Simulation for the Optimization of (s, S) Inventory System and Krush-Kuhn-Tucker Testing

We consider the simulation of constrained optimization problem, the (s, S) inventory system with stochastic lead time and a service level constraint. We allow the orders to cross in time which makes the problem more complicated. We establish the (s, S) inventory model by using Arean and find the estimators by OptQuest. We try to solve several issues: 1) what the true optimal values of (s, S) are in this specified conditions; 2) whether the OptQuest can find the optimal values; 3) how we can prove the outcomes are the estimators of true optimal values. In our conclusion, we give the true optimal estimator of (s*, S*) pairs estimated by Brute Force. Further, we prove that OptQuest can be used in solving the stochastic constrained optimization problem effectively. By testing estimators' KKT conditions under the method of Bettonvil [16], we prove that we can find the good estimator of (s*, S*).