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In real applications, data envelopment analysis models with Russell measures are widely used although their theoretical studies are scattered over the literature. They often have seemingly similar structures but play very different roles in performance evaluation. In this work, we systematically examine some of the models from the viewpoint of preferences used in their production possibility sets (PPS). We identify their key differences through the convexity and free-disposability of their PPS. We believe that this study will provide guidelines for the correct use of these models. Two empirical cases are used to compare their differences.

Anchor points play an important role in data envelopment analysis theory and applications; they delineate the efficient part of the production possibility set (PPS) frontier. In this paper, we propose an approach for finding the anchor points of the PPS of the Banker, Charnes and Cooper (BCC) model. This approach is based on a variant of super-efficiency models and their duals. The necessary and sufficient conditions for the characterization of the anchor points are also provided. Finally, the applicability of the proposed model is illustrated with some numerical examples.

The analysis of efficiency is conducted for two vital purposes: firstly, in order to evaluate the current level of efficiency; secondly, to provide information on how to improve the level of efficiency, which is to provide benchmarking information. The inefficient Decision Making Units (DMUs) are usually able to improve their performance, and Data Envelopment Analysis (DEA) projections provide a prescription for improvement. However, sometimes, an inefficient DMU cannot move its performance toward the best practice by either decreasing its inputs or increasing its outputs. On the other hand, it can scarcely reach its efficient benchmark. This research suggests a method to find an improved region of efficiency through DEA-efficient hyperplanes by providing an algorithm for detecting an improved efficiency path. In addition to the production of reasonable benchmarking information, the proposed algorithm provides the general requirements that satisfy the demands which every professional decision-maker should meet. Finally, we provide a more detailed description of some new issues, extending the insights from this analysis of the benchmark region from the under-evaluated inefficient DMU. Finally, numerical examples are provided to demonstrate the results of the analysis.

Performance evaluation is an importance issue in supply chain management. Yang et al. (Ann. Oper. Res. 38(6):195–211, 2011 ) defined two types of supply chain production possibility sets and proved the equivalence between them. Based on the sub-perfect CRS production possibility set, they proposed a supply chain DEA model to appraise the overall technical efficiency of supply chains. The relationship among efficiency scores of the proposed model, CCR models of system and subsystems are discussed. However, we find that the equivalence between the two types of supply chain production possibility sets is not correct. The proofs of their three theorems are all problematic. In this paper, we correct some results and give three new proofs.

Growing social concerns over the environmental externalities associated with business activities are pushing firms to identify activities that create economic value with less environmental impact and to become more eco-efficient. Over the past two decades, researchers have increasingly used frontier efficiency models to evaluate productive efficiency in the presence of undesirable outputs, such as greenhouse gas emissions or toxic emissions. In this paper, we identify critical flaws in existing frontier models and show that these models can identify eco-inefficient firms as eco-efficient. We develop a new eco-inefficiency frontier model that rectifies these problems. Our model calculates an eco-inefficiency score for each firm and improvements in outputs necessary to attain eco-efficiency. We demonstrate through a Monte Carlo experiment that our eco-inefficiency model provides a more reliable measurement of corporate eco-inefficiency than the existing frontier models. We also extend the single-output Cobb-Douglas production function to multiple desirable and undesirable outputs. This extension allows for greater flexibility in the simulation analysis of frontier models.

A basic discrete-time heterogeneous capital goods competitive environment is considered, its potential for displaying steady growth solutions analyzed and the properties of the latter characterized. A first composite good may be used for consumption or investment on a one-to-one basis, while a second good is only used for accumulation, solely capital inputs being part of the production process. This framework is first considered from the allocative standpoint through the derivation of the frontier of the production possibility set. Having defined the perfect foresight competitive equilibrium that also describes a Pareto optimum over time, attention is then given to the potential for unbounded steady growth solutions. Under interiority, summability, and expansivity restrictions, there is a unique optimal steady growth rate. For unitary depreciation rates of both capital goods, locally there exists a unique convergent sequence to this steady growth solution that exhibits a saddlepoint structure. However, as soon as one of the depreciation rates of the capital goods is non-unitary and the profit share accruing to the first capital stock is greater in the second pure accumulation industry than in the first composite good industry, the steady growth solution shows a loss of stability, and competitive equilibrium growth cycles emerge through the occurrence of a flip bifurcation in its neighborhood. This is the first optimal cycles result based upon a production set that does not explicitly incorporate any exogenously determined primary labor input in its definition.

