This paper explores the paradigm of continuous improvement in construction cost management, emphasizing the utilization of Generative Artificial Intelligence (Generative AI) as a pivotal factor in driving this advancement. Embracing the lean construction principle and the plan-do-check-act approach, the study emphasizes the need for requirements and techniques in cost management. Building Information Modeling (BIM) is recognized as crucial for budgeting construction costs, but it faces challenges related to automation and technology. In this study we explore the use of Generative AI in generating Bills of Quantities (BOQs) for building cost management in small and medium-sized enterprises (SMEs). The exploration combines transformer-based techniques and Large Language Models (LLM), introducing a novel approach to development of BOQs in construction projects. Robustly Optimized BERT Pre-training approach (RoBERTa), an effective and reliable transformer architecture, categorizes substructure and superstructure components with an impressive 91% accuracy, forming a solid foundation. Fuzzy similarity matching connects sub-element records to project cost tables, incorporating cost data for meticulous computations. Leveraging the advanced text-generation capabilities of GPT-4, a state-of-the-art language model, the study automates the construction of a detailed and comprehensive BOQ. This departure from traditional rule based BOQ development offers enhanced flexibility and contextual knowledge. This approach, combining transformer-based models for precise categorization with LLM (GPT-4) for automated BOQ generation, presents a simplified and efficient solution for cost budgeting in building projects. This innovative method not only promises improved project documentation but also signifies potential revolutionary progress in building cost-management procedures. The findings provide valuable insights for construction professionals, paving the way for a more efficient and advanced approach to cost management in the construction industry.