EFFICIENCY DETERMINATION OF THE FOREST SUB- DISTRICTS BY USING FUZZY DATA ENVELOPMENT ANALYSIS (CASE STUDY: İZMİR FOREST REGIONAL DIRECTORATE)

Eurasscience Journals Eurasian Journal of Forest Science (2013) 1(1): 1-19 EFFICIENCY DETERMINATION OF THE FOREST SUBDISTRICTS BY USING FUZZY DATA ENVELOPMENT ANALYSIS (CASE STUDY: İZMİR FOREST REGIONAL DIRECTORATE) İsmail Şafak1*, Altay Uğur Gül2, Mehmet Emin Akkaş1, S. Ümit Portakal3, Mustafa Gediklili4, Ş.Mümtaz Kanat5 1 Aegean Forestry Research Institute () 2 CBU, School of Tobacco Expertise, 3İzmir, 4Trabzon, 5Muğla Forest Regional Directorate Abstract In this research, efficiency covering the years 2007-2009 of the forest sub-districts in the Izmir Forestry Regional Directorate was evaluated using 15 variables by fuzzy data envelopment analysis. Fuzzy data envelopment analysis solutions were carried out using the data range. Fuzzy data was established by defining the lower, central and upper limits on the basis of the triangular membership function. These data are converted into interval data considering the approach of Zimmermann (1991) α cutting set. Thus, the upper and lower limits of efficiency values were obtained at five different α (0; 0.25; 0.50; 0.75 and 1.00) using fuzzy data envelopment analysis. Then inefficient forest sub-districts were listed from best to worst using the Minimax Regret-Based Approach. As a conclusion, Göçbeyli, Sarıgöl, Kınık, YeniŞakran and Kemalpaşa forest sub-districts have the best efficiency. On the other hand, Salihli, Gördes, Akhisar, Manisa, Ödemiş and Tire forest sub-districts have the worst efficiency. Keywords: Forest sub-districts, Efficiency, Fuzzy Data Envelopment Analysis, Izmir INTRODUCTION Efficiency is either expressed as the ratio between maximum output obtained by utilizing the best of the production techniques and the effected output or as capacity and willingness of producing possible maximum output of a decision unit by using data entry technology set (Candemir and Deliktaş 2005). Efficiency is also defined as the capacity to achieve maximum results with minimum effort or expense (Kök 1991). Data Envelopment Analysis (DEA) is one of the methods used in measuring the efficiency. DEA was developed in order to measure and compare the technical efficiency of the public institutions on the basis of article on efficiency measurement of Farrell (1957) by Charnes et al (1978) (Ulucan, 2000). Today eurasscience.com DEA is used in many fields such as production, service and finance. DEA is an effective and practical method assessing the relative efficiency of the decision units during managerial decision-making process by evaluating the sum of weighted outputs by comparing with the sum of weighted inputs with the help of a large number of input and output variables (Wen and Li 2009; Moghaddam and Ghoseiri 2011). By the use of DEA, active and inactive decision units are determined and then the amount of resources more or less those inactive decision units use, output level that has to be produced in accordance with the current input level and the units forming the active reference set are obtained (Ulucan 2000). In DEA while decision units do not have fixed efficiency values, the efficiency values 1 Efficiency Determination of the Forest Sub-Districts – Şafak et al. 1(1): 1-19 (2013) of those units depend on the selection of input and output variables (Haghighat et al. 2005). and comparison of interval efficiency of the decision units, Minimax Regret Approach has been used. In 1965, Lotfi A. Zadeh laid the foundation of the fuzzy logic by proposing the definition of fuzzy sets where qualifications are expressed with the graded membership function instead of the classical sets where qualifications are expressed with the binary membership function. Fuzzy thought system developed by Zadeh, nowadays, has been widely used in the development of fuzzy models within the scope of multi-criteria decision making technique such as data envelopment analysis, analytical hierarchy process, goal programming and linear programming. DEA applications in forestry were initiated by Rhodes (1986) (Balteiro et al. 2006). The first studies that followed this approach have focused on the measurement of technical efficiency of the forestry organizations by means of DEA (Joro and Viitala 1999; Balteiro et al. 2006; Kao and Yang 1991; Kao 1998 and 2000; Viitala and Hanninen 1998). Later, Lebel and Stuart (1998) in determining the contractors who perfom logging production works; Zhang (2002) in determining silvicultural activities; Strange (2003) in determining the effectiveness of reserve fields that were proposed with the intent of the selection of areas of biodiversity and Hof et al. (2004) in defining the maximum potential of the forest and pasture areas, benefited from DEA technique. Again, the fuzzy DEA models developed by Kao and Liu (2007) and Kao (2009) were used in evaluating the effectiveness of forest management units. These studies have shown that it is possible to carry out the evaluation of the efficiency by means of DEA; in the level of forest enterprises/forest sub-districts/forestry class even in the level of sub-units/ activities/staff. In standard DEA models, inputs and outputs are measured by means of the exact numbers in a ratio scale (Haghighat et al. 2005). Due to their more important and realistic role when evaluating the effectiveness of decision units, fuzzy DEA models which cover fuzzy numbers have been developed (Khoshfetrat and DaneshvarS 2011). Fuzzy number is expressed as a fuzzy set that is defined by floating point numbers that are convex, normalized and have finitecontinuous membership function (Baykan and Beyan 2004). Sengupta (1992), by making use of fuzzy sets theory and with the aim of determining the values of decision units that have either missing or inadequate input-output data and showing them in DEA models, has designed fuzzy linear programming model, and thus, has published the first study on fuzzy DEA (Güneş 2006; Saati et al. 2002). DEA studies performed in recent years have been focused on how to convert data with fuzzy value into data with precise value and how to incorporate it into the standard DEA structure. For the solution of fuzzy DEA problems, approaches such as defuzzification, α cutting set and fuzzy sequencing have been developed (Triantis and Girod 1998; Tsaur et al. 1999; Kao and Liu 2000; Guo and Tanaka 2001; Saati et al. 2001; Lertworasirikul 2001; Despotis and Smirlis 2002; Entani et al. 2002). Thereafter, by using inputoutput data with interval and/or fuzzy value, interval DEA model has been developed to measure the smallest and the highest relative efficiency of each decision unit (Wang et al. 2005). Thus, by providing interval efficiency or effective intervals as reference, efficiency value of each decision unit has been characterized as the best lower limit effectiveness or as the best upper limit effectiveness. As for sequencing eurasscience.com In Turkey, several researches were carried out in order to determine the efficiency, productivity, success or performance (...truncated)