Study On DEA Efficiency And Frontier Of The Two-stage Dairy Supply Chain With Cross Structure

After the rapid development in the early twentieth Century,China's dairy industry appears many problems,such as slowing growth,frequent food safety incidents and so on.From the national industrial policy to the enterprise management strategy are aware that in order to fundamentally solve the problem must achieve transformation and improve efficiency,which requires us to study the efficiency firstly.The dairy supply chain presents a complex chain structure from raw milk production to dairy processing,dairy delivery,and final sale.In the case of difficulties in the overall study of its efficiency,we choice to study the efficiency of the two stage supply chain from dairy processing to the dairy delivery is meaningful to study the efficiency of dairy supply chain,because these two stages are usually expressed as the relationship of N dairy processing plants supply to the M distribution centers,such a supply chain structure is complex,and the existing research is usually viewed only as a single chain in series without analysis internal structure of the supply chain.Moreover,such a two-level supply chain is usually under the control of dairy processing enterprises,strong coordination,easy to unify the decision-making objectives,which is suitable as a research object.Based on the research,this paper analyzes the status quo and supply relationship of dairy processing and distribution stages,tries to model the two-stage dairy supply chain in the case of keeping its real structure as much as possible,and constructs open decision-making units with homogeneous and complex internal structure.Based on the idea of constructing the network DEA model by Kao et al.,under the assumption of constant returns to scale,we re-write the two-stage supply chain efficiency measure formula which applies to the specific structure described in this paper and opens the “black box”.Makes it possible to measure the efficiency of decision making units and its sub-decision-making units at the same time,and to be able to identify the reasons for the inefficiency of DMU(for example,one inefficiencies DMSU of the DMU).Then,the frontier of decision making unit(DMU)is calculated by using the dual envelope model.The frontier of the sub-decision making unit(DMSU)is deduced by frontier of the DMU.It is found that when the multistage supply chain is involved,the frontier of DMSUs is not unique.Finally,take the supply chain of L Dairy Group Liquid Milk Division as an example,select the appropriate indicators,and make an empirical study to verify the reliability of the model.The main conclusions are as follows:(1)if and only if the efficiency of all DMSUs in the DMU is 1,the efficiency of the DMU is 1.(2)The intermediate input of an open DMU can be seen as a “structured” DMSU in front of the supply chain in parallel to achieve closure of the DMU.(3)The separate series system has unique frontier and the parallel system results in a specific proportion of the modified values of homogeneous DMSUs.