Using slacks-based model to solve inverse DEA with integer intervals for input estimation
提出一种基于非径向松弛变量模型的逆数据包络分析方法，处理同时包含整数和连续区间的不确定数据，用于在产出增加时估计投入的变化量。
Abstract This paper deals with an inverse data envelopment analysis (DEA) based on the non-radial slacks-based model in the presence of uncertainty employing both integer and continuous interval data. To this matter, suitable technology and formulation for the DEA are proposed using arithmetic and partial orders for interval numbers. The inverse DEA is discussed from the following question: if the output of $$DMU_o$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mi>M</mml:mi> <mml:msub> <mml:mi>U</mml:mi> <mml:mi>o</mml:mi> </mml:msub> </mml:mrow> </mml:math> increases from $$Y_o$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Y</mml:mi> <mml:mi>o</mml:mi> </mml:msub> </mml:math> to $$\beta _o$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>o</mml:mi> </mml:msub> </mml:math> , such the new DMU is given by $$(\alpha _o^*,\beta )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>o</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mo>,</mml:mo> <mml:mi>β</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> belongs to the technology, and its inefficiency score is not less than t-percent, how much should the inputs of the DMU increase? A new model of inverse DEA is offered to respond to the previous question, whose interval Pareto solutions are characterized using the Pareto solution of a related multiple-objective nonlinear programming (MONLP). Necessary and sufficient conditions for input estimation are proposed when output is increased. A functional example is presented on data to illustrate the new model and methodology, with continuous and integer interval variables.