param start; # first year of demand
param end;   # last year of demand

param demand {n in start..end};

param invLimit; 
param prodLimit;

param unitCost {n in start..end};
param setupCost;

param cost{n in start..end, i in 0..prodLimit}:=
	if i=0 then 0 else (setupCost + i * unitCost[n]);
# cost of producing i units in period n

set options{n in start..end, s in 0..invLimit}:=
	{i in 0..prodLimit: i+s >= demand[n] 
	and i+s-demand[n] <= invLimit};
# set of allowed production levels

param f{n in start..end+1, s in 0..invLimit}:=
	if n = end + 1 then 0 else
	min{i in options[n,s]} (cost[n,i] + f[n+1, s+i-demand[n]]);

set opt{n in start..end, s in 0..invLimit}:=
   { i in options[n,s]:
    f[n,s] = cost[n,i] + f[n+1, s+i-demand[n]] };

data;

param start:= 1;
param end:= 3;

param demand:=
1 1
2 2
3 1;

param invLimit:= 2; 
param prodLimit:= 3;

param unitCost:=
1 3
2 5
3 4;

param setupCost:= 10;