Cyanobacteria are an integral part of the Earth's biogeochemical cycles and a promising resource for the synthesis of renewable bioproducts from atmospheric CO2 . Growth and metabolism of cyanobacteria are inherently tied to the diurnal rhythm of light availability. As yet, however, insight into the stoichiometric and energetic constraints of cyanobacterial diurnal growth is limited. Here, we develop a computational platform to evaluate the optimality of diurnal phototrophic growth using a high-quality genome-scale metabolic reconstruction of the cyanobacterium Synechococcus elongatus PCC 7942. We formulate phototrophic growth as a self-consistent autocatalytic process and evaluate the resulting time-dependent resource allocation problem using constraint-based analysis. Based on a narrow and well defined set of parameters, our approach results in an ab initio prediction of growth properties over a full diurnal cycle. In particular, our approach allows us to study the optimality of metabolite partitioning during diurnal growth. The cyclic pattern of glycogen accumulation, an emergent property of the model, has timing characteristics that are shown to be a trade-off between conflicting cellular objectives. The approach presented here provides insight into the time-dependent resource allocation problem of phototrophic diurnal growth and may serve as a general framework to evaluate the optimality of metabolic strategies that evolved in photosynthetic organisms under diurnal conditions.