From the sustainability science point of view, sustainable development is a three-dimensional (3D),discretized state transition problem, where the dimension is determined by the core concept of sustainability, which is triple-bottonyline based, and the state transition reflects a. fundamental feature of sustainability development. These require continuous sustainability assessment, decision analysis, and action taking. In this paper, we formulate sustainability-analysis problems as a general vector-based analysis problem, where the sustainability vector is characterized by the degree of system status change and the direction in a 3D sustainability space. To quantify the balance of triple-bottom-line-based development, we introduce,a parameter called the development imbalance angle. We describe a sustainability space partition method, by which a Prober of zones in the space can be defined and featured. As a sustainability improvement process involves a series of sustainability state transitions, we apply a vector analysis technique to capture key features of state transition options. In addition, we introduce an algorithm to streamline the analysis tasks in a systematic way. A case study on sustainable biodiesel manufacturing is presented to demonstrate the key features and applicability of the proposed methodology.