOL( I, J)) <= CAP( I) * OPEN( I);
 ! Make OPEN binary(0/1);
     @BIN( OPEN( I));
    );
 
 ! Maximum number of plants open;
   @SUM( PLANT(I): OPEN(I)) <= NPOPEN;
 END