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Maintenance groups play an essential role in the successful operation of large companies and factories. Additionally, data envelopment analysis (DEA) is known as a valuable tool for monitoring the performance of maintenance groups. Especially, in contrast to the conventional DEA models that impose the convexity assumption into the technology, the free disposal hull (FDH) model provides a method for assessing the efficiency without the assumption of convexity and can be considered a valuable tool for determining one of the observed groups as the benchmark for each maintenance group. Meanwhile, because of the stochastic structure of data with lognormal distribution in the maintenance groups, this paper extends the FDH model in stochastic data with the lognormal distribution. Moreover, the method's capabilities are confirmed based on some theorems, and a simulation study that illustrated the properties of the developed procedure is also performed. The developed methodology is applied to assess the performance of 21 maintenance groups of AZCO under uncertainty conditions. [ABSTRACT FROM AUTHOR]

This paper presents some variants of minimal point theorem together with corresponding variants of Ekeland variational principle. In the second part of this article, there is a discussion on Ekeland variational principle and minimal point theorem relative to it in uniform spaces. The aim of these series of important results is to highlight relations between them, some improvements and specific applications.

This study proposes a new methodology to quantify the efficiency dynamics of a port over time. While efficiency evaluation has gained full attention in port management, researchers conducting related studies are challenged by temporal variations observed in the collected data. Existing approaches have almost exclusively relied on multivariate normal distributional assumptions of the input and output data, but empirical evidence from real data shows that the port operations data demonstrate long-tail distributions and violate the distributional assumptions. In addition, many existing models are intractable (non-convex) or lack interpretability. Motivated by these challenges, we develop an optimization-based approach for efficiency measurement under uncertainty that is compatible with the conventional non-parametric method. In particular, inspired by the coherent risk measure, we create a risk-based index to measure the efficiency of any operating unit by comparing its observations against a benchmark that is guaranteed to be production possible under a certain risk level. To facilitate the computation of the index, we develop a risk-based port efficiency evaluation (RPE) model, which can be reformulated as an exponential cone program (ECP) and solved efficiently by off-the-shelf solvers. We test our model for a multipurpose port on a real dataset of 3,394 observations showing the proposed approach's merits. We find that the port productivity peaks on Tuesday and Saturday and troughs on Friday. We also provide evidence for the Chinese New Year effect from a port management perspective and draw managerial insights from the study. • This study provides an analytical tool to quantify port efficiency dynamics over time. • A new approach for efficiency measurement under uncertainty is developed. • The model does not require parametric distributional assumptions. • The model can be formulated as an exponential cone program and solved efficiently. • We provide evidence for the Chinese New Year effect and draw managerial insights. [ABSTRACT FROM AUTHOR]

In this paper we extend the notion of stochastic efficiency and inefficiency in portfolio optimization to the case of incomplete information by means of set-valued probabilities. The notion of set-valued probability models the concept of incomplete information about the underlying probability space and the probability associated with each scenario. Unlike other approaches in literature, our notion of inefficiency is introduced by means of the Monge–Kantorovich metric. We provide some numerical examples to illustrate this approach. [ABSTRACT FROM AUTHOR]

Data envelopment analysis (DEA) is a method for evaluating the performance of a set of homogenous decision-making units (DMUs) with multiple inputs and multiple outputs. There are various models for efficiency calculation in DEA, one of which is based on determining a common set of weights (CSW), which is used extensively by DEA experts. In classical data envelopment analysis, all input and output values are clearly specified. However, this assumption might not always be true in realworld applications. One of the important methods for dealing with imprecise data is to explore the use of stochastic data in DEA. This manuscript extends the CSW model to stochastic inputs and outputs. Next, the stochastic CSW model is transformed into a nonlinear model, and then, the deterministic model is transformed into a quadratic programming model. The efficiency obtained using stochastic data is called stochastic efficiency. Finally, the concept presented in this article is demonstrated through a numerical example involving a number of Iranian banks. [ABSTRACT FROM AUTHOR]

