i.e. among N time periods the no. of setups should not exceed any k.
By using dynamic forward equations
Our Wagner Whithin method is this: Let St setup cost in period t Yt a binary variable that assumes value 1 if the product is produced in period t and 0, otherwise Ct variable unit production cost in period t Xt production amount in period t ht unit inventory holding cost in period t (usually constant for all t) It inventory at the end of period t
Minimise Z = Summation (t=1 to T)(StYt + CtXt + htIt) Subject to Xt + It−1 − It = dt (t = 1;:::;T); Yt ∈ {0; 1} (t = 1;:::;T) Xt<=0 It>=0 (t = 1;:::;T):
Now if a extra constraint is put saying no. of setups must is less than any k How can I reconstruct above algorithm?