A Matrix Theory of Constrained Network Flow for Sustainability Assessment: Case Study of Waiheke Island Water Resource

Abstract

This thesis developed a matrix based, mathematical theory for constrained network flow for a novel sustainability assessment metric. The predominant environmental modelling frameworks discussed in industrial ecology, namely footprint analysis, input-output analysis, and LCI, share a common mathematical structure. These frameworks, which aim to establish quality databases, can accurately calculate the total environmental impact of a regional system or industrial process in terms of the quantity of resource extraction and waste/pollutant emissions. This thesis explores an alternative use for these frameworks, by introducing the concept of constraints to the established computation methods. Above mentioned framework can be generalised to a matrix based system of linear inequations, which is similar to linear programming. In contrast to the usual linear programming problems, such as trying to find the optimal solution, the framework focusses on the geometry and volume of the feasible space enclosed by sustainability constraints. In this thesis, the volume of the feasible space is conceptually connected to Bossel’s (1999) accessibility space and can define a metric to express sustainability. Collecting data in regard to the sustainability constraints is the key driver for the proposed theory and has to be accumulated from external studies of physical and social models. Case studies of constraints found in various components of the water resources system in Waiheke Island provided the demonstration of the matrix based constrained network theory and the sustainability metric. The case study showed that the water resource carrying capacity for the island using current infrastructure setting with RWH, aquifer pumping, onsite wastewater treatment is 21300, with land use being limiting factor. Introducing greywater reuse to the island increased the carrying capacity to 31900 and introduction of SWRO did not have large impact on the carrying capacity but provided flexibility on water resource management and thus improved optimal population level from 14000 to 20000.