The objective of this study is to evaluate economically the passive solar heating system. Data collected from tomato greenhouses in the Agriculture Research Center of Northern Greece was analyzed. For Comparison, two other conventional heating systems were used: the traditional anti-frost system and the diesel-fired furnace system. Models have been constructed to assess each heating method and several approaches of appraisal such as net present value, internal rate of return, benefit/cost ratio and payback period were measured in order to fulfill the assessment. The importance of the passive solar system was revealed not only as an energy-saving method but also as a significant contributor to farmer’s income and an appropriate system avoiding the risk of high initial investment, which is generally associated with unconventional systems. Meanwhile, it was indicated that the diesel-fired furnace system is ineffective compared to the passive solar system, this ineffectiveness is particularly due to its high fuel consumption and relatively high initial investment. Finally, sensitivity analysis highlighted the importance of the product price in affecting benefits and indicating that income will increase dramatically with earlier production. [ABSTRACT FROM AUTHOR]

Numerous genetically modified (GM) traits are currently under development. Those currently being developed for corn include traits for drought tolerance, cold tolerance, and nitrogen use efficiency, among others. The value of these traits is random and sporadic, creating challenges in assessing its ex ante value. This study estimates the ex ante value of a GM trait in corn with random characteristics. A real option model is developed to capture risks and returns associated with the traits, and estimates are derived for drought tolerant corn. Base case results indicate a slight chance that the option value would be out-of-the-money during the discovery phase. In all other phases, the expected value is in-the-money. The results are highly sensitive with respect to trait efficiency and regarding assumptions of randomness in some of the other important variables, particularly trait values.

Consistency of functional characteristics in wheat is a concern confronting buyers and sellers. This research analyzes the cost and risk of different procurement strategies for importers. A stochastic simulation model is used to determine the probability of functional characteristics being satisfied subject to quality targets and costs for alternative purchase strategies. Stochastic efficiency was employed to identify purchase strategies that dominate others and to determine the extent of preference. As more specific characteristics are incorporated into a contract, results indicate that the probabilities of meeting end-use requirements increase

The objective of this study was to assess how payments for ecosystem services could assist plantation forestry's integration into pastoral dairy farming in order to improve environmental outcomes and increase business resilience to both price uncertainty and production limits imposed by environmental policies. Stochastic Dominance (SD) criteria and portfolio analysis, accounting for farmers' risk aversion levels, were used to rank different land-use alternatives and landscapes with different levels of plantation forestry integration. The study was focused on a modal 200-ha dairy farm in the Lake Rotorua Catchment of the Central North Island region of New Zealand, where national environmental policies are being implemented to improve water quality and reduce greenhouse gas emissions. Nitrogen and carbon payments would help farmers improve early cash flows for forestry, provide financial leverage to undertake afforestation projects and contribute to improved environmental outcomes for the catchment. The SD criteria demonstrated that although dairy farming generates the highest returns, plantation forestry with nitrogen and carbon payments would be a preferred alternative for landowners with relatively low risk aversion levels who consider return volatility and environmental limits within their land-use change criteria. Using the confidence premium concept, environmental payments to encourage plantation forestry into the landscape were shown to be lower when the majority of landowners are risk averse. The certainty equivalence approach helped to identify the optimal dairy-forestry portfolio arrangements for landowners of different levels of risk aversion, intensities of dairy farming (status quo and intensified) and nitrogen prices. At low nitrogen prices, risk neutral farmers would choose to afforest less than half of the farm and operate at the maximum nitrogen allowance, because dairy farming at both intensities provides the highest return among the different land uses available. However, at relatively low risk aversion levels, farmers would operate at levels below the maximum nitrogen allowance by including plantation forestry to a greater extent, compared to risk neutral farmers, due to its more certain returns. At a high nitrogen price of $400/kg, plantation forestry would completely subsume dairying, across risk aversion and intensity levels. These results confirm that plantation forestry as well as being an environmentally sound land-use alternative, also reduces uncertainty for landowners that are exposed to volatile international markets for dairy commodities. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to develop an analytical model to value traits at different developmental phases and to determine the value of drought tolerance (DT) in wheat using GM technology. Design/methodology/approach – A stochastic binomial real-options model of GM traits was developed to estimate the value of a DT wheat trait. Findings – The results indicate that the value of DT wheat using GM technology is in-the-money at each development phase. The greatest value would accrue for the Prairie Gateway and Northern Great Plains regions in the USA. Research limitations/implications – The approach is useful for valuing high-cost risky investments in technology and results provide guidance for development strategies. Originality/value – The model is original and its applications to wheat are unique. [ABSTRACT FROM AUTHOR]

Stochastic efficiency is evaluated in five case studies: driven Brownian motion, effusion with a thermo-chemical and thermo-velocity gradient, a quantum dot and a model for information to work conversion. The salient features of stochastic efficiency, including the maximum of the large deviation function at the reversible efficiency, are reproduced. The approach to and extrapolation into the asymptotic time regime are documented.

