State−Time−Space Superstructure-Based MINLP Formulation for Batch Water-Allocation Network Design

Abstract

The mathematical technique presented in this work deals with one step design of single- and multicontaminant batch water-allocation network (WAN), where batch production, water-reuse subsystems, and wastewater-treatment subsystems are all taken into account. In the first place, a flexible schedule model combining the merits of discrete and continuous time formulations is introduced to integrate batch production and WAN. Then, two novel state−time−space (STS) superstructures incorporating all basic elements (i.e., states, tasks, equipment, and time) are adopted to capture all production schemes and batch WAN configurations. Specifically, by adding novel components in the original superstructure, a series of optimal network structures with multistage splitting and mixing options which have never been contained within previous superstructure can be easily generated. Finally, a reliable optimization strategy, where deterministic and stochastic searching techniques are combined, is suggested to deal with the resulting mixed integer nonlinear programming (MINLP) model. Two illustrative examples are presented to demonstrate the effectiveness of the proposed approach.