Simulation for the Optimization of ( s , S ) Inventory System with Random Lead Times and a Service Level Constraint by Using Arena and OptQuest ( Date : 18 June , 2006 )

In this paper, 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. Bashyam and Fu (1998) first present this problem and obtained the answer by using Perturbation Analysis. Angun, Gurken, Hertog and Kleijnen (2006) studied the same question by using Response Surface Method. The motivation for our work comes from the difference answers between them for the same model under the same situations. We establish the (s, S) inventory model by using Arean and find the estimators by OptQuest. We try to solve several issues: what the true optimal values of (s, S) are in this specified conditions; whether the OptQuest can find the optimal values more efficiently; how we can prove these different outcomes are the estimators of true optimal values and which one is better. In order to identify the best estimator, we test their KKT conditions by applying two methods: small sample size procedure and large sample size procedure. In our conclusion, we give the true optimal estimator of (s*, S*) pairs estimated by Brute Force and prove that OptQuest can be used in solving the stochastic constrained optimization problem and find the near optimum effectively. Further, we point out that the outcome obtained from Bashyam and Fu is the estimator near the true optimal value, but not as close as the one gained by OptQuest, while the result of Angun et al (2006) gained is far away from the optimum. Furthermore, we also prove that the rejection probability for each null-hypothesis obtained by the KKT testing procedure with large example size is more obvious than that of small example size.