Unoriented two-stage DEA: The case of the oscillating intermediate products

• We introduce an iterative approach to solve the unoriented two-stage DEA model using the classical radial objective.
• Our approach determines optimal levels for each input and output by simultaneously reducing inputs and increasing outputs while the intermediate products oscillate and converge.
• Unlike the slacks-based approach, our model does not require arbitrary weights on inputs and outputs.
• We demonstrate our model by applying it to Major League Baseball teams during the 2009 season. The model has one input, two intermediate products, and one output.

Data envelopment analysis (DEA) allows us to evaluate the relative efficiency of each of a set of decision-making units (DMUs). However, the methodology does not permit us to identify specific sources of inefficiency because DEA views the DMU as a “black box” that consumes a mix of inputs and produces a mix of outputs. Thus, DEA does not provide a DMU manager with insight regarding the internal source of the organization’s inefficiency.Recent methodological developments have extended the basic DEA methodology to allow the analyst to “look inside” the DMU and model the network of production processes that comprise the organization. In such models, sub-DMUs consume inputs from outside the DMU and intermediate products from other sub-DMUs to produce outputs that flow out of the DMU and intermediate products that flow into other sub-DMUs. In this paper, we present an unoriented two-stage DEA model to measure efficiency in situations in which analysts seek to simultaneously reduce input quantities and increase output quantities. The methodology extends previous work in which the model must be either input-oriented or output-oriented. The key to the methodology is an iterative algorithm that alternates between an input-oriented “push backward” step and an output-oriented “push forward” step that is characterized by damped oscillations in the intermediate products. We apply the methodology to Major League Baseball teams during the 2009 season to demonstrate how this approach provides a deeper understanding of each team’s operations.