Mathematical model for decision-making for non-potable water system of residential buildings: decentralised or centralised?

Abstract There are three types of non-potable water building systems: decentralised individual, decentralised or centralised. There is no consensus on which the most efficient type is, since both centralised and decentralised systems have peculiarities that make them either interesting or not in social, economic and environmental aspects. Thus, the aim of this article is to develop the formulation of a mathematical model for decision making regarding the type of non-potable water system and compare decentralised systems with centralised systems over a period of twenty years, with and without the scale effect. The model was developed based on a deterministic mathematical approach, known in the literature as Integer Programming. The difference of this model is that it allows to determine the total accumulated cost, the cost over life cycle and the number of systems necessary to meet a specific demand. The model was applied to a hypothetical residential condominium with a minimum population of 1700 residents. The results indicate that the centralised system is more advantageous than the individual systems in terms of costs of installation, maintenance and operation during a life cycle of twenty years with and without the scale effect.摘要 建筑非饮用水（non-potable water）系统共分为三类：分散式单体系统、分散式系统与集中式系统。目前学界尚未就最优系统类型达成共识，因集中式与分散式系统各有独特特性，使其在社会、经济与环境维度的适配性各有优劣。据此，本文旨在构建面向非饮用水系统选型决策的数学模型，并在考虑与不考虑规模效应（scale effect）的两种情境下，对比分析集中式系统与分散式系统在20年生命周期内的性能表现。本模型基于学术界通用的确定性数学方法——整数规划（Integer Programming）开发。该模型的核心优势在于，可计算累计总成本、全生命周期成本以及满足特定用水需求所需的系统配置数量。本模型已应用于一个最低居住人口为1700人的假想住宅公寓项目。结果显示，在考虑与不考虑规模效应的两种20年生命周期场景中，集中式系统在安装、维护与运营成本层面均优于单体分散式系统。