The RFID reader-tag detection uncertainty comes from the inherent unreliability of the RFID technology due to the collisions between RFID devices and interference from the surrounding environment. The performance of an RFID network is largely affected by detection uncertainty, which should be considered in the network planning phase to minimize its negative impact. In this paper, we formulate a non-linear integer programming (NLIP) model to minimize the cost on a grid-based field while satisfying the given coverage requirement for the target detection and target location. Then, an exact p-order polynomial approximation (POPA) algorithm and heuristic algorithms are designed to solve the model. Through computational experiments, the efficiency of the proposed algorithms is demonstrated. We further apply the heuristic algorithms to an industrial case and illustrate how the proposed model and algorithms are applied to satisfy the demand of practical application in a mixed-model assembly line. The results indicate that the genetic algorithm with GRASP outperforms other algorithms in terms of solution quality and computational robustness.