بحوث العمليات - الكمية

1. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
1
‫اﻟﺮﺣﻴﻢ‬ ‫اﻟﺮﺣﻤﻦ‬ ‫ﷲ‬ ‫ﺴﻢ‬
‫ﻣﻘﺮر‬ ‫ات‬‫ﺮ‬‫ﻣﺤﺎﺿ‬
Lecture Note
‫اﻟﻌﻠﻤﻴﺎت‬ ‫ﺑﺤﻮث‬
OperationResearch
‫ﻣﻘﺪﻣﺔ‬
‫ﻋﻠﻢ‬
‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬
‫ﻳﺼﻨﻒ‬ ‫اﺻﺒﺢ‬
‫اﻟﺘﻄﺒ‬ ‫اﻟﺮﺎﺿﻴﺎت‬ ‫ﻋﻠﻢ‬ ‫ﻓﺮوع‬ ‫ﻣﻦ‬ ‫ﻛﻔﺮع‬
‫ﻌﺮف‬‫و‬ ،‫ﻴﻘﻴﺔ‬
‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬
‫ﻣ‬ ‫ﺎت‬ّ‫ﺴﻤﻴ‬ ُ‫ﻣ‬ ِ‫ﻌﺪة‬
‫ﺎ‬
،‫ﺎﺿﻴﺔ‬ ّ‫اﻟﺮ‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫أو‬ ،‫ار‬‫ﺮ‬‫اﻟﻘ‬ ‫ﻋﻠﻢ‬
‫اﻟﻌﻠﻤﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﻋﻠﻢ‬ ‫ﻮ‬ ‫ﺎ‬ ‫اﻓﻀﻠ‬ ‫ﻟﻜﻦ‬ ‫ﻖ‬ ‫ﺴﻮ‬ ‫اﻟ‬ ‫ﻨﺪﺳﺔ‬ ‫و‬ ،‫اﳌﺎﻟﻴﺔ‬ ‫ﻨﺪﺳﺔ‬ ‫واﻟ‬ ‫اﻟﻨﻈﻢ‬ ‫ﺗﺤﻠﻴﻞ‬ ‫و‬
،‫ﺪﻳﺜﺔ‬ ‫ا‬ ‫اﳌﺠﺎﻻت‬ ‫ﻣﻦ‬ ‫ﺎ‬ ‫ﻏ‬ ‫إ‬ ‫ﺑﺈﺿﺎﻓﺔ‬ ‫اﻟﺴﺎﺑﻘﺔ‬ ‫اﳌﺠﺎﻻت‬ ‫ﺎﻓﺔ‬ ‫ﺸﻤﻞ‬ ‫ﻷﻧﮫ‬
‫ﺣﻴﺚ‬
‫اﻟ‬ ‫ﺬا‬ ‫ﻳﺮﻛﺰ‬
‫ﻌﻠﻢ‬
‫إﻳﺠﺎد‬ ِ
‫ق‬‫وﻃﺮ‬ ِ
‫ﻋﻤﻠﻴﺎت‬ ‫ﻋ‬
‫ﺸﺂت‬ ‫اﳌ‬ ‫ار‬‫ﺮ‬‫اﻟﻘ‬ ‫ﺘﺨﺬ‬ُ‫ﻣ‬ ‫ﺗﻮاﺟﮫ‬ ‫اﻟ‬ ‫ﻞ‬ ‫ﻟﻠﻤﺸﺎ‬ ‫ﺜ‬
ُ
‫اﳌ‬ ‫ل‬‫ﻠﻮ‬ ‫ا‬
‫ﻋﻤﺎل‬ ‫وﻣﺆﺳﺴﺎت‬
‫واﻟﻌﻤ‬
‫ﻞ‬
،‫ﺎ‬ ‫ﺗﺤﺴﻴ‬
‫ﺑ‬ ‫ﻋﻠﻢ‬ ‫ﻳﺪﺧﻞ‬ ‫ﺣﻴﺚ‬
‫ﺤﻮث‬
‫اﻟﻌﻤﻠﻴﺎت‬
‫ﺴﺘﺨﺪﻣﺔ‬
ُ
‫اﳌ‬ ‫ق‬‫ﺮ‬
ُ
‫اﻟﻄ‬ ‫أﺑﺮز‬ ‫وﻣﻦ‬ ،‫ﻘﻴﺔ‬‫ﺴﻮ‬ ‫واﻟ‬ ،‫دارﺔ‬ ‫و‬ ،‫ﻗﺘﺼﺎدﻳﺔ‬ ‫واﻟﻌﻠﻮم‬ ،‫ﻨﺪﺳﺔ‬ ‫اﻟ‬ ‫ﻛﺘﻄﺒﻴﻘﺎت‬ ‫ﻣﺠﺎﻻت‬ ‫ة‬ ّ‫ﻋﺪ‬
‫ا‬ ‫ﺑﺤﻮث‬
‫ﻣﺜﻞ‬ ‫ار‬‫ﺮ‬‫اﻟﻘ‬ ‫اﺗﺨﺎذ‬ ‫إ‬ ‫ل‬‫اﻟﻮﺻﻮ‬ ‫ﻟﻐﺎﻳﺎت‬
ً
