The overhead shuttle (OHS) is a widely used automated material handling system (AMHS) for flat panel display (FPD) manufacturing lines. Recently, an OHS using wireless power transfer (WPT) technology, which transfers power remotely from the contactless power supply (CPS) installed in the track, has been widely applied. The OHS with WPT technology is revolutionary because it removes the need for a battery, as the power is continuously transferred while the OHS is in motion. Unlike a conventional battery-powered OHS, the WPT-based OHS does not need to travel to charging stations to recharge the battery, and therefore, delivery efficiency is increased. One of the key design problems in developing a WPT-based OHS system is determining the power distribution in the track. Typically, the track is divided into multiple zones, and the power supply for each zone is determined independently. This decision is critical because it determines the maximum number of OHSs that can be in a zone at the same time. In this paper, we introduce an optimization algorithm to logically determine the power supply in each zone. The critical problem is that the power supply affects the OHS delivery capacity and the total installation cost. We propose an efficient solution algorithm using the monotonicity and primal dual properties of the optimization model. Two heuristics algorithms are proposed gradient-search and genetic -algorithm-based approaches. The numerical case from an actual system is investigated to cross-validate the proposed algorithms.