Abstract
Performance management is a central point for both public and private organizations. In the data envelopment analysis (DEA) method, performance management takes the form of measuring relative efficiency. Furthermore, considering each organization and or production process as a black box,  inputs are transformed into outputs. In reality, production organizations or processes are composed of different parts that carry out different related activities. For this reason, modeling the internal structure of a production process like a system of interconnected parts makes it possible to measure its performance at the sub-process level. In this paper, we hypothesized a production process, made up of three interconnected parts. It is a new strategy to acquire relative efficiency consisting of building a block inside the system with at least two sub-processes. This step refers to a basic model of relational Network Data Envelopment Analysis (NDEA). Also, we used the additive decomposition formula to measure the efficiency of the whole process. We highlighted the differences in the measurement, between the direct application of the relational NDEA model and the measurement with the block approach model.We compared the cumulative empirical distribution functions of the efficiency scores of a sub-process with the decomposition formula multiplicative and our  approach. In conclusion, the paper proposes, a new strategy to measure the relative performances of a production process model as a network system of three subprocesses, which combines the NDEA and the DEA. This allows us to reevaluate, the indications of policy at the individual sub-process level (block). Moreover, it is a versatile approach which allows aggregation of the sub-processes in blocks, according to the particular policy requirements, legislative technological constraints, etc.
Highlights
The measurement as the response at real problems solution is the core of the Operation Research (OR) among others (Hiller, et al, 2001)
Once obtained the relational Network Data Envelopment Analysis (NDEA) model we propose a novel strategy consisting in building a block of two subprocess to estimate the efficiency of the its parties, The paper is structured as follow: in the section 2 we modeling graphically the internal structure of a production process with three stages, and describe its functioning
The economic modeling of a production process is very often conducted, using the production function approach to represent the maximum level of output attainable for each level of resources
Summary
The measurement as the response at real problems solution is the core of the Operation Research (OR) among others (Hiller, et al, 2001). The objective of this paper is to modeling the internal structure of a production process with three interdependent subprocesses At this end, we take as a cue the relational Network Data Envelopment Analysis (NDEA) model proposed in (Pinto, 2016) where the author modeling and measure the relative efficiency of the hospital acute care production process. The consideration of a third activity (rehabilitative) relatively at the two (medical and assistance) considered in (Pinto, 2016) need to reconsider the relationship among these three activities, as well as will produce a different functioning of the process of the hospital care of the acute This allow us to build a more general NDEA model to apply in others sectors/activities.
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