Model and measure the relative efficiency of a four-stage production process. An NDEA multiplier relational model under different systems of resource distribution preferences between sub-processes

Measuring the relative efficiency of a production process with the DEA considers the production process as a “black box” that uses inputs to transform them into outputs. In reality, many production processes are carried out by carrying out several interconnected activities that are usually grouped into phases that are in turn interconnected. For this reason, measuring the relative efficiency of a production process within the DEA technique requires shaping it as a network system (in others words to consider the production process as interconnected sub-process). In the case of network systems, the NDEA approach has developed many models to measure their relative efficiency: independent models, connected models and relational models. In particular, the relational model allows to measure at the same time both the efficiency of the system and the efficiency of the sub-process once the operations between the latter have been considered. In our opinion, many real production processes can be modelled as a network of four sub-processes that are differently interconnected with each other. In this paper we will model a production process as a network of four sub-processes with shared variables and fixed preferences about the allocation of system resources between them. To measure the relative efficiency of the process and its parts we will develop an input-oriented NDEA model in the multiplier version. To solve the model we will use virtual data under several resources allocation preference’s structure. Then we will conclude that 1) a production process with four interconnected sub-processes can represent a large number of real production processes, so the NDEA model developed here can potentially be used for many applications, 2) the resource allocation preference system inter-sub-process influences the measurement of relative efficiency.