# Bilateral Matching Decision Model and Calculation of High-Speed Railway Train Crew Members
## 1 Introduction  
The research field of high-speed railway crew planning has consistently been a prominent focus within high-speed railway management optimization. Current studies have yielded substantial findings primarily concentrated on optimizing crew routing and formulating crew schedules. [PERSON] [1] modeled the problem as a set-covering model with minimum cost as the optimization objective, utilizing an improved ant colony algorithm for computation. [PERSON] [2] developed a space-time state network integrated with crew regulations, formulated an integer programming model for the network, and designed a Lagrangian algorithm for solving the problem. [PERSON] [3] proposed an arc-flow model aimed at minimizing crew costs, employing column generation techniques to enhance solution efficiency. [PERSON] [4] introduced a crew scheduling model based on network flow to reduce labor costs, further implementing a time-based personnel clustering decomposition approach to solve the problem. [PERSON] [5] designed a two-stage model and devised separate solution algorithms for large-scale instances, validating the model's and algorithm's effectiveness through simulation studies. A review of prior research reveals that the majority of these studies have focused predominantly on reducing labor costs or minimizing working hours, with limited consideration for crew perspectives in the formulation of crew schedules. In the research of similar topics in aviation systems, several studies based on the perspective of crew members have emerged. [PERSON] [6] established a preference-based integer programming model and designed a heuristic algorithm to solve this problem. [PERSON] [7] integrated crew preferences into the objective function of the model, designing a decentralized search algorithm and comparing it with a branch-and-price algorithm based on the constructed integer programming model. [PERSON] [8] incorporated crew preferences into this problem, establishing a preference-based mathematical model and employing a column generation algorithm to solve it. [PERSON] [9] developed a scheduling model based on crew preferences and qualifications, and used a genetic algorithm to solve this problem, aiming to achieve an optimized crew scheduling scheme. In recent years, the efficiency of team collaboration in high-speed railway crew operations has been declining, coupled with increasing personnel turnover. Thus, exploring crew scheduling methods from the perspective of crew members has become particularly important. In practice, the preparation of high-speed railway crew plans typically involves three main steps: first, the matching of crew members; second, the generation of crew routes; and finally, the matching of crew members to the generated crew routes. Steward matching forms the foundation of crew plan preparation. If crew members with high satisfaction can be identified during the matching process, it can significantly enhance their job satisfaction and team collaboration efficiency, while also improving personnel stability. However, current research in this area remains relatively limited. Against this backdrop, the theory of bilateral matching decisions offers a novel research approach. Bilateral matching theory addresses the problem of matching discrete resources between two disjoint sets and has become a research hotspot in recent years. It is widely applied in various fields, including male-female marriage matching, person-position matching, and matching between students and mentors. Numerous scholars have conducted in-depth studies on this problem, focusing on aspects such as stability and satisfaction. [PERSON] et al. [10] established the definitions of stable and optimal matchings through the study of student admissions and marriage issues, confirming the existence of stable matchings using the Gale-Shapley algorithm. [PERSON] [11] designed a bilateral matching model based on intuitionistic fuzzy functions for person-job matching, obtaining optimal results through multi-objective decision-making models.