In a mid-volume mid-variety production system, using flexible fixtures reduces manufacturing costs significantly. They reduce the time and efforts associated with changing fixtures for assembling different parts. In this paper, a modular cradle is used to hold a variety of geometrically different products in a robotic assembly system. These cradles are installed on top of a set of pallets in a "Hold'n Go" conveyor-belt loop moving through the assembly system. The modular cradle has a hole pattern on its adapter plate for jigging-pins to be inserted. Rearrangement of pins enables fixing different product geometries. However, the larger number of changed pins, the longer preparation time for fixtures. In this study, to minimize the total number of pins which have to be changed in fixing different parts, an optimization model is developed to determine the best locations for placing the different products on the cradles and the best locations for inserting pins to fix them. The objective is to minimize the total number of pin changes to minimize fixture preparation time. A mathematical model is proposed, and solved by GAMS using CPLEX solver for different case studies. The model has been proven to be efficient and able to minimize pin changes.