Vector-Based Sustainability Analysis: A Fundamental Study on Sustainable Development

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-bottom-line based, and the state-transition reflects a fundamental feature of sustainability development.  These require continuous assessment, prediction, decision making, and action taking.  In most cases, information for sustainability assessment and decision making is uncertain due to data impreciseness and incompleteness.  This makes solution identification and analysis for sustainable development very challenging. 

In this paper, we formulate sustainability analysis problems as a general vector analysis problem.  Mathematically, we introduce a sustainability vector, which is characterized by its magnitude and direction in a multi-dimensional space.  To quantify the balance of triple-bottom-line-based development, we introduce a development angle.  We also describe a space partition method by which a number of zones in development space can be defined and featured.  As a sustainability improvement process involves a series of sustainability state transitions, we apply a vector calculus technique, in a discrete time-space domain, for decision analysis.   We then introduce an algorithm to streamline the tasks in using this vector-based sustainability analysis method.  A case study on sustainable biodiesel manufacturing is presented to demonstrate the key features and applicability of the proposed methodology.