‫ﻏﺎﻟﺒﺎ‬ ‫واﳌﺴﺘﺨﺪﻣﺔ‬ ،‫ﻲ‬ ‫ﺣﺼﺎ‬ ‫ﺤﻠﻴﻞ‬ّ‫واﻟﺘ‬ ،‫ﺎﺿﻴﺔ‬ ّ‫اﻟﺮ‬ ‫ﻤﺬﺟﺔ‬‫ﱠ‬‫اﻟﻨ‬ ‫ق‬‫ﻃﺮ‬ ‫ﻟﻌﻤﻠﻴﺎت‬
‫اﳌﻄﺮوﺣﺔ‬ ‫اﻟﺒﺪاﺋﻞ‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ن‬ ‫ﺑ‬
.
‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﻒ‬‫ﻌﺮ‬
-
‫ﺗﻮﻓ‬ ‫ﺛﻢ‬ ،‫واﻗﻌﻴﺔ‬ ‫ﻣﺸﻜﻼت‬ ‫اﺳﺔ‬‫ر‬‫ﻟﺪ‬ ‫ﻋﻠﻤﻴﺔ‬
ً
‫وﻃﺮﻗﺎ‬
ً
‫أﺳﺎﻟﻴﺒﺎ‬ ‫ﺴﺘﺨﺪم‬ ‫ﻋﻠﻢ‬‫ﻮ‬ :‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬
.‫اﳌﺘﺎﺣﺔ‬ ‫ﺎﻧﺎت‬ ‫ﻣ‬ ‫ﺿﻤﻦ‬ ‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬‫واﺧﺘﻴﺎر‬ ،‫ﺎ‬ ‫ﻟ‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫أﻛ‬
"
‫ﻠﻔﺔ‬ ‫وﺗ‬ ‫ﺪ‬ ‫وﺟ‬ ‫وﻗﺖ‬ ‫ﺑﺄﻗﻞ‬ ‫ﻠﺔ‬ ‫ﻟﻠﻤﺸ‬ ‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫إ‬ ‫ل‬‫اﻟﻮﺻﻮ‬ ‫ﺪف‬ ‫ﻣﻌﻴﻨﺔ‬ ‫ق‬‫وﻃﺮ‬ ‫ﻋﻤﻠﻴﺎت‬‫اﺧﺘﻴﺎر‬ ‫أو‬ ‫ن‬ ‫ﺑﺘﺤﺴ‬ ‫ﺘﻢ‬ ‫اﻟﻌﻠﻢ‬ ‫ﺬا‬
‫ﻣﻤﻜﻨﺔ‬
‫و‬
‫ﺘﺤﻘﻴﻖ‬
،‫ﻣﻤﻜﻦ‬ ‫ﺢ‬‫ر‬ ‫أﻗ‬
"
‫ﻋﻠﻢ‬ ‫اﺳﺘﺨﺪام‬ ‫ﻣﺠﺎﻻت‬
‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬
-
‫اﻣﺘﺪت‬
‫و‬ ‫اﻟﻌﻠﻤﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﻋﻠﻢ‬ ‫اﺳﺘﺨﺪاﻣﺎت‬
‫ﺗﻄﺒﻴﻘﺎ‬
‫ﺎ‬
‫ﺧﻼل‬ ‫ﻣﻦ‬
‫ﻣﺜﻞ‬ ‫ﻣﺠﺎﻻت‬ ‫ﻋﺪة‬
:
-
،‫ﻨﺪﺳﺔ‬ ‫اﻟ‬
-
،‫واﻟﺼﻨﺎﻋﺔ‬
-
،‫دارة‬ ‫و‬
-
،‫واﻟﻨﻘﻞ‬
-
،‫واﳌﻮاﺻﻼت‬
-
،‫ﻖ‬‫ﺴﻮ‬ ‫واﻟ‬
-
‫واﳌﺠﺎﻻ‬
‫ت‬
‫اﻟﻌﺴﻜﺮ‬
‫ﺔ‬
،‫ى‬‫ﺧﺮ‬ ‫اﳌﺠﺎﻻت‬ ‫ﻣﻦ‬ ‫واﻟﻜﺜ‬ ،
‫ﺑﺤﻮث‬ ‫اﺳﺎﻟﻴﺐ‬
‫اﻟﻌﻠﻤﻴﺎت‬

2. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
2
‫ﻨﺎك‬
‫ﻣﻦ‬ ‫ة‬ ‫ﻛﺒ‬ ‫ﻣﺠﻤﻮﻋﺔ‬
