We study three important production planning problems for flexible manufacturing systems (FMSs) that consist of multiple types of machines. Namely we address machine grouping, workload allocation among machine groups, and batch sizing that maximize system throughput, when part types are selected for the upcoming production period. This differs from earlier related works in that earlier works give either only qualitative characteristics of the optimum solution or provide a solution method for FMSs consisting of only one type of flexible machine. In this paper, we provide both the optimum and heuristic methods to simultaneously solve the three problems for realistic FMSs. Computational results show that the heuristic method always finds the optimum solution at a fraction of computation time and that batch sizing can significantly affect throughput. Development of the heuristic method is necessary since the optimum method can be time-consuming for a moderate size of problems.