روش ﺑﻮتاﺳﺘﺮپ و ﻣﺠﻤﻮﻋﻪ وزنﻫﺎي ﻣﺸﺘﺮك در ﺗﺤﻠﯿﻞ- ﭘﻮﺷﺸﯽ دادهﻫﺎ ﺑﺮاي اﻓﺘﺮاق واﺣﺪﻫﺎي ﮐﺎرا

Bootstrap Method and Common Set of Weights in Data Envelopment Analysis to Differentiate Efficient Units

ﭼﮑﯿﺪه ﺗﺤﻠﯿﻞﭘﻮﺷﺸﯽدادهﻫﺎ )DEA( داﻣﻨﻪي ﮔﺴﺘﺮدهاي از ﻣﺪل ﻫﺎي رﯾﺎﺿﯽ ﺑﺮاي ﺳﻨﺠﺶ ﮐﺎراﯾﯽ ﻧﺴﺒﯽ ﻣﺠﻤﻮﻋﻪاي از واﺣﺪﻫﺎي ﺗﺼﻤﯿﻢﮔﯿﺮي ﻣﺘﺠﺎﻧﺲ ﺑﺎ ورودي و ﺧﺮوﺟﯽ ﻣﺸﺎﺑﻪ اﺳﺖ. ﻣﺪلﻫﺎي ﻣﻀﺮﺑﯽ ﺗﺤﻠﯿﻞ ﭘﻮﺷﺸﯽ دادهﻫﺎ، ﻣﺠﻤﻮﻋﻪاي از وزنﻫﺎ را ﺑﺮاي ﻣﺘﻐﯿﺮﻫﺎي ورودي و ﺧﺮوﺟﯽ ﻫﺮ واﺣﺪ ﺗﺼﻤﯿﻢﮔﯿﺮي ﺑﻪ دﺳﺖ ﻣﯽ آورد و ﺑﺮ اﺳﺎس آن ﮐﺎراﯾﯽ ﻧﺴﺒﯽ ﻫﺮ واﺣﺪ ﺗﺼﻤﯿﻢ-ﮔﯿﺮي را ﻣﺤﺎﺳﺒﻪ ﻣﯽﮐﻨﺪ. ﻣﺤﺎﺳﺒﻪ وزنﻫﺎي ﻣﺨﺘﻠﻒ ﺑﺮاي ﺷﺎﺧﺺﻫﺎي ﯾﮑﺴﺎن در ﻣﺠﻤﻮﻋﻪاي از واﺣﺪﻫﺎي ﺗﺼﻤﯿﻢﮔﯿﺮي ﻣﺘﺠﺎﻧﺲ، واﻗﻊ ﺑﯿﻨﺎﻧﻪ ﻧﯿﺴﺖ. ﺑﺮاي رﻓﻊ اﯾﻦ ﻣﺸﮑﻞ از روش ﻣﺠﻤﻮﻋﻪ وزنﻫﺎي ﻣﺸﺘﺮك )CSW( اﺳﺘﻔﺎدهﺷﺪه اﺳﺖ. ﺑﺮاي ﺑﻪ ﺣﺪاﻗﻞ رﺳﺎﻧﺪن ﺗﻌﺪاد واﺣﺪﻫﺎي ﮐﺎرا ﺑﺎ رﺗﺒﻪ ﯾﮏ از روش ﺑﻮتاﺳﺘﺮپ ﺑﺮاي ﺗﻌﯿﯿﻦ ﻣﺠﻤﻮﻋﻪ وزنﻫﺎي ﻣﺸﺘﺮك اﺳﺘﻔﺎده ﻣﯽﺷﻮد. رﺗﺒﻪ ﯾﮏ واﺣﺪ ﻣﯽ ﺗﻮاﻧﺪ اﻃﻼﻋﺎت ﺳﻮدﻣﻨﺪي درزﻣﯿﻨﻪي ﻓﻌﺎﻟﯿﺖﻫﺎي ﺑﻬﯿﻨﻪ واﺣﺪﻫﺎي ﺗﺼﻤﯿﻢﮔﯿﺮﻧﺪه در اﺧﺘﯿﺎر ﺗﺼﻤﯿﻢﮔﯿﺮﻧﺪه ﻗﺮار دﻫﺪ. اﯾﻨﮑﻪ ﮐﺪام واﺣﺪ ﺑﺮ واﺣﺪ دﯾﮕﺮ اوﻟﻮﯾﺖ دارد، اﯾﻦ ﻣﻔﻬﻮم ﺑﺮﺗﺮي ﯾﮏ واﺣﺪ را ازﻧﻈﺮ ﮐﺎراﯾﯽ و اﺛﺮﺑﺨﺸﯽ ﺑﺮ واﺣﺪﻫﺎي دﯾﮕﺮ ﻣﺸﺨﺺ ﻣﯽﮐﻨﺪ. ﻣﺤﺎﺳﺒﻪ ﮐﺎراﯾﯽ واﺣﺪﻫﺎ ﺑﺮاي ﻣﺪلﻫﺎي ﺗﺤﻠﯿﻞﭘﻮﺷﺸﯽدادهﻫﺎ ﻣﯽ ﺗﻮاﻧﺪ ﻣﻼك ﻣﻨﺎﺳﺒﯽ ﺑﺮاي رﺗﺒﻪﺑﻨﺪي ﯾﮏ واﺣﺪ ﺑﺎﺷﺪ؛ اﻣﺎ ﻣﺸﮑﻞ اﺻﻠﯽ زﻣﺎﻧﯽ اﺳﺖ ﮐﻪ ﭼﻨﺪ واﺣﺪ ﮐﺎرا ﻫﻤﮕﯽ رﺗﺒﻪ ﯾﮏ را ﻟﺤﺎظ ﻣﯽﮐﻨﻨﺪ. ﻫﺪف از اﯾﻦ ﭘﮋوﻫﺶ، اراﺋﻪ ﻣﺪﻟﯽ ﺟﻬﺖ رﺗﺒﻪﺑﻨﺪي واﺣﺪﻫﺎي ﮐﺎرا ﺑﺎ اﺳﺘﻔﺎده از روش ﺑﻮتاﺳﺘﺮپ ﺑﺮاي ﺗﻌﯿﯿﻦ ﻣﺠﻤﻮﻋﻪ وزنﻫﺎي ﻣﺸﺘﺮك در ﺗﺤﻠﯿﻞ ﭘﻮﺷﺸﯽ دادهﻫﺎ اﺳﺖ. ﺗﻌﯿﯿﻦ ﻣﺠﻤﻮﻋﻪ وزن ﻫﺎي ﻣﺸﺘﺮك از ﻃﺮﯾﻖ ﯾﺎﻓﺘﻦ ﯾﮏ ﺑﺎزه اﻃﻤﯿﻨﺎن اﺣﺘﻤﺎﻟﯽ ﺑﺮاي وزنﻫﺎ ﺑﻪ ﮐﻤﮏ ﺑﻮتاﺳﺘﺮپ اﺳﺖ ﮐﻪ ﺑﺮآورد آنﻫﺎ ﻣﯽﺗﻮاﻧﺪ ﯾﮏ ﻣﺠﻤﻮﻋﻪ وزنﻫﺎي ﻣﺸﺘﺮك اﺣﺘﻤﺎﻟﯽ ﺑﺮاي ﺗﺤﻠﯿﻞﭘﻮﺷﺸﯽدادهﻫﺎ ﺑﻪ دﺳﺖ آورد و ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ آن واﺣﺪﻫﺎي ﮐﺎرا از ﻫﻢ اﻓﺘﺮاق و رﺗﺒﻪﺑﻨﺪي ﺑﯿﻦ آنﻫﺎ اﻧﺠﺎم ﻣﯽﺷﻮد .

Data Envelopment Analysis (DEA) is a broad range of mathematical models for measuring the relative efficiency of a set of homogeneous decision units with similar inputs and outputs. Multiple models of data envelopment analysis render a set of weights for input and output variables of each decision unit to calculate the relative efficiency of those units based on them. The calculation of different weights for the same indices in a set of homogeneous decision units is not realistic. Therefore, the Common Set of Weights (CSW) method was used to solve this problem and the Bootstrap method was used to determine which common set of weights would minimize the number of efficient units. The rank of a unit can provide useful information to decision-makers on the optimal activities of decision units. The priority order of units defines the superiority of a unit in terms of efficiency and effectiveness over others. Calculating unit efficiency for data envelopment analysis models can be a good criterion for ranking one unit. However, the main problem arises when several efficient units all rank first. This study aimed at proposing a model for ranking efficient units using the Bootstrap method to determine the common set of weights in data envelopment analysis by finding a possible confidence interval for the weights using the Bootstrap method. This led to the estimation of a set of possible common weights for the data envelopment analysis. Efficient units were then identified and ranked based on these weights..