The ability of a coal-fired power station to meet its generation targets is influenced by periods of coal shortage. In this article, we propose a multi-objective inventory model to assist with the management of coal stockpiles. The model is applicable to power utilities with a network of two or more coal-fired power stations. The aim is to determine the near-optimal amount of coal inventory to stockpile at each station in the network. A Monte Carlo coal stockpile simulator is used to incorporate stochastic uncertainty into the stockpile levels, while a metaheuristic uses the simulator as an estimator of two objective functions. The metaheuristic finds good values for the coal stockpile level at each power station in the network. The algorithm for multi-objective optimisation using the cross-entropy method is proposed as a suitable metaheuristic. A hypothetical case study is used to validate the inventory model and to showcase the optimisation results.