Managing blood product inventories can be challenging due to stochastic supply and demand, varying shelf lives of the products, and the need to account for multiple objectives such as the minimisation of costs, product shortage and expiry. This complex setting makes it difficult to include all relevant aspects, while ensuring that the computation time required to optimise the blood product supply chain remains reasonable. Consequently, existing models typically fail to solve realistic-sized problems and thus have not found much use in supporting decisions faced by blood service practitioners. This research develops a methodological framework for modelling platelet inventories, resulting in robust managerial recommendations. Specifically, we propose a two-stage stochastic programming model to define optimal order-up-to levels that minimise costs, shortage and expiry in a decentralised decision-making setting. We exploit the problem structure to decompose it and make the model computationally tractable. To ensure that the model is practically relevant, we develop it with practitioners from the Finnish Red Cross Blood Service. We use the model to estimate the costs of extending the shelf life of platelets from five to seven days through two methods and assess the impacts of this extension on optimal inventory decisions. These results can be used to optimise the Finnish platelet supply chain and inform future cost-effectiveness analyses regarding shelf life extension.