با همکاری انجمن اقتصاد کشاورزی ایران

نوع مقاله : مقالات پژوهشی

نویسندگان

1 دانشگاه کشاورزی و منابع طبیعی رامین خوزستان

2 دانشگاه زابل

چکیده

یکی از فروض در الگو‌های تحلیل پوششی داده‌ها (DEA) برای برآورد کارایی واحدهای تصمیم‌گیرنده این است که داده‌های ورودی و خروجی الگو بطور کامل شناخته شده و معین بوده که در عمل این فرضی دور از ذهن است. در بسیاری از کاربردهای واقعی، نهاده‏ها و ستاده‏ها اغلب غیردقیق هستند. در مطالعه حاضر به تعیین کارایی مزارع نمونه گندم آبی در شهرستان نیشابور با استفاده از تکنیک تحلیل پوششی داده‌ها با پارامترهای کنترل کننده میزان محافظه‌کاری (RDEA) پرداخته شد. این روش بر پایه رویکرد بهینه‏سازی قوی Bertsimas و Sim است و به‏دنبال بهینه‌سازی یک الگوی DEA تحت شرایط عدم قطعیت است. نتایج نشان داد که میانگین کارآیی فنی خالص در تمام سطوح احتمال انحراف هر محدودیت از کران خود بالاتر از میانگین کارآیی فنی بوده که نشان دهنده قابلیت و مهارت زیاد کشاورزان مزارع نمونه در شهرستان نیشابور در تولید گندم است. در هر دو الگوی DEA و RDEA بیشترین میزان اختلاف بین میانگین مقدار مصرف مطلوب و مقدار مصرف واقعی نهاده‌ها مربوط به دو نهاده آفت‌کش و سطح ‌زیرکشت است. بر این اساس، برگزاری کلاس‌های ترویجی آموزش کشاورزان با هدف استفاده بهینه از زمین‌های کشاورزی موجود با همکاری کشاورزان کاملاً کارا توصیه می‌گردد. استفاده از نتایج الگوی RDEA برای انجام مراحل اصلاح‌سازی رفتار غیربهینه کشاورزان ناکارا در منطقه مورد مطالعه بعلت انعطاف‌پذیری بسیار زیاد آن در مقابل داده‌های غیردقیق (بر اساس نتایج شبیه‌سازی مونت کارلو) توصیه می‌شود.

کلیدواژه‌ها

عنوان مقاله [English]

Determining the Efficiency of Irrigated Wheat Farmsin Neyshabur County under Uncertainty

نویسندگان [English]

  • M. Mardani 1
  • S. Ziaee 2

1 Khozestan

2 University of Zabol

چکیده [English]

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.

کلیدواژه‌ها [English]

