Final answer:
The best project management methodology for a project with clearly defined tasks that proceed sequentially and where changes are expensive after the start is the Waterfall methodology. It provides a structured and sequential approach, which makes it suitable for projects with fixed requirements and scope.
Step-by-step explanation:
The project management methodology that is best for a project where each task begins only after a preceding task is completed and where changes become expensive once the project starts is the Waterfall methodology. The Waterfall model is a sequential design process, which means that the project development proceeds through a series of distinct phases like requirements, design, implementation, verification, and maintenance, and each phase begins only upon completion of the previous one. This is the traditional approach to project management and contrasts with methodologies like Agile or Scrum, which have iterative and incremental design processes that accommodate change more readily and involves frequent revisiting and revising of project stages.
While the Agile approach in project management, specifically represented by methodologies such as Scrum, caters to projects that require flexibility and have high levels of uncertainty, the Waterfall method is more suited to projects with well-defined requirements and scope, which does not change throughout the project lifecycle. The Lean methodology focuses on eliminating waste and improving efficiency, which is not specifically aligned with the described need to follow a strict sequence of tasks. This indicates that for projects that have clearly defined steps and costly changes after initiation, the structure and discipline of the Waterfall method is best.