This paper reports a new genetic algorithm (GA) for solving a general machine/part grouping (GMPG) problem. In the GMPG problem, processing times, lot sizes and machine capacities are all explicitly considered. To evaluate the solution quality of this type of grouping problems, a generalized grouping efficacy index is used as the performance measure and fitness function of the proposed genetic algorithm. The algorithm has been applied to solving several well-cited problems with randomly assigned processing times to all the operations. To examine the effects of the four major factors, namely parent selection, population size, mutation rate, and crossover points, a large grouping problem with 50 machines and 150 parts has been generated. A multi-factor (34) experimental analysis has been earned out based on 324 GA solutions. The multi-factor ANOVA test results clearly indicate that all the four factors have a significant effect on the grouping output. It is also shown that the interactions between most of the four factors are significant and hence their cross effects on the solution should be also considered in solving GMPG problems.