خلاصة:
ﺑﻬﻴﻨﻪﺳﺎزی ﺳﺒﺪ ﭘـﺮوژه ﺳـﺎزﻣﺎﻧﻲ ﺑـﻪدﻟﻴـﻞ ﭘﻴﭽﻴـﺪﮔﻲ ارزﻳـﺎﺑﻲ ﭘـﺮوژهﻫـﺎ و ﻫﻤﭽﻨـﻴﻦ ﻣﺤﺪودﻳﺖ ﻣﻨﺎﺑﻊ ﻫﻤﻮاره ﺑﺎ ﭼﺎﻟﺶﻫﺎی ﺗﺼﻤﻴﻢﮔﻴﺮی ﻣﺘﻌﺪدی روﺑﺮو اﺳﺖ. ﻣﻄﺎﻟﻌﺎت ﺑﺴﻴﺎری ﺑﺮای اراﺋﻪ و ﺑﺮرﺳﻲ ﻋﻤﻠﻜﺮد ﻣﺪلﻫﺎ و اﻟﮕﻮرﻳﺘﻢﻫﺎی ﺑﻬﻴﻨﻪﺳﺎزی ﺳﺒﺪ ﭘﺮوژه اﻧﺠﺎم ﺷﺪه اﺳـﺖ. ﺑـﺎ اﻳـﻦ وﺟﻮد ﻟﺤﺎظ اﺛﺮات ﻣﺘﻘﺎﺑﻞ ﺑﻴﻦ ﭘﺮوژهﻫﺎ در ﺑﺴﻴﺎری از اﻳﻦ ﭘﮋوﻫﺶﻫﺎ ﻣﻐﻔﻮل ﻣﺎﻧﺪه اﺳـﺖ. اﮔﺮﭼـﻪ ﻟﺤﺎظ ﻛﺮدن اﺛﺮات ﻣﺘﻘﺎﺑﻞ ﺑﻴﻦ ﭘﺮوژهﻫﺎ ﺑﺎﻋﺚ ﭘﻴﭽﻴـﺪﮔﻲ ﻣﻀـﺎﻋﻒ ﻣﺴـﺌﻠﻪ اﻧﺘﺨـﺎب ﺳـﺒﺪ ﭘـﺮوژه ﻣﻲﺷﻮد، ﺻﺮف ﻧﻈﺮﻛﺮدن از ﻣﺤﺎﺳﺒﻪ اﻳﻦ اﺛﺮات ﻣﻤﻜـﻦ اﺳـﺖ ﻛـﺎراﻳﻲ ﻓﺮآﻳﻨـﺪ ﺗﺼـﻤﻴﻢﮔﻴـﺮی و ﻣﻄﻠﻮﺑﻴﺖ ﺳﺒﺪ ﭘﺎﻳﺎﻧﻲ ﭘﺮوژه را ﺑﻪﺷﺪت ﺗﺤﺖ ﺗﺄﺛﻴﺮ ﻗﺮاردﻫﺪ. در اﻳﻦ ﻣﻘﺎﻟﻪ اﺑﺘﺪا ﺮﻣﻮﻻﺳﻴﻮن ﻣﺴﺌﻠﻪ اﻧﺘﺨﺎب ﺳﺒﺪ ﭘﺮوژه ﺑﺎ درﻧﻈﺮ ﮔﺮﻓﺘﻦ اﺛﺮات ﻣﺘﻘﺎﺑﻞ ﺑﻴﻦ ﭘﺮوژه ﻫﺎ اﻧﺠﺎم ﺷﺪه اﺳـﺖ. ﺳـﭙﺲ ﻣﺴـﺌﻠﻪاﻧﺘﺨﺎب ﺳﺒﺪ ﭘﺮوژه ﺑﺎ درﻧﻈﺮ ﮔﺮﻓﺘﻦ اﺛﺮات ﻣﺘﻘﺎﺑﻞ ﭘﺮوژهﻫﺎ ﺑﺎ اﺳﺘﻔﺎده از اﻟﮕﻮرﻳﺘﻢﻫﺎی ﺑﻬﻴﻨﻪﺳـﺎزی ICAﺑﺮرﺳﻲ ﺷﺪه اﺳﺖ. ﻟﺤﺎظ ﻛﺮدن اﺛﺮات ﻣﺘﻘﺎﺑـﻞ در اﻧﺘﺨـﺎب ﺳـﺒﺪ ﻧﻬـﺎﻳﻲ و ﺑﺮازﻧـﺪﮔﻲ آن را ﺗﺤﺖ ﺗﺄﺛﻴﺮات ﻗﺎﺑﻞﺗﻮﺟﻪ ﺑﺎﻻﻳﻲ ﻗﺮار ﻣﻲدﻫﺪ. ﻧﺘﺎﻳﺞ ﺣﺎﺻﻞ ﻧﺸﺎن ﻣﻲدﻫﺪ ﻛﻪ روش ICAﻧﺴﺒﺖﺑﻪ روش اﻟﮕﻮرﻳﺘﻢﻫﺎی PSO ،GAو CPSOﻛﻪ ﭘﻴﺶ از اﻳﻦ در اﻳﻦﮔﻮﻧﻪ ﻣﺴﺎﺋﻞ ﺑﻪﻛﺎر رﻓﺘـﻪ اﺳـﺖ ﺑﺮﺗﺮی دارد.
