Personnel selection in competitive two-sided markets presents challenges for organizations seeking to attract high-quality candidates while managing their costs. However, existing models often overlook the optimization of job-offer packages to address both candidate preferences and organizational objectives. This paper addresses this research gap by proposing a novel mathematical model for determining the optimal job offer package. Our model integrates candidate preferences and organizational costs, offering a solution to the selection process. Utilizing a two-stage Mixed-Integer Linear Programming (MILP) approach, we employ the Gale and Shapley algorithm to facilitate efficient two-sided matching. Through a case study, we validate the effectiveness of our model in providing actionable insights for organizations seeking to enhance their hiring processes and attract top talent. This innovative approach marks a significant advancement in the realm of personnel selection, offering organizations a robust framework to navigate the complexities of two-sided market dynamics with precision and efficacy.