A hybrid genetic algorithm for two-stage multi-item inventory system with stochastic demand

We study a two-stage, multi-item inventory system where stochastic demand occurs at stage 1, and nodes at stage 1 replenish their inventory from stage 2. Due to the complexity of stochastic inventory optimization in multi-echelon system, few analytical models and effective algorithms exist. In this paper, we establish exact stochastic optimization models by proposing a well-defined supply–demand process analysis and provide an efficient hybrid genetic algorithm (HGA) by introducing a heuristic search technique based on the tradeoff between the inventory cost and setup cost and improving the initial solution. Monte Carlo method is also introduced to simulate the actual demand and thus to approximate the long-run average cost. By numerical experiments, we compare the widely used installation policy and echelon policy and show that when variance of stochastic demand increase, echelon policy outperforms installation policy and, furthermore, the proposed heuristic search technique greatly enhances the search capacity of HGA.