A dual-gantry component placement tool for mounting electronic components on the surfaces of printed circuit boards has several operational decision problems. We examine the gantry task scheduling problem when the feeders arrangement decision is given. Each gantry repeats alternate pick and placement work cycles. Since the two gantries cannot simultaneously access the PCB for mounting operations because of collision risk, a gantry that completes the picking operations should wait until the other gantry finishes the placement operations. The waiting times depend on the sequence in which each gantry performs the work cycles, and the sequence in which the two gantries perform the placement operations. The gantry scheduling decision determines the two sequences so that the gantry waiting time and hence the makespan are minimized. We identify the problem complexity and find some critical characteristics of the problem. Based on the results, we develop an efficient algorithm for reducing the gantry idle time by classifying the work cycles into three groups. The computational performance is examined using random data and real industrial data.