Due to Project evaluation complexity and resource constraints، the project portfolio optimization is numerous decision making challenges. Hence، many researches have been done to introduce model and methods for portfolio optimization. But most of them have not considered the interaction between projects. Considering the interactions between projects increase complexity of portfolio optimization problem and if these interactions be ignored، the efficiency of decision making process and final portfolio utility maybe influenced dramatically. In this paper، the portfolio optimization problem with considering interactions between the projects is formulated. Then، The portfolio optimization problem with regard the interactions between projects using ICA optimization algorithm was investigated. Interactions at the projects optimization، final solution and its fitness show the important effects. It was shown ICA method is better in comparison with the GA، the PSO and CPSO algorithm technique used before in such problems.
ملخص الجهاز:
اﮔﺮﭼـﻪ ﻟﺤﺎظ ﻛﺮدن اﺛﺮات ﻣﺘﻘﺎﺑﻞ ﺑﻴﻦ ﭘﺮوژهﻫﺎ ﺑﺎﻋﺚ ﭘﻴﭽﻴـﺪﮔﻲ ﻣﻀـﺎﻋﻒ ﻣﺴـﺌﻠﻪ اﻧﺘﺨـﺎب ﺳـﺒﺪ ﭘـﺮوژه ﻣﻲﺷﻮد، ﺻﺮف ﻧﻈﺮﻛﺮدن از ﻣﺤﺎﺳﺒﻪ اﻳﻦ اﺛﺮات ﻣﻤﻜـﻦ اﺳـﺖ ﻛـﺎراﻳﻲ ﻓﺮآﻳﻨـﺪ ﺗﺼـﻤﻴﻢﮔﻴـﺮي و ﻣﻄﻠﻮﺑﻴﺖ ﺳﺒﺪ ﭘﺎﻳﺎﻧﻲ ﭘﺮوژه را ﺑﻪﺷﺪت ﺗﺤﺖ ﺗﺄﺛﻴﺮ ﻗﺮاردﻫﺪ.
ﺳـﭙﺲ ﻣﺴـﺌﻠﻪ اﻧﺘﺨﺎب ﺳﺒﺪ ﭘﺮوژه ﺑﺎ درﻧﻈﺮ ﮔﺮﻓﺘﻦ اﺛﺮات ﻣﺘﻘﺎﺑﻞ ﭘﺮوژهﻫﺎ ﺑﺎ اﺳﺘﻔﺎده از اﻟﮕﻮرﻳﺘﻢﻫﺎي ﺑﻬﻴﻨﻪﺳـﺎزي ICAﺑﺮرﺳﻲ ﺷﺪه اﺳﺖ.
