Nonparametric Production Technologies with Multiple Component Processes

Abstract

We develop a nonparametric methodology for assessing the efficiency of decision making units operating in a production technology with several component processes. The latter is modeled by the new multiple hybrid returns-to-scale (MHRS) technology, formally derived from an explicitly stated set of production axioms.In contrast with the existing models of data envelopment analysis (DEA), the MHRS technology allows the incorporation of component-specific and shared inputs and outputs that represent several proportional (scalable) component production processes, as well as nonproportional inputs and outputs. Our approach does not require information about the allocation of shared inputs and outputs to component processes or any assumptions about this allocation. We demonstrate the usefulness of the suggested approach in an application in the context of secondary education, and also in a Monte Carlo study based on a simulated data generating process.

Optimal solutions of multiplier DEA models

“…1 In this paper we give a further example based on the nonincreasing returns-to-scale technology in which the traditional interpretation of optimal solutions of the multiplier model is clearly incorrect. These examples show that we do not have a general meaningful explanation of the multiplier models for arbitrary polyhedral technologies, except for the CRS and VRS models and a few other models for which alternative bespoke interpretations, that apply only to a particular model, have been developed in the literature (see, e.g., Cherchye et al 2013, Podinovski et al 2018. 2 A new way to interpret optimal solutions of the multiplier model was recently suggested in a special case of polyhedral technology, namely, for the VRS and CRS technologies expanded by production trade-offs.…”

“…The class of polyhedral technologies including the standard CRS and VRS technologies of Charnes et al (1978) and Banker et al (1984), the non-increasing and non-decreasing returns-to-scale technologies (Färe et al 1983, Seiford andThrall 1990), and their extensions by production trade-offs which are dual terms to weight restrictions (Podinovski 2004b). Further examples include the hybrid returns-to-scale technology based on the idea of selective proportionality between certain subsets of inputs and outputs (Podinovski 2004a), technologies with multiple component processes, including those with joint or shared inputs and outputs (Cherchye et al 2013, Podinovski et al 2018, and models based on (selective) weak disposability of inputs and outputs (Mehdiloo and Podinovski 2019). Finally, the underlying technologies of various network DEA models (Färe and Grosskopf 2000) are also polyhedral.…”

“…It is specific to models with weight restrictions and is not considered in this paper. 2 For example, Podinovski et al (2018) consider a technology with multiple component processes characterized by shared inputs and outputs. They show that an optimal solution of the corresponding multiplier model can be seen as the most favorable for DMU o in the sense that it identifies the most favorable input and output weights and also the proportions in which the shared inputs and outputs are allocated to the component processes.…”

“…The alternative approaches ofPodinovski (2004b) andPodinovski et al (2018) allow the specification and interpretation of weight restrictions and multi-component processes in terms of the underlying production technology T and both envelopment and multiplier models based on it.…”

Direct estimation of marginal characteristics of nonparametric production frontiers in the presence of undesirable outputs

“…Zhou, Zhou and Fan (2014) survey the evaluation of marginal rates in models with undesirable outputs using both the parametric and nonparametric methodologies. production trade-offs and weight restrictions (Podinovski, 2004b;Podinovski & Bouzdine-Chameeva, 2013), technologies with weakly disposable inputs and outputs (Mehdiloo & Podinovski, 2019;Mehdiloozad & Podinovski, 2018), technologies with multiple component processes (Cherchye, De Rock, Dierynck, Roodhooft, & Sabbe, 2013;Podinovski, Olesen, & Sarrico, 2018), and various network technologies (Kao, 2014). Podinovski et al (2016) prove that the evaluation of different marginal characteristics in any polyhedral technology can be performed by solving essentially the same linear programs.…”