Abstract: Finding a sequence of workpiece orientations such that the number of setups is minimized is an important optimization problem in manufacturing industry. In this paper we present some interesting notes on this optimal workpiece setup problem. These notes show that (1) The greedy algorithm proposed in Comput. Aided Des. 35 (2003), pp. 1269-1285 for the optimal workpiece setup problem has the performance ratio bounded by O(ln n-ln ln n+0.78), where n is the number of spherical polygons in the ground set; (2) In addition to greedy heuristic, linear programming can also be used as a near-optimal approximation solution; (3) The performance ratio by linear programming is shown to be tighter than that of greedy heuristic in some cases.