‫ﺳﺎﻟﻴﺐ‬
‫اﻟ‬
‫ﻣﺜﻞ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﺎ‬ ‫ﻋﻠ‬ ‫ﻌﺘﻤﺪ‬
:
-
،‫ﺎﺿﻴﺔ‬‫اﻟﺮ‬ ‫اﻟﻨﻤﺎذج‬ ‫ﺗﺼﻤﻴﻢ‬
-
،‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬
-
،‫اﻟﺸﺒﻜﻴﺔ‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬
-
،‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ﻟ‬ ‫ل‬‫ارواﻟﻮﺻﻮ‬‫ﺮ‬‫اﻟﻘ‬ ‫ﻻﺗﺨﺎذ‬ ،‫ﻲ‬ ‫ﺣﺼﺎ‬ ‫اﻟﺘﺤﻠﻴﻞ‬
‫ﺧﺮى‬ ‫ﺑﺎﻟﻌﻠﻮم‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﻋﻼﻗﺔ‬
‫ﳌﺎم‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﺗﺘﻄﻠﺐ‬
‫ﻣﺜﻞ‬ ‫ﺎﺿﻴﺔ‬‫اﻟﺮ‬ ‫اﻟﻌﻠﻮم‬ ‫ﻣﻦ‬ ‫ﺑﺎﻟﻌﺪﻳﺪ‬
:
‫ﺣﺘﻤﺎﻻ‬ ‫وﻋﻠﻢ‬ ‫اﳌﺼﻔﻮﻓﺎت‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫ﺴﺎب‬ ‫ا‬
‫ت‬
.‫ﺎ‬ ‫وﻏ‬
‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﺦ‬‫ﺗﺎر‬
‫ﻳﺼﻌﺐ‬
‫ﻟ‬ ‫اﻟﻔﻌﻠﻴﺔ‬ ‫اﻟﺒﺪاﻳﺔ‬ ‫ﺗﺤﺪﻳﺪ‬
‫ﻌﻠﻢ‬
‫ﺑﺤﻮث‬ ‫اﺳﺘﺨﺪﻣﻮا‬ ‫ﻗﺪ‬ ‫اﳌﺠﺎﻻت‬ ‫ﺷ‬ ‫واﺋﻞ‬ ‫اﻟﻘﺎدة‬ ‫ﻣﻦ‬ ‫اﻟﻜﺜ‬ ‫أن‬ ‫ن‬‫ﻮ‬ ،‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬
،‫اﻟﻮاﻗﻊ‬ ‫أرض‬ ‫ﻋ‬
ً
‫ﺗﻄﺒﻴﻘﻴﺎ‬ ‫اﻟﻌﻤﻠﻴﺎت‬
ً
‫ﻣﺜﻼ‬‫ﻧﺬﻛﺮ‬
ُ
‫اﳌ‬ ‫اﻟﻘﺎﺋﺪ‬ ‫اﺳﺘﺨﺪم‬
‫اﻟﻮﻟﻴﺪ‬ ‫ﺑﻦ‬ ‫ﺧﺎﻟﺪ‬ ‫ﺴﻠﻢ‬
‫ﻋﻨﮫ‬ ‫ﷲ‬ ‫ر‬
‫ﺗﻄﺒﻴ‬ ‫اﻟﻌﻠﻢ‬ ‫ﺬا‬
ً
‫ﻘﻴﺎ‬
‫اﻟﺸﺎم؛‬ ‫ﻟﺒﻼد‬ ‫ﺳﻼﻣﻴﺔ‬ ‫اﻟﻔﺘﻮﺣﺎت‬ ‫أﺛﻨﺎء‬ ‫ﻣﻌﺎرﻛﮫ‬
‫ﺧﺎﺻﺔ‬
ً
‫ﺑﺪﻻ‬ ‫ﻣﻤﻜﻦ‬ ‫أﻗﺼﺮوﻗﺖ‬ ‫اﻟﺮوم‬ ‫ﺶ‬ ‫ﺟ‬ ‫وﻣﻔﺎﺟﺄة‬ ،‫ﻣﺜﻞ‬ ‫ﻖ‬‫اﻟﻄﺮ‬ ‫ﻟﺴﻠﻮك‬
‫اﳌﺘﻮﻗﻊ‬ ‫اﳌﻌﺘﺎد‬ ‫ﻖ‬‫اﻟﻄﺮ‬ ‫ﺳﻠﻮك‬ ‫ﻣﻦ‬
.
