Diffusion equations are generally solved forwardly, namely, for a given core loading condition one solves for the flux and power distribution. For fuel management applications, a theory of backward diffusion calculation is developed which for a given power distribution solves the diffusion equation backwardly for the core reactivity distribution. Loading pattern searches can be facilitated by matching the available fuel assemblies to the reactivity distribution predicted backwardly from the desired power distribution. Optimization of fuel utilization can also be performed by determining the optimum power shape, under imposed constraints, that gives a reactivity distribution requiring the least fuel loading.