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In many real applications of data envelopment analysis(DEA), the decision making units(DMUs) may be separated into different components, in which each component consumes inputs to produce outputs. The idea of measuring efficiency relative to certain components of a DMU is not new. Fare and Grosskopf(1996) proposed the multi-stage production process. Cook et al.(2000) extended the usual DEA structure to one that determines the aggregate efficiency of DMUs accompanying with component measures. In our study, each component produces two types of outputs. The first one go onto the outside of the DMU and the second one can be used as inputs to the later component. The second output is a k-tuple vector and we would like to select an r-tuple sub-vector from this k-tuple vector to use as inputs to the later component to optimize the aggregate efficiency score. It is shown that the aggregate efficiency measure is a convex combination of the component measures.