Error Analysis of an Approximate Optimal Policy for a Non-stationary Inventory System with Setup Costs

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.