A Multi-Commodity Flow Formulation for the Optimal Design of Wastewater Treatment Networks

Abstract The wastewater treatment network (WWTN) optimization problem can be viewed as an extension of the generalized pooling problem (GPP), where not only the different streams are mixed and split, but also some chemical components are removed from the system. It is well known that a strong formulation is key to efficient global solution of GPP, and multi-commodity flow formulations have been recognized as such strong formulations. The paper presents the first multi-commodity flow formulation for the WWTN optimization problem. We discuss the challenges in adapting the classical multi-commodity flow approaches for a WWTN, and propose the conditions under which the selected commodities are adequate for modeling a WWTN. We prove that the proposed formulation is at least as strong as a classical component based formulation. We show the significant computational advantage of the proposed formulation over the component based formulation through 16 problem instances from the literature.