Stakeholders carry out construction projects under fast-changing conditions. The conditions can undermine the concept of a stable and prosperous construction plan without an appropriate permit and an active and targeted plan for environmental management. Therefore, the decision maker often faces many challenges of Multi-Criteria Decision-Making (MCDM) when it comes to solving the construction management proper response selection problem for planning delay changes when sustainable environment requirements are essential. Any addition, reduction, or modification of the original project plan is a change to the project and impacts the environment. Change occurrence is a probable issue while projects are implemented. One of the most complex tasks for the project manager is to work correctly and to find the most suitable decisions for the not precisely predetermined future expectations of a change. Therefore, the relevant criteria of values must reflect the uncertain properties of the problem model. Similar problems require fuzzy or grey MCDM methods. The paper introduces a new MCDM approach, which combines four different MCDM methods with grey numbers: the SWARA, TOPSIS-GM, Additive Ratio ASsessment with Grey Numbers (ARAS-G) techniques and Geometric Mean to cover uncertainty and improve the problem-solving model. An analysis of a case study has examined and highlighted four possible alternatives described by eight performance criteria (cost, duration, and some linguistic criteria). Stakeholders determined the best alternative, calculated the efficiency of choice, and practically implemented the best option.