‫ﺗﻢ‬
‫ﻋﻤﻠﻴ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫اﺳﺘﺨﺪم‬
‫أﻣﻌﻨﺎ‬‫وﻟﻮ‬ .‫ﺑﺬاﺗﮫ‬ ‫ﻗﺎﺋﻢ‬ ‫ﻋﻠﻢ‬ ‫إ‬ ‫ﺎ‬ ‫ﻓ‬ ‫ل‬‫ﺗﺤﻮ‬ ‫اﻟ‬ ‫اﳌﺮﺣﻠﺔ‬ ‫إ‬ ‫وﺻﻞ‬ ‫ﺣ‬ ‫اﳌﺠﺎﻻت‬ ‫ﻣﻦ‬ ‫اﻟﻜﺜ‬
ً
‫ﺎ‬
،‫ﺔ‬‫اﻟﻨﻈﺮ‬ ‫اﻟﻨﺎﺣﻴﺔ‬ ‫ﻣﻦ‬ ‫ﺣﺪﻳﺚ‬ ‫ﻋﻠﻢ‬‫ﻮ‬ ‫و‬ ،‫ي‬‫اﻟﻌﺴﻜﺮ‬ ‫ﺑﺎﳌﻴﺪان‬ ‫وﺛﻴﻘﺔ‬ ‫ﻋﻼﻗﺔ‬ ‫اﳌﺼﻄ‬ ‫ﺬا‬ ‫ﻟ‬ ‫أن‬ ‫ﺴﺘﺪل‬ "‫"ﻋﻤﻠﻴﺎت‬ ‫ﻠﻤﺔ‬ ‫اﻟﻨﻈﺮإ‬
‫اﻟﻌﻠﻢ‬ ‫ﺬا‬ ‫ﻟ‬ ‫اﻟﻌﻤﻠﻴﺔ‬ ‫اﻟﺒﺪاﻳﺔ‬ ‫ﺎﻧﺖ‬
‫اﺳﺘﺨﺪﻣ‬
‫ﮫ‬
‫ﺧﻼل‬
‫اﻟ‬ ‫ﺮب‬ ‫ا‬
‫ﻲ‬ ‫ﻳﻄﺎ‬ ‫اﻟ‬ ‫ﺶ‬ ‫ا‬ ‫ﺣﻘﻘﮫ‬ ‫ﻧﺘﺼﺎراﻟﺬي‬
ً
‫ﺒﺎ‬ ‫ﺳ‬ ‫ﺎن‬ ‫و‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫ﻌﺎﳌﻴﺔ‬
.
.‫ﺮب‬ ‫ا‬ ‫ﺎء‬ ‫اﻧ‬ ‫ﻌﺪ‬ ‫اﳌﺪﻣﺮة‬ ‫ﺎ‬‫أورو‬ ‫ﺑﻨﺎء‬ ‫إﻋﺎدة‬ ‫اﺳﺘﺨﺪﻣﺖ‬
ً
‫أﻳﻀﺎ‬ ‫ﺎ‬ ‫ﻓﺈ‬ ‫ﺮب‬ ‫ا‬ ‫اﺳﺘﺨﺪﻣﺖ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫أن‬ ‫وﻛﻤﺎ‬
‫أن‬ ‫ﻧﺠﺪ‬
،‫ﺸﺎرﻩ‬ ‫اﻧ‬ ‫وﺳﺮﻋﺔ‬ ‫اﻟﻌﻠﻢ‬ ‫ﺬا‬ ‫ﺗﻄﻮر‬ ‫ﻤﺎ‬ ‫أﺳ‬ ‫ﻗﺪ‬ ‫ﻤﺎن‬ ‫ﻣ‬ ‫ﻋﺎﻣﻼن‬ ‫ﻨﺎك‬
-
‫ل‬‫و‬
:
‫اﻟﺘﻘﺪم‬‫ﻮ‬
‫اﻟﻘﺮن‬ ‫ﺬا‬ ‫ﻣﻦ‬ ‫ﻨﺎت‬ ‫ﻤﺴ‬ ‫ا‬ ‫ﻣﻨﺬ‬ ‫ﺴﺎرع‬ ‫اﳌ‬ ‫اﻟﻜﺒ‬ ‫اﻟﺘﻜﻨﻮﻟﻮ‬
،
-
‫و‬
‫ﻲ‬ ‫اﻟﺜﺎ‬
:
‫ﺔ‬ ‫اﻟﻴﺪو‬ ‫ﺑﺎﻟﻄﺮق‬ ‫ﺎ‬ ‫ﺣﻠ‬ ‫ﺴﺘﺤﻴﻞ‬ ‫أو‬ ‫ﻳﺼﻌﺐ‬ ‫اﻟ‬ ‫اﳌﻌﻘﺪة‬ ‫اﳌﺴﺎﺋﻞ‬ ‫ﺣﻞ‬ ‫ﻤﺖ‬ ‫أﺳ‬ ‫واﻟ‬ ‫ﺎﺳﺒﺎت‬ ‫ا‬ ‫ﺛﻮرة‬‫ﻮ‬
