تعيين محدوده نهايي در شرايط عدم قطعيت عيار با استفاده از مدل خطي تصادفي

Determination of ultimate pit limit in case of grade uncertainty using a stochastic linear model

ﺗﻌﯿﯿﻦ ﻣﺤﺪوده ﻧﻬﺎﯾﯽ از اﺳﺎﺳﯽﺗﺮﯾﻦ ﻣﺮاﺣﻞ ﻃﺮاﺣﯽ و ﺑﺮﻧﺎﻣﻪرﯾﺰي ﻣﻌﺎدن ﺑﻪ ﺷﻤﺎر ﻣﯽرود. ﻣﺤﺪوده ﻧﻬﺎﯾﯽ ﺑﻪ ﻣﺤﺪودهاي اﻃﻼق ﻣﯽﺷﻮد ﮐﻪ اﮔﺮ ﺑﺎ رﻋﺎﯾﺖ ﻣﺤﺪودﯾﺖﻫﺎي ﻓﻨﯽ، ﻫﻤﯿﻦ اﻣﺮوز اﺳﺘﺨﺮاج ﺷﻮد، ﺑﯿﺸﺘﺮﯾﻦ ﺳﻮد را ﺧﻮاﻫﺪ داﺷﺖ. ﺑﻪ ﻋﺒﺎرت دﯾﮕﺮ، ﻣﺤﺪوده ﻧﻬﺎﯾﯽ، ﻣﯿﺰان ذﺧﯿﺮه ﻗﺎﺑﻞ اﺳﺘﺨﺮاج ﺑﻪ روش روﺑﺎز را ﺑﺪون در ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﻧﺮخ ﺗﻨﺰﯾﻞ، ﺗﻌﯿﯿﻦ ﻣﯽﮐﻨﺪ. ﻋﯿﺎر ﻣﺎده ﻣﻌﺪﻧﯽ و ﻋﺪم ﻗﻄﻌﯿﺖﻫﺎي ﻧﺎﺷﯽ از آن ﺗﺎﺛﯿﺮ ﻗﺎﺑﻞ ﺗﻮﺟﻬﯽ در ﻃﺮاﺣﯽ ﻣﺤﺪوده ﻧﻬﺎﯾﯽ ﻣﻌﺎدن روﺑﺎز دارد. در اﯾﻦ ﻣﻘﺎﻟﻪ، ﻋﺪم ﻗﻄﻌﯿﺖ ﻋﯿﺎر ﺑﺎ اﺳﺘﻔﺎده از روش ﺷﺒﯿﻪﺳﺎزي ﺷﺮﻃﯽ ﻣﺪﻟﺴﺎزي ﺷﺪه اﺳﺖ. ﺳﭙﺲ دو ﻣﺪل ﺧﻄﯽ ﺑﺮاي ﺗﻌﯿﯿﻦ ﻣﺤﺪوده ﻧﻬﺎﯾﯽ در ﺷﺮاﯾﻂ ﻗﻄﻌﯽ و ﻋﺪم ﻗﻄﻌﯿﺖ ﻋﯿﺎر اراﺋﻪ ﺷﺪه اﺳﺖ. اﯾﻦ ﻣﺪل در ﻣﻌﺪن ﺳﻨﮓ آﻫﻦ ﺟﻼل آﺑﺎد اﺟﺮا ﺷﺪ. ﻧﺘﺎﯾﺞ ﻧﺸﺎن ﻣﯽدﻫﺪ ﮐﻪ ﻣﺤﺪوده ﻧﻬﺎﯾﯽ اﯾﻦ ﻣﻌﺪن در ﺷﺮاﯾﻂ ﻋﺪم ﻗﻄﻌﯿﺖ ﻋﯿﺎر، ﺷﺎﻣﻞ 143 ﻣﯿﻠﯿﻮن ﺗﻦ ﺳﻨﮓ آﻫﻦ ﺑﺎ ﻋﯿﺎر ﻣﺘﻮﺳﻂ 40/6 % اﺳﺖ

Ultimate Pit Limit (UPL) determination is the initial and basic step of an open pit mine design and planning. UPL refers to those parts of the deposit that are profitable to be exploited by open pit mining methods. In other word, the UPL determines the mineable reserve without considering the time value of money. Moreover, ore grade uncertainty affects the quantity and quality of the ore reserve and thus it affects the ultimate pit limit. UPL optimization problem is equal to a single period precedence constraint knapsack problem. In this paper, a stochastic linear programming model is applied to determine the UPL in case of ore grade uncertainty. The model is applied in Jalal-Abad iron ore mine. According to the results -in case of grade uncertainty- the UPL of the mine contains 143 million tons of iron ore with an average grade of 40.6%.