In this study, we proposed a novel closed form optimization model for the Conflict Neutralization Problem (CKP) and implemented an efficient algorithm for solving the problem. A novel tableau representation of the CNP model was presented and described in detail. We implemented a special structured branch and bound algorithm to solve the problem. Key components of the implementation were described. To test the computation performance of our algorithm, we designed and conducted three sets of experiments. The experiment results were reported and analyzed in this report. The test results showed the efficiency of the algorithm for solving the Conflict Neutralization Problem.