An axiomatic production model for circular directional indirect network technologies with undesirable output production and relational NDEA models

Abstract In the production economics, the behavior’s assumptions on the production’s unit with production of final undesirable output can be very numerous. For example, it is possible to assume the simple maximization of revenues as well as assuming maximization of revenues net of costs generated by undesirable outputs. Alternatively, it is possible to assume simple minimizing costs or assuming minimizing costs added by those generated by undesirable outputs. Yet, it is possible to assume simple maximizing profits or assuming maximizing profits net of costs generated by undesirable outputs. As well as it is possible to assume the simple minimization of inputs, or minimization of undesirable outputs or the maximization of desirable final outputs as well as their combinations. Therefore, we will have many ways to build an optimization models. The behavior’s assumptions can be technologically and economically constrained. Among these latter, budgetary constraints and revenue targets are the more common. However, models may also take into account other types of constraints, such as those that model the laws of governing the production of undesirable outputs and/or those that model their relationships with other outputs and inputs (as is the case with the constraint of material balance). In addition models can have constraints on the circularity of a subset of outputs (intermediate or final), or constraints on free availability or not of a subset of intermediate outputs and inputs and so on. In this paper, we will present an axiomatic production model for an interconnected linear DEA technology with final reversed outputs (mainly undesirable) subject to three different types of economic constraints. Then we will build optimization models exploiting the network data envelopment analysis approach. One solved the NDEA models we will use the optimal solutions for the calculation of economic quantities such as shadow price of undesirable output. To build our NDEA models we will exploit the duality relationship between indirect technological set, indirect directional distance functions and indirect profit functions.