The nuclear fuel cycle is modelled as a cyclic, multi-stage production-to-inventory system. The objective is to meet a known deterministic demand for energy while minimizing acquisition, production, and inventory holding costs for all stages of the fuel cycle. The model allows for cyclic flow (feedback) of materials, material flow conversion factors at each stage, production lag times at each stage, and for escalating costs of uranium ore. It does not allow shortages to occur in inventories. The model is optimized by the application of the calculus of variations and specifically through recently developed theorems on the solution of functionals constrained by inequalities. The solution is a set of optimal cumulative production trajectories which define the stagewise production rates. Analysis of these production rates reveals the optimal nuclear fuel cycle costs and that inventories (stockpiles) occur in uranium fields, enriched uranium hexafluoride, and fabricated fuel assemblies. An analysis of the sensitivity of the model to variation in three important parameters is performed. / Ph. D.