Final answer:
The method often used during the project transition from defining to planning phase for project cost estimation is the apportion method, which relates project costs to similar past projects and is complemented by cost-benefit analysis.
Step-by-step explanation:
The method often used as the project transitions from the defining to the planning phase, which requires that an overall project cost be provided based on the customer's budget or similar projects, is the apportion method. This method utilizes a mathematical model to estimate costs by apportioning the costs of similar previous projects to the new project, considering variables such as materials, fabrication, operation, and maintenance. Cost-benefit analysis complements this by comparing the marginal costs and marginal benefits to evaluate the feasibility of the project.