An effective planning and management of deadlines are crucial for global software development (GSD) project success. Establishing a schedule is essential, and one effective method is to propose a planning platform that uses a constraint satisfaction solver. This approach helps project managers analyze the feasibility of their projects and create effective schedules, considering all the variables of global software development. Our paper presents a systematic mapping study that provides a comprehensive summary of existing research on the aspects, techniques, and challenges related to planning and managing deadlines in GSD contexts, with a focus on studies that propose models using constraint satisfaction solvers. We found that successful deadline management requires thorough planning, including effective task allocation, management of requirement changes, risk management, and effort estimation. Consequently, our systematic mapping will concentrate on these four aspects, and we will examine whether there are articles that propose solutions using constraint satisfaction solvers.