A mixed-integer programming approach for clustering demand data for multiscale mathematical programming applications

Across all sectors within the energy and process industry, tremendous efforts have been devoted toward the development and operation of agile manufacturing techniques to respond to customer needs and volatile markets while at the same time control costs, improve efficiency, and reduce pollution. This has created a demand for systems to solve complex integrated planning and scheduling problems that bridge the gap between the different functional and strategic decision-making levels. Integration across supply chain decision levels is key to improving investment returns. Different approaches have been proposed to tackle this problem. However, most of them are problem-specific or applicable only to short time horizons. Clustering has the potential to handle such problems by grouping similar input parameters together and considerably reduce the model size while not compromising solution accuracy. This work presents a new class of clustering algorithms to support the integration of planning applications of different time scales. The clustering algorithms were formulated using integer programming with integral absolute error as similarity measure. The algorithms were successfully applied to clustering electricity demand data and applied to the unit commitment problem. The computational performances of the proposed normal and sequence clustering algorithms were compared against a full planning model that does not employ clustering. The results show a clear advantage in terms of solution time compared to the full-scale case while maintaining solution accuracy.