This paper provides an outline of possible uses of complete information on the facial structure of a polyhedral empirical production possibility set obtained by DEA. It is argued that an identification of all facets can be used for a characterization of basic properties of the empirical production frontier. Focus is on the use of this type of information for (i) the specification of constraints on the virtual multipliers in a cone-ratio model, (ii) a characterization of the data generation process for the underlying observed data set, and (iii) the estimation of isoquants and relevant elasticities of substitution reflecting the curvature of the frontier. The relationship between the so-called FDEF approach and the cone-ratio model is explored in some detail. It is demonstrated that a decomposition of the facet generation process followed by the use of one of the available (exponential) convex hull algorithms allows for an explicit identification of the facial structure of the possibility set in fairly large DEA data sets. It is a main point to be made that the difficulties encountered for an identification of all facets in a DEA-possibility set can be circumvented in a number of empirical data sets and that this type of information can be used for a characterization of the structural properties of the frontier.

Context Intensified human activities have disrupted landscape patterns, causing a reduction in the supply of ecosystem services (ESs) and an increase in demand, especially in urban agglomerations. This supply-demand imbalance will eventually lead to unsustainable landscapes and needs to be optimized. Objective Based on ES supply-demand mismatch and trade-off relationships across urban–rural landscapes, this study explored which ESs need to be optimized and identified priority restoration regions of ESs that require optimization to promote landscape sustainability in Beijing-Tianjin-Hebei urban agglomeration. Methods A methodological framework for ES supply-demand optimization in urban–rural landscapes was developed. urban–rural landscapes were identified using Iso cluster classification tool. ES supply was quantified using biophysical models and empirical formulas, and demand was quantified through consumption and expectations. Restoration Opportunities Optimization Tool was then adopted to identify priority regions. Results From 2000 to 2020, most of ES supply were lowest in urban areas and highest in rural areas, while demand exhibited the opposite. Although supply was increasing, it did not match demand. ES deficits were dominant in urban areas; both deficits and trade-offs were dominant in urban–rural fringe; and trade-offs were dominant in rural areas. There were 13,175 km 2 of priority regions distributed in urban–rural landscapes, and their spatial heterogeneity was influenced by ES deficits and trade-offs. Conclusion Differences in ESs supply-demand relationships affected the necessity of optimizing ESs zoning in urban–rural landscapes. Assigning weights reasonably according to trade-off curves to determine priority regions could facilitate both efficient use of resources and sustainable ES management for urban–rural regions.

In efforts to increase human well-being while maintaining the natural systems and processes upon which we depend, navigating the trade-offs that can arise between different ecosystem services is a profound challenge. We evaluated a recently developed simple analytic framework for assessing ecosystem service trade-offs, which characterizes such trade-offs in terms of their underlying biophysical constraints as well as divergences in stakeholders’ values for the services in question. Through a workshop and subsequent discussions, we identified four different types of challenging situations under which the framework allows important insights to clarify the nature of stakeholder conflicts, obstacles to promoting more sustainable outcomes, and potential enabling factors to promote efficiency and sustainability of ecosystem service yields. We illustrated the framework’s analytical steps by applying them to case studies representing three of the challenging situations. We explored the fourth challenging situation conceptually, using published literature for examples. We examined the potential utility and feasibility of using the framework as a participatory tool in resource management and conflict resolution. We concluded that the framework can be instrumental for promoting pluralism and insightful analysis of tradeoffs. The insights offered here may be viewed as hypotheses to be tested and refined as additional unforeseen challenges and benefits are revealed as the framework is put into practice.

Effective management of ecosystem services requires understanding the biophysical relationships governing the trade-offs, as well as stakeholder preferences for the trade-offs. However, useful tools to guide the complex decision-making process are often lacking. This study demonstrates an approach that combines biophysical and economic models to identify socially preferred solutions. We demonstrate in the context of dam-removal decisions across thousands of dams in Maine, U.S. The results demonstrate the practical usability of this framework for identifying key trade-offs, areas in which people are in agreement and conflicted, along with solutions that are more preferred by society overall. The results also reveal a 30–47% welfare gain from optimizing across all ecosystem services, compared to a more common, visual approach of optimizing two services at a time. This approach may be useful to identify restoration projects that are likely to garner broad public support, particularly when there are trade-offs between ecosystem services, numerous potential solutions, and communities with diverging preferences.