Optimal layout of multi-floor process plants using MILP

In this work, a new mixed integer linear programming (MILP) model is proposed for the multi-floor process plant layout problem with additional considerations. Multi-floor process plant layout determines the spatial arrangement of process plant units considering their connectivity amongst other factors and affects the cost of constructing the plant, the ease of plant operation and expansion, general safety levels within the plant and its neighbouring environment, as well as operational costs. Over the past years, mathematical programming models have been developed to describe the layout problem considering connectivity costs, pumping costs, installation of safety devices, and piping, in single and multiple floors. Features such the representation of irregularly shaped items, tall equipment spanning multiple floors and others have been successfully modelled. This work builds on such past considerations with additional features that allow multi-floor equipment items extend above the maximum potential number of floors, and the selection of an available number of floors less than the maximum number required by any equipment item. Integer cuts are also developed for the proposed model to enhance its efficiency. The performance and limitations of the proposed model are demonstrated with industry-relevant case studies of up to 25 units, and results show a potential cost savings when compared to existing models with additional computational benefits of the integer cuts in all of the cases explored.