ﻫﻤﭽﻨﻴﻦ از آﻧﺠﺎﻳﻲ ﻛﻪ ﻧﺘﺎﻳﺞ ﻣﺴﺌﻠﻪ ﺑﺮﻧﺎﻣﻪرﻳﺰي ﺧﻄﻲ ﻋﺪد ﺻﺤﻴﺢ ﭼﻨﺪﻫﺪﻓـﻪ ) (MOILPاز ﺑﺮرﺳﻲ ﺗﻤﺎﻣﻲ ﺳﺒﺪﻫﺎي ﻣﻤﻜﻦ ﺣﺎﺻﻞ ﻣﻲﺷﻮد، اﮔﺮ ﺗﺄﺛﻴﺮ ﻣﺘﻘﺎﺑﻞ ﺑﻴﻦ ﭘﺮوژهﻫﺎ ﻟﺤﺎظ ﺷﻮد، اﻳﻦ روش ﻓﻘﻂ ﺑﺮاي ﻣﺴﺎﺋﻠﻲ ﻛﻪ ﺣﺪاﻛﺜﺮ ﺳﻲ ﭘﺮوژه را ﺷﺎﻣﻞ ﺷﻮد ﻗﺎﺑﻞﻛﺎرﺑﺮد اﺳﺖ.
ﺑﺮ اﻳـﻦ اﺳـﺎس ﻣﺴـﺌﻠﻪ اﻧﺘﺨـﺎب ﺳﺒﺪ ﭘﺮوژه ﭼﻨﺪﻣﻌﻴﺎره ﺑﺎ درﻧﻈﺮ ﮔﺮﻓﺘﻦ اﺛﺮات ﻣﺘﻘﺎﺑﻞ ﭘﺮوژهﻫﺎ ﺑﺮﺣﺴﺐ ﻣﻌﻴﺎرﻫﺎي اﻧﺘﺨﺎب ﭼﻨﺪﮔﺎﻧﻪ را ﻣﻲﺗﻮان ﺑﻪﺻﻮرت زﻳﺮ ﻓﺮﻣﻮﻟﻪ ﻛﺮد: ⎛ ⎞L I J J K L ∑∑ ∑∑ ∑ ∏ ()) ⎜ w j (d j (S k ⎟ ) cij = Max V + w j cij )xi ( xi ⎜ ⎟ راﺑﻄﻪ )2( ⎝ 1= j =1 k 1= ⎠ i 1= i 1= j 1= i ∑x =M .
ﮔﻔﺘﻨﻲ اﺳﺖ، اﮔﺮ اﺛﺮات ﻣﺘﻘﺎﺑﻞ ﺑﻴﻦ ﭘﺮوژهﻫﺎ ﻟﺤﺎظ ﻧﺸﻮد، ﻣﺴﺌﻠﻪ ﺑﺮﻧﺎﻣﻪرﻳـﺰي ﻋـﺪد ﺻـﺤﻴﺢ ﻏﻴﺮﺧﻄﻲ1 ) (NIPﺻﻔﺮ و ﻳﻚ ﻣﺪل )2( ﺑﻪ ﻳﻚ ﻣﺴﺌﻠﻪ ﺑﺮﻧﺎﻣﻪرﻳﺰي ﻋﺪد ﺻﺤﻴﺢ ) (IPﺻﻔﺮ و ﻳـﻚ اﺳﺘﺎﻧﺪارد ﺗﺒﺪﻳﻞﻣﻲﺷﻮد )ﻫﻤﺎنﮔﻮﻧﻪ ﻛﻪ در ﻣﺪل )1( ﻧﺸﺎن داده ﺷﺪه اﺳﺖ( ﻛﻪ ﻣـﻲﺗـﻮان آن را ﺑـﻪ ﺳﺎدﮔﻲ ﺗﻮﺳﻂ اﻟﮕﻮرﻳﺘﻢ ﺑﺮﻧﺎﻣﻪرﻳﺰي ﻋﺪد ﺻـﺤﻴﺢ ﺑـﺎﻳﻨﺮي2 ) (BIPاﺳـﺘﺎﻧﺪارد ﺣـﻞ ﻛـﺮد.
دادهﻫﺎي ﻣﺮﺑﻮطﺑﻪ اﻳﻦ ﭘﺮوژهﻫﺎ در ﺟﺪول ﺷﻤﺎره )1( ﻧﺸﺎن داده ﺷﺪه اﺳﺖ.