  In this paper, we consider a finite horizon non-stationary inventory system
with setup costs. We detail an algorithm to find an approximate optimal policy
and the basic idea is to use numerical procedure for computing integrals
involved in the standard method. We provide analytical error bounds, which
converge to zero, between the costs of an approximate optimal policy found in
this paper and the optimal policy, which are the main contributions of this
paper. To the best of our knowledge, the error bound results are not found in
the literature on finite horizon inventory systems with setup costs. A
convergence result for the approximate optimal policy is also provided. In this
paper, algorithms to find the above error bounds are also provided. Several
numerical examples show that the performance of Algorithms in this paper is
satisfactory.
