M. Mardani Najafabadi; S. Ziaee
Abstract
Introduction: Several techniques are used to evaluate decision making units in DMUs with a restricted multiplier. DEA is recognized as a methodology widely used to evaluate the relative efficiency of a set of decision-making units (DMUs) involved in a production process. This approach assumes that the ...
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Introduction: Several techniques are used to evaluate decision making units in DMUs with a restricted multiplier. DEA is recognized as a methodology widely used to evaluate the relative efficiency of a set of decision-making units (DMUs) involved in a production process. This approach assumes that the input and output data of the different decision making units (DMUs) are measured with precision. Although DEA is a powerful tool to use measure efficiency, there are some restrictions that need to be considered. One important restriction involves the sensitivity of DEA to the specific data under analysis. In this paper, the linear robust optimization framework of Bertsimas and Sim is used to concentrate on the DEA with uncertain data to determine the efficiency of irrigated wheat farms in Neyshabur County.
Materials and Methods: This paper proposes a linear robust data envelopment analysis (LRDEA) model using imprecise data represented by an uncertainty set. The method is based on the robust optimization approach of Bertsimas and Sim to seek maximization of efficiency under uncertainty (as does the original DEA model). In this approach, it is possible to vary the degree of conservatism to allow for a decision maker to understand the tradeoff between a constraint’s protection and its efficiency. The method incorporates the degree of conservatism in the maximum probability bound for constraint violation. The most significant uncertainties for a DEA model are input and output data that arise from errors. Application of the proposed model (LRDEA) to the case study (Neishabour district irrigated wheat farms) demonstrates the reliability and flexibility of the model. Monte Carlo simulation was implemented to examine the quality of the LRDEA model 100 random numbers were generated for each input and output of DMUs.
Results and Discussion: In this section, a case study of Neishabour county irrigated wheat farms is presented to illustrate the use of the methodology in this proposal, which consists of 95 DMUs, one input and five outputs. For the input and output data uncertainty, ten given maximums of a constraint’s violation probability were considered with respect to nominal values: 10%, 20%, up to 100% (i.e. we used Γ = 0.10, 0.20, up to1.00). The results show that the Gamma value decreases as the probability of constraint violation increases. The LRDEA model result shows how efficiency declines as the level of conservatism of the solution increases, that is, as the constraint violation probability decreases. According to the method, if all Gammas equal 0, then robust and original DEA models are the same. The most of the difference between the mean of optimal and actual amount of inputs is related to the two inputs of pesticide and cultivation land in both of the DEA and RDEA models. Accordingly, holding participatory extension classes to train farmers to increase yield and optimal use of existing agricultural land with a cooperative of efficient farmers is recommended. Also, the extinction of integrated pest management (IPM) to increasing non-optimal use of pesticide in the study area is proposed. Monte Carlo simulation was implemented to examine the quality of the LRDEA model 100 random numbers were generated for each input and output of DMUs. In the simulation violation probabilities ranging from 0.1 to 1.0 (at a constant the level of ε), percentages of average conformity are quite high. . However, it declines very rapidly as P approaches 0.7.
Conclusions: Evaluating the performance of many activities by a traditional DEA approach requires a precise input and output data. However, input and output data in real-world problems are often imprecise or vague. To deal with imprecise data, this study uses a robust optimization approach as a way to quantify vague data in DEA models. It is shown that the Bertsimas and Sim approach can be a useful tool in DEA models without introducing additional complexity into the problem (we called linear robust data envelopment analysis (LRDEA)). A case study of Neishabour county irrigated wheat farms is presented to illustrate the reliability and flexibility of the proposed model. The problem was solved for a range of given uncertainty and constraint violation probability levels using the GAMS software. This example suggests that our approach identifies the tradeoff between levels of conservatism and efficiency. As a result, efficiency decreases as the constraint violation probability increased. Additionally the LRDEA approach provides both a deterministic guarantee about the efficiency level of the model, as well as a probabilistic guarantee that is valid for all symmetric distributions.
H. Sakhdari; M. Sabouhi
Abstract
In a region, optimal allocation of lands to various agricultural products is one of the most important issue associated with optimal use of agricultural resources. Meta-Goal Programming is one of the multiple criteria decision models. This Programming provides more flexible decisions for decision makers ...
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In a region, optimal allocation of lands to various agricultural products is one of the most important issue associated with optimal use of agricultural resources. Meta-Goal Programming is one of the multiple criteria decision models. This Programming provides more flexible decisions for decision makers than other goal Programming. In the current study, optimal cropping pattern was determined using Goal and Meta-Goal Programming for agriculture in Neyshabour district. Results showed that, the total cultivated area is estimated less in the Goal Programming than Meta-Goal Programming. Furthermore, the cultivated area of wheat was estimated as the largest area in the all optimal cropping pattern. Considering the huge changes in the policies associated with allocation of resource subsidies and a sharp reduction in the water resources during the recent years, the study recommends using the optimal cropping pattern by which goal deviation is assumed low.
M. Shahvali; L. Shahmorad
Abstract
In the recent years, increasing demand for products such as protein-rich meals and oilseeds has caused the food basket to shift towards the proteins and fats consumption. This change has been happening in Iran too. Shortage in oilseed productions has been a serious problem in Iran. To overcome the problem, ...
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In the recent years, increasing demand for products such as protein-rich meals and oilseeds has caused the food basket to shift towards the proteins and fats consumption. This change has been happening in Iran too. Shortage in oilseed productions has been a serious problem in Iran. To overcome the problem, the government planed some programs to encourage oilseed productions. Beside government’s programs to encourage oilseed productions, educational programs are required. The educational programs should be organized based on the farmers’ educational needs. To achieve the goal, an accurate educational model is required. This study attempted at assessing Canola growers’ educational needs in Zebarkhan county of Neyshabour, using Ortiz's model. The survey was based on a structured questionnaire. To select the study interviewees, simple classified random sampling was used and eventually 60 farmers completed the study questionnaires. The results showed that canola grower's education needs differ between two canola growers groups. Those farmers who ceased canola cultivation needed 50% more training than those who continued canola production in the study year.. The practical programs were not effective and appropriate for farmers. As a result of that, farmers who ceased canola cultivation were not interested in re-cultivating the plant. Due that the canola cultivation is manageable, continuous studies on scientific and indigenous knowledge integration is suggested.