Victor V. Podinovski’s research while affiliated with Loughborough University and other places

This paper provides a comprehensive analysis of Professor Rajiv Banker’s significant impact on the field of Data Envelopment Analysis (DEA). Through an extensive review of his scholarly contributions, we explore three major clusters within DEA research: (1) Returns-to-Scale (RTS) and Most Productive Scale Size (MPSS), (2) Statistical Inference in DEA, and (3) Contextual Analysis. Banker’s pioneering research has significantly advanced DEA methodologies, addressing fundamental challenges related to scale efficiency, statistical robustness, and the influence of contextual variables on performance. His work has bridged theoretical developments and practical applications, influencing diverse fields such as economics, finance, and management science. By examining citation trends and bibliometric data, we trace the evolution and enduring relevance of his contributions, highlighting key papers that have shaped the trajectory of DEA research. This paper also discusses the evolution of DEA models and approaches, including the integration of stochastic elements and second-stage analyses. In recognising Banker’s lifetime dedication to DEA, we celebrate his lasting legacy and his transformative influence on both the academic community and practical implementations of DEA worldwide.

In practical applications of data envelopment analysis, inputs and outputs are often stated as ratio measures, including various percentages and proportions characterizing the production process. Such ratio measures are inconsistent with the basic assumptions of convexity and scalability required by the conventional variable and constant returns-to-scale (VRS and CRS) models. This issue has been addressed by the development of the Ratio-VRS (R-VRS) and Ratio-CRS (R-CRS) models of technology, both of which can incorporate volume and ratio inputs and outputs. In this paper, we provide a detailed standalone development of the special case of the R-CRS technology, referred to as the F-CRS technology, in which all ratio inputs and outputs are of the fixed type. Such ratio measures can be used to represent environmental and quality characteristics of the production process that stay constant while simultaneously allowing the scaling of the volume of production. We illustrate the use of the F-CRS technology by an application in the context of school education.

Conventional models of data envelopment analysis (DEA) typically assume that the underlying production technology is a convex set. It is known that such assumption may be clearly unsubstantiated in certain cases. Examples include studies in which some inputs or outputs are stated as proportions or percentages, or are represented by categorical measures. Excluding such “problematic” inputs and outputs from the assumption of convexity while assuming the latter for the remaining measures leads to the notion of selective convexity. Further examples of selectively convex technologies include technologies parameterized by an environmental factor and technologies in which only the input or output sets are convex. In this paper, we consider the identification of efficient targets and reference sets of decision making units in a selectively convex technology, which has not yet been explored in the literature. We show that, for such technologies, the conventional method based on the solution of the additive DEA model may not correctly identify the reference sets and needs an adjustment.

Free disposal hull (FDH) is a nonparametric model of production technology based on the single assumption of free disposability of all inputs and outputs. In this paper, we consider multicomponent production technologies in which every decision making unit (DMU) consists of several parallel component processes that can in principle operate independently of each other, provided they have sufficient resources. An example is universities viewed as DMUs, with their departments or groups of departments viewed as component processes. Each component process uses its own set of inputs and an unknown part of the shared inputs in order to produce its own set of outputs and an unknown part of the shared outputs. We allow combinations of component processes taken from different DMUs in order to construct new hypothetical DMUs, and refer to the resulting model of technology as the multicomponent FDH (MFDH) model. We further develop a larger, and mathematically nontrivial, variant of MFDH for the case in which we can specify certain bounds on the proportions in which shared inputs and outputs are allocated to component processes. We use an illustrative example in the context of universities to demonstrate the increasing discriminatory power of the new MFDH models over the standard FDH models in the multicomponent setting.

Applications of data envelopment analysis (DEA) often include inputs and outputs that are embedded in some other inputs or outputs. For example, in a school assessment, the sets of students achieving good academic results or students with special needs are subsets of the set of all students. In a hospital application, the set of specific or successful treatments is a subset of all treatments. Similarly, in many applications, labour costs are a part of overall costs. Conventional variable and constant returns-to-scale DEA models cannot incorporate such information. Using such standard DEA models may potentially lead to a situation in which, in the resulting projection of an inefficient decision making unit, the value of an input or output representing the whole set is less than the value of an input or output representing its subset, which is physically impossible. In this paper, we demonstrate how the information about embedded inputs and outputs can be incorporated in the DEA models. We further identify common scenarios in which such information is redundant and makes no difference to the efficiency assessment and scenarios in which such information needs to be incorporated in order to keep the efficient projections consistent with the identified embeddings.

We consider production technologies in which several parallel component processes are characterized by both component-specific and shared inputs and outputs. The recently developed multicomponent variable and constant returns-to-scale (MVRS and MCRS) models of such technologies are based on the assumption that we have no information about the actual allocation of the shared inputs and outputs to the component processes, which is a common scenario in many applications. The MVRS model treats each component process as a separate convex technology. The MCRS model additionally assumes that each process is a scalable technology. Both models account for the most conservative, or worst-case, allocation of the shared inputs and outputs to the individual processes, which does not require any knowledge of the actual allocation of such measures. In the current paper, we develop a new class of MVRS and MCRS models, by integrating a mechanism for the specification of lower and upper bounds on the proportions in which the shared inputs and outputs can be allocated to different component processes. We show that such bounds may be supported by data and generally lead to a larger model of technology and improved differentiation on efficiency. As an illustration, we discuss the application of the developed approach in the context of higher education.

Applications of data envelopment analysis (DEA) often include inputs and outputs represented as percentages, ratios and averages, collectively referred to as ratio measures. It is known that conventional DEA models cannot correctly incorporate such measures. To address this gap, the authors have previously developed new variable and constant returns-to-scale models and computational procedures suitable for the treatment of ratio measures. The focus of this new paper is on the scale characteristics of the variable returns-to-scale production frontiers with ratio inputs and outputs. This includes the notions of the most productive scale size (MPSS), scale and overall efficiency as measures of divergence from MPSS. Additional development concerns alternative notions of returns to scale arising in models with ratio measures. To keep the exposition as general as possible and suitable in different contexts, we allow all scale characteristics to be evaluated with respect to any selected subsets of volume and ratio inputs and outputs, while keeping the remaining measures constant. Overall, this new paper aims at expanding the range of techniques available in applications with ratio measures.