Numerous genetically modified (GM) traits are currently under development. Those currently being developed for corn include traits for drought tolerance, cold tolerance, and nitrogen use efficiency, among others. The value of these traits is random and sporadic, creating challenges in assessing its ex ante value. This study estimates the ex ante value of a GM trait in corn with random characteristics. A real option model is developed to capture risks and returns associated with the traits, and estimates are derived for drought tolerant corn. Base case results indicate a slight chance that the option value would be out-of-the-money during the discovery phase. In all other phases, the expected value is in-the-money. The results are highly sensitive with respect to trait efficiency and regarding assumptions of randomness in some of the other important variables, particularly trait values. [ABSTRACT FROM AUTHOR]

A recent contribution by Meyer et al. (2009, p. 521) corrected an error of fact by Hardaker et al. (2004b, p. 253) about the comparison between stochastic dominance with respect to a function (SDRF) and stochastic efficiency with respect to a function (SERF). While both methods compare risky prospects for a bounded range of degrees of risk aversion, SERF, unlike SDRF, also demands an assumption that a chosen measure of risk aversion is constant over all levels of outcomes being evaluated. It is argued that it is generally reasonable to make such an assumption, especially when the form of the utility function and the bounds on the degree of risk aversion are carefully chosen. Then SERF has the advantage that it can lead to a smaller efficient set than that identified by SDRF. SERF also has advantages of ease and transparency in use. [ABSTRACT FROM AUTHOR]

We construct a discrete-time, multi-period replenishment plan that integrates the inventory, production and distribution functions and that satisfies the conditions of a very demanding cycle service level. The corresponding optimization problem takes the form of a very complex mixed-integer stochastic program. We develop a new enumerative algorithm that identifies the stochastically efficient demand trajectories at an authorized level of stockout, and derive three algorithmic preprocessing techniques used to discriminate the above trajectories. The application of the enumerative and preprocessing algorithmic approaches transforms the stochastic program into a disjunctive integer program solved through a column generation that reduces the risk of a bottleneck in the distribution resources of the supply chain. Computational results evaluate the efficiency of the algorithmic developments proposed in this paper, and attest the quality and robustness of the solution method. The solution methodology is validated on a real-life problem. [ABSTRACT FROM AUTHOR]

Consistency of functional characteristics in wheat is a concern confronting buyers and sellers. This research analyzes the cost and risk of different procurement strategies for importers. A stochastic simulation model is used to determine the probability of functional characteristics being satisfied subject to quality targets and costs for alternative purchase strategies. Stochastic efficiency was employed to identify purchase strategies that dominate others and to determine the extent of preference. As more specific characteristics are incorporated into a contract, results indicate that the probabilities of meeting end-use requirements increase. [ABSTRACT FROM AUTHOR]

Abstract: In economic terms, resilience in farming has to do with the capacity of a farm business to survive various risks and other shocks. Despite its importance, resilience has seldom been directly considered in evaluations of economic sustainability. A whole-farm stochastic simulation model over a 6-year planning horizon was used to analyse organic and conventional cropping systems using a model of a representative farm in Eastern Norway. The relative economic sustainability of alternative systems under changing assumptions about future technology and price regimes was examined in terms of financial survival to the end of the planning period. The same alternatives were also compared in terms of stochastic efficiency. To model the risk of business failure adequately there is a need to deal with the risk of bankruptcy, and a modification of traditional analysis was used for that purpose. The organic farming system was found to be somewhat less economically sustainable than the conventional system, especially if the organic price premiums and the organic area payments were to be phased out. The results illustrate possible conflicts between pursuit of risk efficiency and economic sustainability. The model developed could be used to support farmers’ choices between farming systems as well as to help policy makers develop more sharply targeted policies. [Copyright &y& Elsevier]

