تخصیص بهینه آب سد قلعه چای عجب‌شیر بین محصولات کشاورزی در شرایط عدم حتمیت

Introduction: Qaleh Chay dam basin is one of the largest irrigation regions for food production in Ajabshir and household livelihood mostly depends on agriculture but the occurrence of drought periods and extraction of underground water has led to a reduction in surface water and underground aquifers. Continuing this process will reduce the agricultural production and consequently the region will encounter economic crisis. On the other hand, the uncertainties of various factors such as rainfall and temperature, which are not easily quantified, would affect agricultural resource system. in current study in order to response to mentioned crisis and uncertainties, interval two-stage stochastic programming (ITSP) has been proposed for water allocation of Ajbashir Qaleh chay dam among agricultural products and the results have been compared with extended ITSP.
Materials and Methods: Interval two-stage stochastic programming (ITSP) is an effective alternative to deal with uncertainties and it can be formulated as follows:




 

 



Subject to:




(water availability constraint)

 



(water allocation goal constraint)

 



(non- negativity and technical constraint)

 



  where = system benefit; = net benefit to crop  per m3 of water allocated; = promised target of water allocation quantity for crop ; = deficit to crop  per m3 of water not delivered; = water deficit to crop  when the flow is ;  = the total amount of flow that take values   with probabilities  ; = water loss rate in transport process; = the maximum allowable allocation for crop ; = the total amount of crops; = type of crop. Extended ITSP is an effective alternative to cope with water scarcity. The model can be formulated as follows:




 

 



Subject to:


 



 

 



 

 



 

 



 

 



 

 



 

 



 
 
 



Where = cost of increasing 1 m3 water for crop  while using alternative ; = total number of alternatives; = available amount of water for crop  while using alternative ;  is a binary decision variable that takes 1 if crop  when using alternative  and the seasonal flow is .
Results and Discussion: The data for the selected products (wheat, barley, potato, onion, grape, walnut, almond and apple) were collected from Regional Water Authority and Agriculture Jihad Organization of East Azarbaijan in 2015-16, and in some cases, completed by a questionnaire. The model was written in the GAMS package. Results of ITSP showed that under the low flow level, the total amount of water allocated to all crops would be zero with the exception of almonds where the final allocation of water for it would be [3.64, 20.61]. therefor,Under the medium flow level, the allocation of water for potato, onions, walnuts, almonds and apples would be[0, 5.49], [0, 28.57], [1.30, 35.71], 31.43 and 20 ×1000 m3 respectively and it would be zero for others. Finally under high flow level there would be no water shortage for all products. Water shortages may occur when the seasonal water flows do not be adequate for the promised water allocation for each crop. In such cases users will have to utilize supplementary resources. The results of extended ITSP showed that for wheat, barley, onion, grape and almond the third alternative under low level and the first one under medium flow level can be used. For potato and apple under low level the first alternative and under medium flow level the third one can be applied. Both the first and the third alternative could be utilized for walnut if the flow level was low. Finally, comparing the value of the objective function of ITSP and extended ITSP showed that with the utilization of supplementary resources for satisfying the water needs, the net profit of the system decreases slightly.
Conclusion: In this paper, ITSP method was used to allocate water to agriculture products. The results showed that there was water scarcity for products on drought and normal years. Users can utilize supplementary resources to cope with water scarcity. An extended ITSP method is based on retrieving water shortage and its results revealed that the system net benefit decreases as supplementary water reservoirs were used for water shortages. Based on the results obtained, highlighting the irrigation efficiency is recommended.