Integrating internal and external attributes in clustering: a goal programming-data envelopment analysis model
摘要
Conventional clustering methods group objects based on similarities in external data, often overlooking internal characteristics of decision-making units (DMUs), such as their production functions. In contrast, data envelopment analysis (DEA), a data-oriented nonparametric methodology, enables clustering based on the production frontier. However, traditional DEA models do not account for the distance between DMUs, and the resulting clusters are often non-unique, allowing a DMU to be assigned to multiple clusters. To address both internal and external characteristics, this paper proposes a goal programming–DEA (GP-DEA) model that clusters DMUs using both the production function and the distances between them. First, an envelopment form of the DEA model is applied to identify the initial clusters. Then, a GP-DEA model is used to determine a set of common weights for the input and output variables of the DMUs within each cluster. In each cluster, the efficiency scores of DMUs are recalculated using the new common weights. If the new efficiency of a DMU does not match the efficiency generated by the traditional DEA model, the DMU is removed from the cluster. In addition, a DMU initially assigned to multiple clusters is ultimately allocated to the cluster where its efficiency score remains unchanged. To illustrate the effectiveness of our approach, we present numerical examples and analyze a case study of 288 hospitals using the proposed GP-DEA model.