Nowadays QKD plays a critical role in unconditionally-secure and quantum-safe key distribution. Commercially available QKDdevices are getting more popular for institutional and governmental national and international networks, but are expensive andoffer limited key rates. We provide a formalization of QKD-generated key forwarding and redistribution at the KMS level byextending the network graph of physical QKD links to the complete graph with logical links, and we investigate its application onthree practical scalable scenarios (all-to-all, one-to-all, one-to-one). We define a maximization goal for each scenario, andprovide a linear programming problem statement to compute the optimal redistribution. We perform an extensive analysis ofthe algorithm in terms of forwarding results and key consumption on simulated QKD networks and discuss the implications ofnetwork size and graph topology on the algorithm’s performance and complexity.