Determining Optimal Weights of Intermediate Variables in Network Structures Using a Goal Programming Approach

Data Envelopment Analysis (DEA) is a widely used non-parametric approach for evaluating the relative efficiency of decision-making units (DMUs) with multiple inputs and outputs. Traditional DEA models treat DMUs as black boxes and ignore internal structures, which limits their ability to identify sources of inefficiency in multi-stage systems. Network DEA (NDEA) addresses this limitation by explicitly modeling intermediate products that link different stages of a system. However, a major challenge in NDEA is determining optimal weights for intermediate variables, as these variables act as outputs of one stage and inputs of another, leading to conflicting objectives between stages. This study proposes a goal programming (GP)–based approach to determine optimal and common weights for intermediate variables in a two-stage network DEA structure. First, the independent efficiencies of each stage are calculated separately using conventional DEA models. These efficiency scores are then treated as aspiration levels in a GP framework, which simultaneously considers the goals of both stages and resolves the conflict in weighting intermediate variables. The proposed model yields consistent weights for intermediate measures and enables the calculation of stage efficiencies and overall system efficiency. A numerical example is provided to illustrate the applicability and effectiveness of the proposed approach. The results demonstrate that the GP-based NDEA model offers more balanced and informative efficiency evaluations, making it a valuable tool for performance assessment in multi-stage and network-structured systems.

کلیدواژه ها:

NDEA ، Efficiency ، Goal Programming