While operating a crane for maximum productivity, the time of operation and the required energy are two important conflicting factors faced by a crane operator. In such a case, trying to reach the destination too quickly demands a large energy supply, while a small powered motion requires longer time. In this paper, we consider such a problem for two different pairs of objectives and employ a multi-objective genetic algorithm for the task. Besides finding a set of trade-off optimized solutions (operating conditions), an analysis of these solutions reveals salient operating principles, which would be difficult to achieve by other means. The methodology demonstrated in this paper can be used for other similar engineering design and application problems.