Policy learning for lot-sizing stochastic inventory control problem: A neuro-evolutionary approach

The lot-sizing stochastic inventory control problem with non-stationary demand is a well-known control problem. It takes into account the fixed cost of placing an order, and linear inventory holding and shortage costs, while the demand is a random variable with a known probability distribution. This problem can be solved using the well-known (s, S) policy, which has been proved optimal despite having a remarkably simple form. However, the conventional approach to determining the policy parameters uses Stochastic Dynamic Programming which is computationally expensive. Other approaches (mainly heuristics) exploit background information related to the structural properties of the optimal policy or the solution. We propose neuro-evolutionary approaches for finding near-optimal policies. Our approach combines machine learning techniques (neural networks) to express possible policies, with optimization techniques (evolutionary computation) to find near-optimal policies. We show that our approach finds near-optimal policies without exploiting any background information related to the structural properties of the optimal policy or the solution. We also find that there are many near-optimal policies with a very different structure to (s, S). We finally report numerical experiments that show the effectiveness of the proposed approach.