Simulation-based optimization framework for multi-echelon inventory systems under uncertainty

• Optimizing multi-echelon inventory systems under uncertainty.
• Novel simulation-based optimization framework.
• Integration of agent-based modeling and cutting plane algorithm.
• Statistical hypothesis tests on functions estimated by Monte-Carlo method.
• Local optimal solution validated by statistical test on KKT conditions.

Inventory optimization is critical in supply chain management. The complexity of real-world multi-echelon inventory systems under uncertainties results in a challenging optimization problem, too complicated to solve by conventional mathematical programing methods. We propose a novel simulation-based optimization framework for optimizing distribution inventory systems where each facility is operated with the (r, Q) inventory policy. The objective is to minimize the inventory cost while maintaining acceptable service levels quantified by the fill rates. The inventory system is modeled and simulated by an agent-based system, which returns the performance functions. The expectations of these functions are then estimated by the Monte-Carlo method. Then the optimization problem is solved by a cutting plane algorithm. As the black-box functions returned by the Monte-Carlo method contain noises, statistical hypothesis tests are conducted in the iteration. A local optimal solution is obtained if it passes the test on the optimality conditions. The framework is demonstrated by two case studies.

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