Mixed-integer simulation optimization for multi-echelon inventory problems with lost sales

We propose a mixed-integer simulation optimization framework for solving multi-echelon inventory problems with lost sales. We want to seek optimal settings of the order-up-to levels and the review intervals for warehouse and retailers. The aim is to minimize the total expected costs including the inventory holding cost, the ordering cost and the penalty cost. The proposed optimization method represents a complementary combination of ranking-and-selection procedures and stochastic-approximation algorithms for both integer-valued and real-valued variables. We provide a proof for the finite-time statistical validity of the developed algorithm. We also discuss the convergence conditions for the asymptotic optimality of our algorithm. The algorithmic performance is examined with experiments under different parameter settings and stopping conditions. During the experiments, our algorithm performs favorably in comparison to the popular Arena optimization tool, OptQuest.