Machine intelligence is increasingly entering roles that were until recently dominated by human intelligence. As humans now depend upon machines to perform various tasks and operations, there appears to be a risk that humans are losing the necessary skills associated with producing competitively advantageous decisions. Therefore, this research explores the emerging area of human versus machine decision-making. An illustrative engineering case involving a joint machine and human decision-making system is presented to demonstrate how the outcome was not satisfactorily managed for all the parties involved. This is accompanied by a novel framework and research agenda to highlight areas of concern for engineering managers. We offer that the speed at which new human-machine interactions are being encountered by engineering managers suggests that an urgent need exists to develop a robust body of knowledge to provide sound guidance to situations where human and machine decisions conflict. Human-machine systems are becoming pervasive yet this research has revealed that current technological approaches are not adequate. The engineering insights and multi-criteria decision-making tool from this research significantly advance our understanding of this important area.