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

declarations
  anni = 1..4
  zone = 1..3
  
  A: array(zone,anni) of integer !disponibilitą
  d: array(anni) of integer !domanda
  
  x: array(zone,anni) of mpvar! quantitą raccolta per bosco e per anno
  y: array(anni) of mpvar !quantitą raccolta per anno
  z: array(anni) of mpvar !quantitą in eccesso
  
end-declarations

writeln("Begin running model")

A::[10,12,7,16,
	4,2,10,9,
	6,8,11,5]

d::[16,23,26,25]

forall(j in anni) do
	y(j) = sum(i in zone) x(i,j)
	y(j)  + if(j>1,sum(k in 2..j) (y(k-1) - d(k-1)),0) >= d(j)
end-do

forall(i in zone, j in anni) do
	x(i,j) <= if(j=1,A(i,j),A(i,j)+A(i,j-1)-x(i,j-1))
end-do
	
forall(j in anni) do
	z(j) >= y(j) - d(j)
	z(j) >= -(y(j) - d(j))
end-do
		

mincost := sum(j in anni) z(j)

minimize(mincost)

writeln("End running model")

end-model