Final answer:
Aviva uses management science to allocate resources within her department through the application of mathematical models, which differentiates her approach from administrative management, Theory X and Theory Y, or scientific management.
Step-by-step explanation:
Aviva is making use of management science in her approach to resource allocation within her department. Management Science incorporates the use of mathematical models to improve decision-making in organizations. This discipline often applies rigorous methods to investigate and understand the complexity of management processes, with the core objective of enhancing efficiency and effectiveness. By deploying mathematical models at the start of each new project, Aviva is able to forecast resource needs, analyze data, and optimize her department's performance. This is in contrast to administrative management, which focuses on the organization and its hierarchy; Theory X and Theory Y, which are different approaches to workforce motivation and management; and scientific management, which looks at improving economic efficiency through labor productivity. In the context of Aviva's work, management science helps her to develop, test, and implement models that cater to various scenarios, guiding cost and resource allocation based on mathematical validation.