The research described in this paper aimed to develop a cost optimisation model for determining the optimal approach to expanding airport capacity in metropolitan areas, taking into account demand uncertainties. The study began by analysing airport capacity expansion cases from diverse global regions to identify potential metropolitan-level solutions and key cost functions associated with airport capacity issues. A deterministic optimisation model was then developed using mixed-integer nonlinear programming (MINLP), incorporating six cost functions: capital cost, operation cost, delay cost, noise cost, operational readiness airport transfer (ORAT) cost and passenger access cost. The model was validated through a case study of the Sydney metropolitan area in Australia over a 50-year horizon and further tested for reliability using six additional experimental models. Subsequently, the deterministic model was adapted into a stochastic optimisation model employing Monte Carlo simulation to address the uncertainties in future traffic demand. This stochastic model was evaluated under three different demand scenarios, including the impact of the COVID-19 pandemic. The findings highlight the model’s reliability and reveal the trade-offs among the six cost functions over time, as well as the influence of demand uncertainty on identifying optimal solutions. The research underscores the effectiveness of integrating MINLP and Monte Carlo simulation methods for long-term airport capacity planning in metropolitan areas and addressing the diverse needs of airport stakeholders. This article is also included in The Business & Management Collection which can be accessed at https://hstalks.com/business/.