An inverse data envelopment analysis model for inputs/outputs estimate

In this paper we discuss such problems: if among a group of decision making units, we increase certain inputs to a particular unit and asume that the DMU maintains its current efficiency level with respect to other units, how much more outputs could the unit produce? Or, if the outputs need to be increased to a certain level and the efficiency of the unit remains unchanged, how much more inputs should be provided to the unit? we treat them as inverse Data Envelopment Analysis (DEA) problems and propose a method to solve such problems. The problem is transformed into a multi-objective programming problem to solve, though in some special cases it can be answered by solving just one single-object LP problem. We use two examples to illustrate our computation method.