Nesting and scheduling for parallel additive manufacturing machines with uncertain processing times: a simulation-optimisation approach

Additive manufacturing (AM) plays a crucial role in meeting the growing demand for mass customisation, where on-time delivery is critical. While most existing AM scheduling studies address deterministic scenarios, the impact of processing time uncertainties on on-time delivery remains less explored. To bridge this gap, we investigate the nesting and scheduling problem for parallel AM machines with uncertain processing times, focussing on selective laser melting technologies. The objective is to minimise the expected number of tardy parts. We formulate a mixed-integer programming model for the deterministic case. To effectively handle processing time uncertainties, we propose a simulation-optimisation approach that combines Monte Carlo simulation with an adaptive large neighbourhood search method. Experimental results demonstrate the benefits of accounting for these uncertainties in reducing delivery delays. Additionally, we analyze the factors influencing these benefits and the underlying drivers of solution robustness.