This paper considers the allocation and engagement scheduling problem of interceptor missiles, and the problem was formulated by using MIP (mixed integer programming) in the previous research. The objective of the model is the maximization of total intercept altitude instead of the more conventional objective such as the minimization of surviving target value. The concept of the time window was used to model the engagement situation and a continuous time is assumed for flying times of the both missiles. The MIP formulation of the problem is very complex due to the complexity of the real problem itself. Hence, the finding of an efficient optimal solution procedure seems to be difficult. In this paper, an efficient genetic algorithm is developed by improving a general genetic algorithm. The improvement is achieved by carefully analyzing the structure of the formulation. Specifically, the new algorithm includes an enhanced repair process and a crossover operation which utilizes the idea of the PSO (particle swarm optimization). Then, the algorithm is throughly tested on 50 randomly generated engagement scenarios, and its performance is compared with that of a commercial package and a more general genetic algorithm, respectively. The results indicate that the new algorithm consistently performs better than a general genetic algorithm. Also, the new algorithm generates much better results than those by the commercial package on several test cases when the execution time of the commercial package is limited to 8,000 seconds, which is about two hours and 13 minutes. Moreover, it obtains a solution within 0.13 ~33.34 seconds depending on the size of scenarios.