Geo-obfuscation serves as a location privacy protection mechanism (LPPM), enabling mobile users to share obfuscated locations with servers, rather than their exact locations. This method can protect users' location privacy when data breaches occur on the server side since the obfuscation process is irreversible. To reduce the utility loss caused by data obfuscation, linear programming (LP) is widely employed, which, however, might suffer from a polynomial explosion of decision variables, rendering it impractical in largescale geo-obfuscation applications. In this paper, we propose a new LPPM, called Locally Relevant Geo-obfuscation (LR-Geo), to optimize geo-obfuscation using LP in a time-efficient manner. This is achieved by confining the geo-obfuscation calculation for each user exclusively to the locally relevant (LR) locations to the user's actual location. Given the potential risk of LR locations disclosing a user's actual whereabouts, we enable users to compute the LP coefficients locally and upload them only to the server, rather than the LR locations. The server then solves the LP problem based on the received coefficients. Furthermore, we refine the LP framework by incorporating an exponential obfuscation mechanism to guarantee the indistinguishability of obfuscation distribution across multiple users. Based on the constraint structure of the LP formulation, we apply Benders' decomposition to further enhance computational efficiency. Our theoretical analysis confirms that, despite the geo-obfuscation being calculated independently for each user, it still meets geo-indistinguishability constraints across multiple users with high probability. Finally, the experimental results based on a real-world dataset demonstrate that LR-Geo outperforms existing geo-obfuscation methods in computational time, data utility, and privacy preservation.