This study proposes a novel, efficient means of encoding genetic algorithms to solve the generalized plant allocation problem. The problem relates to allocating products across plants to minimize a total cost function. The proposed encoding method can reduce the search space of solutions more efficiently than the penalty encoding method does. The new encoding method thus exhibits higher performance. It need involve only a few more generations to yield sufficiently good solutions when the number of plants is increased. The penalty encoding method, however, requires many more generations to yield the same solutions. Additionally, a new simultaneous crossover and mutation operation is proposed to enable the new method of encoding chromosomes to run correctly following standard genetic algorithm procedures. In addition to the mathematical certification, the performance of this approach is evaluated using some test problems of various sizes. Solutions obtained by this approach are always efficient.