  • Data Envelopment Analysis
  • Mont Carlo simulation
  • Neishabour
  • Uncertainty
1- Ahmad Z., and Jun M. 2015. Agricultural Production Structure Adjustment Scheme Evaluation and Selection Based on DEA Model for Punjab (Pakistan). Journal of Northeast Agricultural University (English Edition), 22: 87-91.
2- Babaei M., Paknejad H., Mardani M., and Salarpour M. 2012. Evaluating crop efficiency of Jahrom city using interval data envelopment analysis (IDEA). Journal of Operations Research applications, 35: 43-53.(in Persia)
3- Banker R.D., Charnes A., and Cooper W.W. 1984. Some models for estimation technical and scale efficiencies in data envelopment analysis. Management Science, 30 1078-1092.
4- Ben-Tal A., and Nemirovski A. 1999. Robust solutions to uncertain programs. Journal of Operations Research Letters, 25: 323-331.
5- Ben-Tal A., and Nemirovski A. 2000. Robust solutions of linear programming problems contaminated with uncertain data. Journal of Mathematical Programming, 88: 411-424.
6- Bertsimas D., and Sim M. 2003. Robust discrete optimization and network flows. Journal of Mathematical Programming, 98: 49-71.
7- Bertsimas D., and Sim M. 2004. The price of robustness. Operations Research 52: 35–53.
8- Charnes A., Cooper W.W., Golany B., and Seiford L. 1985. Foundation data envelopment analysis of Pareto–Koopmans efficient empirical production functions. Journal of Econometrics, 30: 91–107.
9- Charnes A.W., Cooper W., and Rhodes D. 1978. Measuring the efficiency of decision making unit. European Journal of Operational Research, 2: 429-444.
10- Cochran W.G. 1977. Sampling Techniques. New York: Willey.
11- Coeli T., Parsada R., and Battese E. 1998. An introduction to efficiency and productivity analysis. Bostone: Kluwer Academic Pub.
12- Department of Jehad Keshavarzi of Khorasan razavi. 2012. Statistical Yearbook of Agriculture Unpublished results.(in Persia)
13- Despotis D.K., Maragos E.K., Smirlis Y.G. 2006. Data envelopment analysis with missing values: An interval DEA approach. European Journal of Operational Research, 140: 24–36.
14- Dupacova J., Growe-Kuska N., and Romish W. 2003. Scenario reduction in stochastic programming: an approach using probability metrics. Mathematical Programming Series A, 95: 493–511.
15- El-Ghaoui L., Oustry F., and Lebret H. 1998. Robust solutions to uncertain semidefnite programs. SIAM Journal on Optimization, 9: 33-52.
16- Faramarzi M., Yang H., Schulin R., and Abbaspour K.C. 2010. Modeling wheat yield and crop water productivity in Iran: Implications of agricultural water management for wheat production. Agricultural Water Management, 97: 1861-1875.
17- Gaspar F.J., Mesias M., and Pulido F. 2009. Assessing the technical efficiency of extensive livestock farming systems in Extremadura, Spain. Livestock Science, 121: 7–14.
18- Guo P., and Tanaka H. 2001. Fuzzy DEA: A perceptual evaluation method. Fuzzy Sets and Systems, 119:149–160.
19- Han Y., Geng Z., Zhu Q., and Qu Y. 2015. Energy efficiency analysis method based on fuzzy DEA cross-model for ethylene production systems in chemical industry. Energy, 83: 685-695.
20- Jahanshahloo G.R., and Alirezaee M.R. 1992. Measuring the efficiency of academic units at the Teacher Training University. In Proc.26th Annul Iranian Mathematic, Conference, pp. 167-171.
21- Kao C., and Liu S.T. 2003. A mathematical programming approach to fuzzy efficiency ranking. International Journal of Production Economics, 86: 145-154.
22- Kazemi M., and Nikkhah Z. 2009. Application of DEA in measuring and analyzing the relative performance of counties of Khorasan Razavi province in wheat-rainfed cultivation. Journal of Economics and Agricultural Development, 23: 87-94.(in Persia)
23- Lertworasirikul S., Shu-Cherng F., Joines J.A, and Nuttle H.L.W. 2003. Fuzzy data envelopment analysis (DEA): A possibility approach. Fuzzy Sets and Systems, 139: 379–394.
24- Mardani M., Sakhdari H., and Sabouhi M. 2010. Application of multi objective programming and Controller parameters of conservatism in agricultural planing, Case study: Mashhad city. Journal of Agricultural Economics Research, 2: 161-187.(in Persia)
25- Mazhari M., and Mohades Hoseini S.A. 2007. Measuring and comparing the production factors of agricultural strategic products in Khorasan-razavi. Journal of Economic and Agriculture, 4: 115-121.(in Persia)
26- Mojaverian M.S. 2006. Studying the relationship between productivity and production efficiency with the size of the rice fields of Mazandaran. Journal of Economic and Agriculture, 1: 12-21.(in Persia)
27- Movahedi M.M., and Hoseini S.M. 2009. nvestigating and ranking the different areas of the railway of Islamic Republic of Iran using data envelopment analisis. Journal of Applied Mathematics of Lahijan, 24: 49-64.(in Persia)
28- Sabouhi M., and Mardani M. 2010. Investigating The effect of rainfall on cropping pattern and total gross margin in right irrigation network of nekouabad diversion dam. Journal of Agricultural Economics Research, 5: 202-221.(in Persia)
29- Sabouhi M, and Mardani M. 2013. Application of Robust Optimization Approach for Agricultural Water Resource Management under Uncertainty. Journal of Irrigation and Drainage Engineering, 139: 571-581.(in Persia)
30- Shokouhi AH, Hatami-Marbini A., Tavana M., and Saati S. 2010. A robust optimization approach for imprecise data envelopment analysis. Computers and Industrial Engineering, 59: 387-397.
31- Singh A., and Kathuria LM. 2016. Understanding drivers of branded food choice among low-income consumers. Food Quality and Preference, 52: 52-61.
32- Skevas T., Stefanou SE., and Oude Lansink A. 2014. Pesticide use, environmental spillovers and efficiency: A DEA risk-adjusted efficiency approach applied to Dutch arable farming. European Journal of Operational Research, 237: 658-664.
33- Toma E., Dobre C., Dona I., and Cofas E. 2015. DEA Applicability in Assessment of Agriculture Efficiency on Areas with Similar Geographically Patterns. Agriculture and Agricultural Science Procedia, 6: 704-711.
34- Tsionas EG. 2003. Combining DEA and stochastic frontier models: An empirical Bayes approach. European Journal of Operational Research, 147: 499-510.
35- Yang D., and Liu Z. 2012. Does farmer economic organization and agricultural specialization improve rural income? Evidence from China. Economic Modelling, 29: 990-993.
36- Yilmaz B., Yurduse M., and Harmancioglu N. 2009. The Assessment of Irrigation Efficiency in Buyuk Menderes Basin. Water Recourses Management, 23: 1081-1095.
37. Yu JR., Tzeng YC., Tzeng GH., Yu TY., and Sheu HJ. 2004. A fuzzy multiple objective programming to DEA with imprecise data, International Journal of Uncertainty. Fuzziness & Knowledge-Based Systems, 12: 591-600.
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