# AMPL model for the NSC problem

param MONTHS;	# Number of months in the planning horizon

param c {1 .. MONTHS};   # c[i] = cost of producing one ton of steel in month i
param d {1 .. MONTHS};   # d[i] = tons of steel needed in month i

var P {1 .. MONTHS} >= 0; # P[i] = tons of steel produced in month i
var I {0 .. MONTHS} >= 0; # I[i] = tons of steel in inventory at the end of month i


minimize cost: sum{i in 1 .. MONTHS} (c[i]*P[i] + 120*I[i]);

subject to demand {i in 1 .. MONTHS}: P[i] + I[i-1] >= d[i];
subject to inventory {i in 1 .. MONTHS}: I[i] = P[i] + I[i-1] - d[i];
subject to initial_inventory: I[0] = 1000;
subject to final_inventory: I[MONTHS] >= 1500;
subject to max_production {i in 1 .. MONTHS}: P[i] <= 4000;