A heuristic for improving clustering in biomass supply chains

Clustering is commonly used in various fields such as statistics, geospatial analysis, and machine learning. In supply chain modelling, clustering is applied when the number of potential origins and/or destinations exceeds the solvable problem size. Related methods allow the reduction of the models' dimensionality, hence facilitating their solution in acceptable timeframes for business applications. The weighted minimum sum-of-square distances clustering problem (Weighted MSSC) is a typical problem encountered in many biomass supply chain management applications, where large numbers of fields exist. This task is usually approached with the weighted K-means heuristic algorithm. This study proposes a novel, more efficient algorithm for solving the occurring weighted sum-of-squared distances minimisation problem in a 2-dimensional Euclidean surface. The problem is formulated as a set-partitioning problem, and a column-generation inspired approach is applied, finding better solutions than the ones obtained from the weighted version of the K-means heuristic. Results from both benchmark datasets and a biomass supply chain case show that even for large values of K, the proposed approach consistently finds better solutions than the best solutions found by other heuristic algorithms. Ultimately, this study can contribute to more efficient clustering, which can lead to more realistic outcomes in supply chain optimisation.