Automated materials handling systems (AMHS) play a key role in semiconductor manufacturing. Vehicle fleet sizing is one of the critical issues when designing an effective AMHS. However, due to complexity of AMHS design and uncertainty involved in the production process, for example, random processing time, vehicle fleet sizing is a challenging problem, especially when there are multiple objectives, for example, minimized delivery time and maximized delivered lots are simultaneously desired. In this paper, we formulate the multi-objective vehicle fleet sizing problem and propose a framework that integrates simulation optimization and data envelopment analysis techniques to determine the optimal vehicle fleet size under multiple objectives for the AMHS. Numerical experiments show that the proposed framework allows for better performance of AMHS than the traditional methods. Moreover, an empirical study conducted at the end verifies the effectiveness and the viability of the proposed framework in real settings.