Efficiency measurement in multi-period production systems

The paper aims at efficiency measurement in multi-period production systems. A common approach how to analyze efficiency in multi-period systems in Malmquist index, window analysis, and the Park and Park model (PP model) formulated in [6] that attempts to measure the aggregative efficiency within multiple periods. The disadvantage of this model consists in its orientation to the "best" period of the decision making unit (DMU) under evaluation, i.e. the aggregative efficiency is given as the "best" efficiency score across all periods. The paper formulates original modifications of the PP model - the model that is oriented on the "worse" period of the DMU under evaluation, and the model that computes average efficiency across all periods. In addition, we propose a multi-period SBM and super-efficiency SBM models that measure inefficiencies using relative slacks, i.e. negative relative deviations in the input space and positive ones in the output space. The results of all models are illustrated and compared on the three-period example taken from [6]. The differences among the results of presented models are discussed.