set vessels;
set ports;
param cost{vessels};
param capacity{vessels};
param I{ports};
param II{ports};
param III{ports};
param available{ports};
param fcost{ports};
param demand >= 0;

#amout of cargo picked up by vessel i at port j
#var x{vessels,ports};
var x{vessels,ports}>=0;
var x1{vessels,ports} >= 0;
var x2{vessels,ports} >=0;
var x3{vessels,ports} >=0;

#1 if port j was used, else 0
var y{ports} binary >= 0;
#1 if vessel i was used, else 0;
var z{vessels} binary >= 0;
#1 if ship i visited port j else 0
var k{vessels,ports} binary >=0;

var p1{vessels,ports} binary>=0;
var p2{vessels,ports} binary>=0;
var p3{vessels,ports} binary>=0;

#sum {i in vessels,j in ports} x[i,j] * t[i,j]+
minimize totcost: sum{i in vessels,j in ports} (x1[i,j]*I[j]+x2[i,j]*II[j]+x3[i,j]*III[j])+
                  sum {i in ports} y[i]*fcost[i]+
                  sum {i in vessels} z[i]*cost[i];

#y=1 if x>0 and makes sure availability restrictions on each port is met
subject to port_Capacity{j in ports}:
        sum {i in vessels} x[i,j] <= available[j]*y[j];

#demand should be met
subject to DEMAND: sum{i in vessels,j in ports} x[i,j] = demand;

#z=1 if x>0 and makes sure capacity on each ship is met
subject to FIXED_COST {i in vessels}:
        sum {j in ports} x[i,j] <= z[i]*capacity[i];

#each vessel allowed to visit max 2 ports
subject to maxVisits {i in vessels}:
        sum {j in ports} k[i,j] <= 2;

#k is 1 when x is > 0
subject to Amount {i in vessels, j in ports}:
        k[i,j]*999999999>=x[i,j];

#k is 0 when x is 0
subject to kFollowX{i in vessels, j in ports}:
        k[i,j]<=x[i,j];


subject to one{i in vessels,j in ports}:
        p1[i,j]+p2[i,j]+p3[i,j]<= 1;

subject to X1{i in vessels, j in ports}:
        x1[i,j]<=99999*p1[i,j];

subject to X1small{i in vessels, j in ports}:
        x1[i,j]>=0;

subject to X2small{i in vessels,j in ports}:
		100000*p2[i,j]<=x2[i,j];

subject to X2big{i in vessels,j in ports}:
		x2[i,j]<=179999*p2[i,j];

subject to X3small{i in vessels,j in ports}:
		180000*p3[i,j]<=x3[i,j];

subject to X3big{i in vessels,j in ports}:
		x3[i,j]<=999999999*p3[i,j];

subject to xp1{i in vessels,j in ports}:
		p1[i,j]<=x1[i,j];

subject to xp2{i in vessels,j in ports}:
		p2[i,j]<=x2[i,j];

subject to xp3{i in vessels,j in ports}:
		p3[i,j]<=x3[i,j];

subject to X{i in vessels,j in ports}:
		x[i,j]=x1[i,j]+x2[i,j]+x3[i,j];