Optimising Ventilation System Preplanning: Duct Sizing and Fan Layout Using Mixed-Integer Programming

Traditionally, duct sizing in ventilation systems is based on balancing pressure losses across all branches, with fan selection performed subsequently. However, this sequential approach is inadequate for systems with distributed fans in the central duct network, where pressure losses can vary significantly. Consequently, when designing the system topology, fan placement and duct sizing must be considered together. Recent research has demonstrated that discrete optimisation methods can account for multiple load cases and produce ventilation layouts that are both cost- and energy-efficient. However, existing approaches usually concentrate on component placement and assume that duct sizing has already been finalised. While this is sufficient for later design stages, it is unsuitable for the early stages of planning, when numerous system configurations must be evaluated quickly. In this work, we present a novel methodology that simultaneously optimises duct sizing, fan placement, and volume flow controller configuration to minimise life-cycle costs. To achieve this, we exploit the structure of the problem and formulate a mixed-integer linear program (MILP), which, unlike existing non-linear models, significantly reduces computation time while introducing only minor approximation errors. The resulting model enables fast and robust early-stage planning, providing optimal solutions in a matter of seconds to minutes, as demonstrated by a case study. The methodology is demonstrated on a case study, yielding an optimal configuration with distributed fans in the central fan station and achieving a 5 reduction in life-cycle costs compared to conventional central designs. The MILP formulation achieves these results within seconds, with linearisation errors in electrical power consumption below 1.4%, confirming the approach’s accuracy and suitability for early-stage planning.