# Second AMPL model for the NSC problem

set PRODUCTS;

param MONTHS;	# Number of months in the planning horizon

param c {1 .. MONTHS, PRODUCTS};   
# c[i,p] = cost of producting one ton of product p in month i

param d {1 .. MONTHS,PRODUCTS};   
# d[i,p] = tons of product p needed in month i

var P {1 .. MONTHS,PRODUCTS} >= 0; 
# P[i,p] = tons of product p produced in month i

var I {0 .. MONTHS,PRODUCTS} >= 0; 
# I[i,p] = tons of product p in inventory at the end of month i


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

subject to demand {i in 1 .. MONTHS, p in PRODUCTS}: 
  P[i,p] + I[i-1,p] >= d[i,p];

subject to inventory {i in 1 .. MONTHS, p in PRODUCTS}:  
  I[i,p] = P[i,p] + I[i-1,p] - d[i,p];

subject to initial_inventory {p in PRODUCTS}: I[0,p] = 0;
subject to final_inventory {p in PRODUCTS}: I[MONTHS,p] >= 1500;
subject to max_production {i in 1 .. MONTHS}: 
  sum{p in PRODUCTS} P[i,p] <= 5000;