model ModelName
uses "mmxprs"; !gain access to the Xpress-Optimizer solver

declarations
  tratte = 1..4
  modi = 1..3
  
  C: array(modi,tratte) of integer
  D: array(modi, modi) of integer
  
  x: array(modi, tratte) of mpvar
  y: array(modi, modi,2..4) of mpvar
end-declarations

C::[30, 40, 30, 60,
	20, 40, 50, 50,
	40, 10, 60, 40]

D::[1, 20, 20,
	20, 1, 10,
	20, 10, 1]

forall(i in modi, k in tratte) x(i,k) is_binary

forall(i, j in modi, k in 2..4) y(i,j,k) is_binary

forall(k in tratte) sum(i in modi) x(i,k) = 1

forall(i, j in modi, k in 2..4) do
   ! y(i,j,k) <= x(i,k-1)
   ! y(i,j,k) <= x(j,k)
	 y(i,j,k) >= x(i,k-1) + x(j,k) - 1
end-do

costo := 20*(sum(i in modi, k in tratte) C(i,k)*x(i,k) + sum(i,j in modi,k in 2..4) D(i,j)*y(i,j,k))

minimize(costo)

writeln("Soluzione 1: ",getobjval)

sum(k in tratte) x(3,k) <= 4*sum(k in tratte) x(1,k)

minimize(costo)

writeln("Soluzione 2: ",getobjval)

forall(k in 2..4) do 
	y(1,3,k) = 0
	y(3,1,k) = 0
end-do

minimize(costo)

writeln("Soluzione 3: ",getobjval)


end-model