کاربرد روش کارایی متقاطع در تعیین امتیاز و رتبه‌ی استان‌های کشور در تولید پیاز

Introduction:In agriculture sector, the yield indicator is usually used to compare production units with each other, which is called “partial productivity measure” in literature review. however as it is not consider other inputs, it is always urged by researchers. To produce some better criteria, Farrell (1957) proposed some ways to make a frontier by using the existing information, and then compare units with this frontier. The approach can consider two inputs and one output. His work in 1978 developed by Charnes, Cooper and Rhodes, using mathematical programming methods, which is now known CCR model. Sexton in 1986 introduced the cross efficiency method (CEM) to complete the ranking ability of the basic models. In this study CEM was used to rank Iranian 25 provinces in onion production and their results were compared with some other extended models like super efficiency model (SE) introduced by Andersen and Petersen (1993) and CCR with correlation coefficients model (CCRCOR) proposed by Mecit and Alp (2013).
Materials and methods: Data envelopment analysis (DEA) tries to identify the production frontier using mathematical programming approach. To get this target, all inputs that are needed to produce one unit of output, are calculated for every decision making units (DMUs). If there is no better performance, then that unit is on the frontier and gets the score of one, so the other units will be relatively inefficient and their inefficiency degree is determined by comparing them with the frontier. The basic model is introduced in equation 1:
(1)



Where , and are the efficiency score for , outputs and inputs weights, respectively. The above equation which is called input orientated CCR model can not rank all units, so Sexton introduced CEM and used other unit weights to estimate the efficiency scores. He used the equation 2, to get efficiency score for every unit:
(2)
Finally by using the equation 3, the efficiency score for the unit was calculated:
(3)
In above relation, is the average efficiency for .
Results and Discussion : The results showed that the basic Charnes, Cooper and Rhodes model (CCR) could only identify the efficiency score of seven provinces but the super efficiency (SE) method ranked all of the provinces except Kurdistan and Gilan. The findings illustrated that correlation coefficients in the basic model (CCRCOR) increased the discrimination power of model by reducing the number of unranked provinces from 18 to 12. It was showed that the cross efficiency method (CEM) produced the most complete ranking among others. According to this model, the provinces of Qom, Khorasan-e-Razavi and Hormozgan with 0.3141, 0.3225 and 0.3934 scores took the 25th, 24th and 23rd places and the provinces of Ilam, Sistan & Baluchestan and Hamedan with 0.9047, 0.9015 and 0.8564 scores took the first, second and third places, respectively. The correlation coefficients analysis showed that the ranking of CCRCOR model was more similar to CEM ranking model. If the results from efficiency ranking compared with those yield or production rankings, it could be observed that the provinces of Lorestan, Esfahan and Yazd with 74,722, 64,073 and 60,032 kg production per hectare had the highest yield in the country, but their efficiency ranks were 5, 7 and 8, respectively. In terms of total production, the provinces of East Azerbaijan, Hormozgan and Esfahan were ranked from first to third, but their efficiency ratings were 17, 23 and 7, respectively.
Conclusion: If results from efficiency ranking are compared with those yield or production rankings, it can be observed that the provinces of Lorestan, Esfahan and Yazd with 74,722, 64,073 and 60,032 kg per hectare had the highest yield in the country, but their efficiency ranks were 5, 7 and 8, respectively. In terms of total production, the provinces of East Azerbaijan, Hormozgan and Esfahan were ranked from first to third, but their efficiency ratings were 17, 23 and 7, respectively. So it is a necessity to produce and use other indexes like efficiency measures in comparing and monitoring the performance of different reigns for better evaluating and planning in Iranian agriculture sector.