A Mixed-Integer Programming Approach on Clustering Problems with Segmentation Application Customer

As a marketing strategy, segmentation involves categorizing customers into specific groups based on their loyalty to a brand. This process is crucial in shaping an effective business strategy, as identifying various customer types enables businesses to target their marketing efforts more precisely. This research focuses on solving the cluster optimization problem by applying a combinatorial optimization approach to develop a cluster optimization method. The combinatorial optimization utilized here operates on a binary system, using 0s and 1s to identify the optimal cluster for each object. Specifically, a value of 1 indicates that an object is assigned to an optimal cluster, while a value of 0 signifies that the object belongs to a non-optimal cluster. By designating clusters with a value of 1, the method ensures that the best optimization value is achieved. The 0-1 non-linear problem model ensures that objects with the shortest distances between them are grouped in the same cluster. Additionally, the model guarantees that each object belongs to only one cluster and that, across k tests, every cluster contains at least one object. This model can also be used to determine the ideal number of clusters for a given dataset, ensuring optimal segmentation results for business applications.