Combination of Top-down and Bottom-up DEA models using PCA: A Two-Stage Network DEA with Shared Input and Undesirable Output for Evaluation of the Road Transport Sector
This paper presents a network data envelopment analysis (NDEA) model to assess road transport sector by considering energy and non-energy inputs, shared input, and desirable and undesirable outputs. The sector is considered as a two-stage framework where in stage 1, energy-environmental efficiency is calculated and in stage 2, technical efficiency is estimated. There are two general approaches for evaluation of the network structures using NDEA models: bottom-up and top-down. In the bottom-up approach of this study, a goal programming NDEA (GP-NDEA) model is proposed to calculate the efficiency of the two stages at the same time and then overall efficiency is obtained using the results of the two stages. In the top-down approach, both non-radial SBM-NDEA and RAM-NDEA models are applied to calculate the overall efficiency and then the efficiencies of stage 1 and stage 2 are estimated using the results of the overall efficiency. Three different models GP-NDEA, SBM-NDEA, and RAM-NDEA lead to different results and to obtain the final efficiencies and ranks, principal component analysis (PCA) method is applied. The efficiency generated by different bottom-up and top-down approaches are considered as indicators in PCA, and the final scores for both stages are calculated using PCA. To illustrate the capability of the proposed approach, an actual dataset of road transport sector in provinces of Iran is gathered and the results of the different models are analyzed.