Measure the Relative Efficiency of a Four-Stage Production Process with NDEA

The measurement of the relative efficiency of a production process with the DEA approach considers the process itself as a "black box" that uses inputs to produce outputs. In reality, many production processes require the carrying out of many activities grouped into phases and interconnected with each other. For this reason, modeling a production process as a network system in which its sub-parts are differently interconnected certainly represents a modeling closer to reality. The NDEA approach born within the DEA methodology has developed several models to measure the relative efficiency of network systems such as independent models, or connected models or relational models. The latter differs from the other two in that it allows you to measure the relative efficiency of the entire process and its parts once the operations between the parts of the system have been considered. In this paper, as well as modeling a production process with four stages with shared variables, we propose a relational NDEA model under different preference systems in the distribution of resources between sub-processes to measure their relative efficiency. The proposed NDEA model is in the multiplicative version. We will use non-real data to solve the model. Our conclusions are that 1) a four-stage production process can represent numerous real processes, 2) the proposed NDEA model can therefore be used for multiple different applications and 3) the system of preferences on the distribution of resources among subs processes influences the measurement of relative efficiency both for the whole process and for its sub-processes.