The design of the optimal nonrandomized hard decision fusion rule under the Neyman-Pearson criterion is known to be exponential in complexity. In this letter, we formulate a more generalized version of this problem called the 'generalized decision fusion problem (GDFP)' and relate it to the classical \text{0-1} knapsack problem. Consequently, we show that the GDFP has a worst-case polynomial time solution. Numerical results are presented to verify the effectiveness of the proposed solution. © 1994-2012 IEEE.