Simulation-Based Optimization of Capacitated Assembly Systems under Beta-Service Level Constraints

Abstract

We study a class of capacitated assembly systems operated by base-stock policies and address the problem of finding base-stock levels that minimize holding costs under beta-service level (fill rate) constraints over an infinite horizon. To solve this nonconvex constrained optimization problem, we develop a new simulation-based optimization approach using the constrained level method (CLM) and infinitesimal perturbation analysis. The key idea of the algorithm is a novel family of convex approximations of the beta-service level, which is iteratively refined during the course of the algorithm. The algorithm can easily handle integrality requirements for the base-stock levels by combining the CLM with a cutting plane approach without significantly increasing the solution time on typical instances. We apply our approach to a comprehensive multi-echelon assembly benchmark system from the literature and study the algorithm's behavior for different target service levels, capacity configurations, and simulation horizons. A comparison with a state-of-the-art interior point algorithm shows that for realistic capacity constraints, our algorithm is on average 8%–20% better. Compared with the guaranteed service model, our approach reduces costs by 10%–15% while keeping the same service level.