يك مدل راسل توسعه يافته براي اندازه گيري كارايي تجميعي سيستم‌هاي توليد چند دوره‌اي

An enhanced Russell model to measure aggregate efficiency of multi-period production systems

ارزﯾﺎﺑﯽ ﻋﻤﻠﮑﺮد ﺳﯿﺴﺘﻢﻫﺎي ﺗﻮﻟﯿﺪ ﺑﺎ در ﻧﻈﺮ ﮔﺮﻓﺘﻦ دادهﻫﺎي ﻣﺮﺑﻮط ﺑﻪ دورهﻫﺎي زﻣﺎﻧﯽ ﻣﺨﺘﻠﻒ ﯾﮑﯽ از ﻣﻬﻤﺘﺮﯾﻦ ﻣﺴﺎﺋﻞ ﻧﻈﺮﯾﻪ ﺗﻮﻟﯿﺪ اﺳﺖ. در اﯾﻦ ﻣﻘﺎﻟﻪ ﯾﮏ روش ﺟﺪﯾﺪ ﺑﺮاي اﻧﺪازه ﮔﯿﺮي ﮐﺎراﯾﯽ ﺗﺠﻤﯿﻌﯽ ﺳﯿﺴﺘﻢﻫﺎي ﺗﻮﻟﯿﺪ ﭼﻨﺪ دورهاي ﺑﺎ اﺳﺘﻔﺎده از روش ﺗﺤﻠﯿﻞ ﭘﻮﺷﺸﯽ دادهﻫﺎ اراﺋﻪ ﻣﯽﺷﻮد. روﯾﮑﺮد اراﺋﻪ ﺷﺪه را ﻣﯽﺗﻮان ﺑﻪ ﻋﻨﻮان ﺗﻮﺳﻌﻪاي از روشﻫﺎي ﺷﻌﺎﻋﯽ در ادﺑﯿﺎت در ﻧﻈﺮ ﮔﺮﻓﺖ. ﯾﮏ ﻣﺪل ﻣﺒﺘﻨﯽ ﺑﺮ راﺳﻞ ﺗﻮﺳﻌﻪ ﯾﺎﻓﺘﻪ ﺑﺮاي اوﻟﯿﻦ ﺑﺎر ﺑﺮاي اﻧﺪازهﮔﯿﺮ ي ﮐﺎراﯾﯽ ﺗﺠﻤﯿﻌﯽ ﺑﺎ در ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﺑﺎزهﻫﺎي زﻣﺎﻧﯽ ﻣﺮاﺣﻞ ﺗﻮﻟﯿﺪ اراﺋﻪ ﻣﯽﺷﻮد. ﯾﮑﯽ از وﯾﮋﮔﯽﻫﺎي ﻣﻔﯿﺪ ﻣﺪل ﭘ ﯿﺸﻨﻬﺎد ي اﯾﻦ اﺳﺖ ﮐﻪ ﻧﺎﮐﺎراﯾﯽ روﯾﮑﺮد ﺗﺠﻤﯿﻌﯽ ﻣﻮﺟﻮد در ﯾﮏ ﻣﺮﺣﻠﻪ ﺑﺪون ﻧﯿﺎز ﺑﻪ در ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﻣﺮﺣﻠﻪ دوم ﺑﺮاي ﺑﻬﯿ ﻨﻪ ﺳﺎزي ﻣﺘﻐﯿﺮﻫﺎي ﮐﻤﮑﯽ، ﻗﺎﺑﻞ ﺗﺸﺨﯿﺺ اﺳﺖ. وﯾﮋﮔﯽﻫﺎ و ﻣﺰاﯾﺎي ﻣﺪل ﺟﺪﯾﺪ ﺑﺤﺚ ﻣﯽﺷﻮﻧﺪ. در ﭘﺎﯾﺎن، ﺑﺮ اي ﻧﺸﺎن دادن ﻗﺎﺑﻠﯿﺖ اﺟﺮاي روﯾﮑﺮد ﺟﺪﯾﺪ، دو ﻣﺜﺎل ﮐﺎرﺑﺮدي ﺑﺮرﺳﯽ و ﺗﺤﻠﯿﻞ ﻣﯽﺷﻮﻧﺪ. ﻧﺘﺎﯾﺞ، ﻋﻤﻠﮑﺮد ﺧﻮب روش ﭘﯿﺸﻨﻬﺎدي را ﻧﺸﺎن ﻣﯽدﻫﻨﺪ .

Performance evaluation of the production systems by considering data related to different time periods is one of the most important issues of production theory. In this paper, a new method for measuring the aggregative efficiency of multi-period production systems using the data envelopment analysis (DEA) technique is proposed. The provided approach could be considered as extension of the radial methods in the literature. An extended Russell based model is presented for the first time to measure aggregative efficiency with respect to the time intervals of the production stages. One of the useful features of the proposed model is that the inefficiency of the existing aggregative approach is detected in one step without need to account for the second stage of optimizing slack variables. Some properties and advantages of the new model is discussed. Finally, to illustrate the applicability of the new approach, two practical examples are investigated and analyzed. The results show the good performance of the proposed method.