Multiprocessors have become the main architecture trend in modern systems due to the superior performance; nevertheless, the power consumption remains a critical challenge. Global power management (GPM) aims at dynamically finding the power state combination that satisfies the power budget constraint while maximizing the overall performance (or vice versa). Due to the increasing number of cores in amultiprocessor system, the scalability of GPM policies has become critical when searching satisfactory state combinations within acceptable time. This article proposes a highly scalable policy based on combinatorial optimization with theoretical proofs, whereas previous works take exhaustive search or heuristic methods. The proposed policy first applies an optimum algorithm to construct a state combination table in pseudo-polynomial time using dynamic programming. Then, the state combination is assigned to cores with minimum transition cost in linear time by mapping to the network flow problem. Simulation results show that the proposed policy achieves better system performance for any given power budget when compared to the state-of-the-art heuristic. Furthermore, the proposed policy demonstrates its prominent scalability with 125 times faster policy runtime for 512 cores.