This research generated stochastically efficient farm plans in the relevant range of risk aversion and calculated the efficiency measures for the three representative farm sizes in the central Anatolian region of turkey. Utility-efficient programming was used to determine an efficient set of farm plans. Research results showed that total net farm revenue increases for all farm sizes as risk aversion decreases. An economic efficiency score of 0.54 for both small and medium size farms indicated that there is considerable scope for farmers to increase their total net farm revenue using existing technology without additional inputs. Allocative and technical inefficiencies of sampled farms were 0.22 and 0.24, respectively. Thus, supplying complete technical packages for farms may stimulate the adoption of new technologies. Focusing on production practices and marketing efficiency in farmers' training and extension programmes may also help to increase economic efficiency in the research area. [ABSTRACT FROM AUTHOR]

This paper presents stochastic models in data envelopment analysis (DEA) for the possibility of variations in inputs and outputs. Efficiency measure of a decision making unit (DMU) is defined via joint probabilistic comparisons of inputs and outputs with other DMUs and can be characterized by solving a chance constrained programming problem. By utilizing the theory of chance constrained programming, deterministic equivalents are obtained for both situations of multivariate symmetric random disturbances and a single random factor in the production relationships. The linear deterministic equivalent and its dual form are obtained via the goal programming theory under the assumption of the single random factor. An analysis of stochastic variable returns to scale is developed using the idea of stochastic supporting hyperplanes. The relationships of our stochastic DEA models with some conventional DEA models are also discussed. [ABSTRACT FROM AUTHOR]

DEA (Data Envelopment Analysis) models and concepts are formulated here in terms of the ‘P-Models’ of Chance Constrained Programming, which are then modified to contact the ‘satisficing concepts’ of H.A. Simon. Satisficing is thereby added as a third category to the efficiency/inefficiency dichotomies that have heretofore prevailed in DEA. Formulations include cases in which inputs and outputs are stochastic, as well as cases in which only the outputs are stochastic. Attention is also devoted to situations in which variations in inputs and outputs are related through a common random variable. Extensions include new developments in goal programming with deterministic equivalents for the corresponding satisficing models under chance constraints. [ABSTRACT FROM AUTHOR]

Pareto-Koopmans efficiency in Data Envelopment Analysis (DEA) is extended to stochastic inputs and outputs via probabilistic input-output vector comparisons in a given empirical production (possibility) set. In contrast to other approaches which have used Chance Constrained Programming formulations in DEA, the emphasis here is on "joint chance constraints." An assumption of arbitrary but known probability distributions leads to the P-Model of chance constrained programming. A necessary condition for a DMU to be stochastically efficient and a sufficient condition for a DMU to be non-stochastically efficient are provided. Deterministic equivalents using the zero order decision rules of chance constrained programming and multivariate normal distributions take the form of an extended version of the additive model of DEA. Contacts are also maintained with all of the other presently available deterministic DEA models in the form of easily identified extensions which can be used to formalize the treatment of efficiency when stochastic elements are present. [ABSTRACT FROM AUTHOR]

In fields on which decisions need to be taken including health, as we are seeing nowadays in the COVID-19 crisis, decision-makers face multiple criteria and results with a random component. In stochastic multicriteria decision-making models, the risk attitude of the decision maker is a relevant factor. Traditionally, the shape of a utility function is the only element that represents the decision maker's risk attitude. The eduction process of multi-attribute utility functions implies some operational drawbacks, and it is not always easy. In this paper, we propose a new element with which the decision maker's risk attitude can be implemented: the selection of the stochastic efficiency concept to be used during a decision analysis. We suggest representing the risk attitude as a conflict between two poles: risk neutral attitude, associated with best expectations, and risk aversion attitude, associated with a lower uncertainty. The Extended Goal Programming formulation has inspired the parameter that is introduced in a new risk attitude formulation. This parameter reflects the trade-off between the two classical poles with respect to risk attitude . Thus, we have produced a new stochastic efficiency concept that we call Compromise Efficiency .