3.2. Sustainability Efficiency of Biodiesel SystemsThe concept of sustainability has been defined as the ratio of the sum of the weighted outputs to the sum of the weighted inputs, and the inputs comprise transformity, environmental load ratio, and environmental investment ratio, the outputs comprise emergy index of sustainability, emergy yield ratio and product, as shown in (16):hj=v1ESI+v2EYR+v3Pu1Tr+u2ELR+u3EIR,(16)where relatively v1, v2, and v3 represent the weights of ESI, EYR, and P, respectively; u1, u2, and u3 represent the weights of Tr, ELR and EIR respectively.The production of biodiesel can be considered as a system; similarly, the alternatives for biodiesel production can also be considered as decision-making units (DMUs).

The inputs of these DMUs comprise transformity (Tr), environmental loading ratio (ELR) and emergy investment ratio (EIR), the outputs include emergy sustainable index (ESI) emergy yield ratio (EYR) and product yield (P). The structure of DEA assessment system for biodiesel production is shown in Figure 10.Figure 10DEA assessment system for biodiesel production.In order to calculate more conveniently, all the data including inputs and output should be processed in the following ways, as r=1,2,��,m;??j=1,2,��,t,(17)where Xrj is the?shown in (17):Xrj=xrj��j=1txrj/t (j) th input or output in the (r) th DMU; t is the total number of the DMUs.Based on the data shown in Table 8 and the data processed method, the emergy indices involved in the DEA assessment model are shown in Table 9.Table 9The processed data of the inputs and outputs of DEA assessment system.

Based on the data shown in Table 9, the DEA assessment methodology can be utilized to measure the sustainability efficiency of each biodiesel production system; the calculating results including effective value, slack value and surplus value can be calculated, as shown in Table 10. According to Definitions 1 and 2, it can be summarized that the biodiesel production systems based on soybean, sunflower, and palm are DEA efficient, but the other two based on rapeseed or jatropha are non-DEA efficient.Table 10The calculating results: effective value, slack value, and surplus value.Ye et al. had introduced a projection improvement analysis methodology to improve the non-DEA-efficient DMU to DEA efficient one [38]. Assume the optimal solution of linear programming (14) and (15) is gj, srj?, sij+ for DMUjwhich is non-DEA-efficient, then the projection of the inputs and outputs on the relative efficient surface can be calculated using (18):x?rj=gjxrj?srj?y?ij=yij+sij+,(18)where x?rj and Cilengitide y?ij are the improved inputs and outputs, respectively.