Fixtures are devices used in manufacturing systems to locate, immobilize, and hold workpieces. There are many different numerical measures proposed in the literature to quantify the locating accuracy of a fixture, and its capability in firmly holding the workpiece in the presence of external loads. These numerical measures are useful in fixture layout design and the related area of grasp synthesis. As a number of numerical measures are available, a user may face the problem that how to choose an appropriate one as the optimality criterion in practice for fixture design. In this paper, we present a comparative study on several widely used optimality criteria, based on both theoretical analysis and simulation studies. First, we establish a set of inequalities, which describe the relations between several widely used numerical measures. Second, comparisons between optimality criteria are demonstrated by numerical examples.