Exact Simulation for Assemble-To-Order Systems

Abstract: We develop exact simulation (also known as perfect sampling) algorithms for a family of assemble-to-order systems. Due to the finite capacity, and coupling in demands and replenishments, known solving techniques are inefficient for larger problem instances. We first consider the case with individual replenishments of items, and derive an event based representation of the Markov chain that allows applying existing exact simulation techniques, using the monotonicity properties or bounding chains. In the case of joint replenishments, the state space becomes intractable for the existing methods. We propose new exact simulation algorithms, based on aggregation and bounding chains, that allow a significant reduction of the state space of the Markov chain. We also discuss the coupling times of considered models and provide sufficient conditions for linear (in the single server replenishment case) or quadratic (many server case) complexity of our algorithms in terms of the total capacity in the system.