# AMPL model file for the inventory model 
# (WV-IMP problem 1 from page 104: discussed in class)
#
#   min  z =  5 x1 + 8 x2 + 4 x3 + 7 x4 + 2 (s1+s2+s3) - 6 s4 (net cost)
#
#   s.t. s1 = x1     -  50  (inventory month 1)
#	 s2 = x2+s1  -  65  (inventory month 2)
#	 s3 = x3+s2  - 100  (inventory month 3)
#	 s4 = x4+s3  -  70  (inventory month 4)
#        all vars >= 0      (non-negativity)


param n;                      # No. of months
param Demand   {i in 1..n};   # demand for each month
param Cost     {i in 1..n};   # production cost for each month
param Store_Cost;   	      # storage cost (same for each month)
param Price;                  # selling price (at the end of month n)

var   x {j in 1..n} >= 0;     # No. units made in month j
var   s {j in 0..n} >= 0;     # inventory at the end of month j
			      # s[0] - inventory at the start of month 1 = 0

minimize net_cost: sum {k in 1..n} Cost[k]*x[k] + Store_Cost*(sum{j in 0..n-1} s[j]) - Price*s[n];

subject to inventory_balance {i in 1..n}: s[i] = x[i] + s[i-1] - Demand[i];
subject to set_initial_inventory: s[0] = 0;