We propose a penalty-based and constraint Bayesian optimization methods with an agent-based supply-chain (SC) simulator as a new Monte Carlo optimization approach for multi-echelon inventory management to improve key performance indicators such as inventory cost and sales opportunity loss. First, we formulate the multi-echelon inventory problem and introduce an agent-based SC simulator architecture for the optimization. Second, we define the optimization framework for the formulation. Finally, we discuss the evaluation of the effectiveness of the proposed methods by benchmarking it against the most commonly used genetic algorithm (GA) in simulation-based inventory optimization. Our results indicate that the constraint Bayesian optimization can minimize SC inventory cost with lower sales opportunity loss rates and converge to the optimal solution 22 times faster than GA in the best case.