Cross-efficiency is a ranking technique based on the peer-evaluation that can increase the discriminating power between efficient decision-making units. This paper intends to assess the two-stage processes consisting of undesirable outputs by applying the cross-efficiency evaluation. Given undesirable outputs, the directional distance function under the weak disposability assumption is utilized. The proposed model under variable returns to scale is designed, which makes it different from the previous models. Furthermore, it can reduce the zero optimal coefficients. By measuring the inputs and outputs inefficiency, the whole system and each of its two stages rank, simultaneously. To analyze the suggested method, an application on the industrial productions of 30 regions of China is used. تفاصيل المقالة

The importance of the issue of environmental pollution is so great that the attention of many researchers has drawn attention to the recycling issue in recent decades. Since a proper evaluation can improve the performance of a system in various situations, the presentation of an appropriate method that can evaluate a production system correctly is necessary. Therefore, first, we introduce a two-stage network structure consists of undesirable intermediate measures. Then, by considering the weak disposability assumption to handle desirable and undesirable outputs, and also links between the subsections of the process, a non-radial model to evaluate the performance of the proposed structure is introduced. The proposed model is developed from the perspective of the centralized approach. Also, it is defined based on the Russell-based model. The introduced model can calculate the efficiency of the whole system without the need to evaluate the efficiency of its subsections. A real case on an industrial production system of 30 regions in China is used to illustrate the proposed model. تفاصيل المقالة

Due to the nonlinear and discrete nature of BCC (Banker, Charnes, and Cooper, [11]) models for determining the most efficient decision-making unit, it is practically impossible to evaluate the models' dual and, consequently, optimistic case. Thus, in this paper, the linear model with linear constraints proposed by Akhlaghi et al. [2] is used to investigate the dual equality of the model's robust problem and the optimistic case of the new model's dual under VRS uncertainty. The model proposed in this paper is novel in comparison to previous models because it solves the most efficient decision-making unit only once, without relying on uncertain data to determine its rank. The paper demonstrates how the proposed robust model can also ascertain the most efficient decision-making unit when uncertainty exists. Furthermore, the dual issues raised by robust counterparts in the new linear programming (LP) model are addressed to identify the most efficient decision-making unit. The robust counterpart is demonstrated to be equivalent to a linear program under interval uncertainty, and the dual of the robust counterpart is shown to be equal to the optimistic counterpart of the dual problem. Consequently, this study aims to demonstrate that the dual problem is equivalent to a decision-maker operating under optimal data, whereas the primal robust problem is equivalent to a decision-maker operating through the worst-case possible data scenario. تفاصيل المقالة

Performance measurement with undesirable outputs is an important subject in production processes. There are papers in which works can be divided into two groups. First group develops production models which undesirable outputs are considered as inputs and in second one undesirable outputs are modeled as outputs. We provide a comparison between these two groups and we axiomatically show that production technology with weak disposability assumption is complete and correct technology. تفاصيل المقالة

Conventional data envelopment analysis (DEA) models normally assume all inputs and outputs are real valued and continuous. However in problems some inputs and outputs can only take integer values, also, both desirable and undesirable outputs can be generated . In this paper the effect of undesirable outputs in integer DEA model is discussed. The proposed model distinguishes weak disposability of outputs imposing non-uniform abatement factor. تفاصيل المقالة

Regular NDEA models for calculating the efficiency of DMUs with two-stage construction requires the data set to be deterministic. In the real world, however, there are many observations that have stochastic behavior. This paper proposes a network DEA with two-stage structures models by the attention to stochastic data. The stochastic two-stage network DEA models are formulated based on the P-models of chance constrained programming and leader-follower concepts. تفاصيل المقالة

The current study investigates performance in two-stage production systems through the measurement of capacity utilization (CU). In short-run, the degree of capacity utilization depends on the ability of decision making units to utilize fixed production factors. To develop this indicator in two-stage production processes, a modified SBM network DEA model is proposed. A numerical example is also presented to point out the applicability and effectiveness of current model. تفاصيل المقالة

DEA as an effective approach to evaluate the relative efficiency of DMUs, recently applied in many production and operation systems. This paper proposed a new k-stage DEA based MOLP model for target setting in the serial network structures, considering undesirable outputs. Since the proposed model takes the size of DMUs into account, the new idea ensures the possibility of the results. The results showed the applicability of the proposed plan. تفاصيل المقالة

In many situations, the performance and the changes of outputs related to dynamic systems should be estimated while the convexity property is relaxed. Accordingly, first, a dynamic free disposal hull (FDH) model is proposed in this paper to address the efficiency of processes in multiple period of time while the convexity assumption is unsatisfied. Also, two problems, including a mixed integer linear programming and a linear programming model are provided to compute the dynamic FDH model that is a mixed integer non-linear programming problem. Then the changes of multi-period outputs are dealt with for changes of inputs related to several periods using the proposed inverse dynamic FDH model while the efficiency levels are preserved. A case study of gas industry is, moreover, presented to demonstrate the introduced models. The results show the proposed technique is useful to analyze the performance and to estimate outputs in dynamic processes without including convexity. تفاصيل المقالة

In this research, two-stage networks are considered in which there are common resources between both stages. Also, there are links between the first and second stages that are undesirable for the first stage. Two models are rendered, the first is a model for calculating the efficiency of the mentioned two-stage processes under the non-convex technology and the second model is an inverse model for calculating output values through input changes. The changes are such that efficiency values remain constant. Actually, at first, a non-radial network free disposal hull (FDH) model is planned to evaluate the entire and stage efficiencies of two-stage processes with shared resources. The introduced framework is a mixed integer nonlinear programming plan and is computed using a heuristic approach. Then, an inverse two-stage FDH approach is presented to determine outputs related to two stages for perturbing inputs of each stage while the efficiency values remain unchanged. To clarify the proposed models, an application from the literature is used. تفاصيل المقالة