‫ﺒﺎ‬ ‫ﺴ‬ ‫اﻟﻌﺎﻣﻼت‬ ‫ﺬان‬
.‫ﻣﺎم‬ ‫إ‬ ‫ﻧﻮﻋﻴﺔ‬
ً
‫ﻧﻘﻠﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﻧﻘﻞ‬
‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﺗﻄﺒﻴﻘﺎت‬
‫ﻌﺾ‬ ‫ﺳﻨﺬﻛﺮ‬ ‫اﻟﻔﻘﺮة‬ ‫ﺬﻩ‬ ‫ﻨﺎ‬ ‫و‬ ،‫ﺔ‬‫واﻟﻌﺴﻜﺮ‬ ‫اﳌﺪﻧﻴﺔ‬ ‫اﳌﺠﺎﻻت‬ ‫ﻣﻦ‬ ‫اﻟﻜﺜ‬ ‫أﺳﻠﻔﻨﺎ‬ ‫ﻛﻤﺎ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﺴﺘﺨﺪم‬
:‫ﺎ‬ ‫ﺗﻄﺒﻴﻘﺎ‬

3. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
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‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
3
-
‫أو‬ ‫ﻣﺼﻨﻊ‬ ‫أو‬ ‫ﺟﺴﺮ‬ ‫إﻗﺎﻣﺔ‬ ‫أو‬ ،‫ﺮ‬ ‫ﻋ‬ ‫ﺳﺪ‬ ‫ﺸﺎء‬ ‫إ‬ ‫ﻣﺜﻞ‬ ،‫ن‬ ‫ﻣﻌ‬ ‫ﻣﺸﺮوع‬ ‫ﻹﻗﺎﻣﺔ‬ ‫ﻮاﻧﺐ‬ ‫ا‬ ‫ﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫ﻣﺜﻞ‬ ‫ﺎن‬ ‫اﳌ‬ ‫ﺗﺤﺪﻳﺪ‬
‫ﺛﻼ‬ ‫ﻨﺎك‬ ‫أن‬‫ﻟﻮ‬ ‫اﳌﺜﺎل‬ ‫ﻴﻞ‬ ‫ﺳ‬ ‫ﻓﻌ‬ .. ‫ﺸﻔﻰ‬ ‫ﻣﺴ‬
‫أن‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﻟﺒﺤﻮث‬ ‫ﻓﻴﻤﻜﻦ‬ ،‫ﺟﺒﻞ‬ ‫ﻣﻦ‬‫ﻟﻴﻤﺮ‬ ‫ﻖ‬‫ﻃﺮ‬ ‫ﻹﻗﺎﻣﺔ‬ ‫ات‬‫ر‬‫اﺧﺘﻴﺎ‬ ‫ﺛﺔ‬
‫ﺸﺎء‬ ‫ﺑﺈ‬ ‫ﻧﻘﻮم‬ ‫أم‬ ،‫ﺒﻞ‬ ‫ا‬ ‫داﺧﻞ‬ ‫ﻣﻦ‬ ‫ﻧﻔﻖ‬ ‫ﺑﺤﻔﺮ‬ ‫ﻧﻘﻮم‬ ‫ﻞ‬ ،‫ﺒﻞ‬ ‫ا‬ ‫ل‬‫ﺣﻮ‬ ‫اﻟﻄﺮﻖ‬ ‫ﻳﻠﺘﻒ‬ ‫ﻞ‬ ،‫ﻣﺜﻞ‬ ‫ﺧﺘﻴﺎر‬ ‫ﻋ‬ ‫ﺗﺪﻟﻚ‬
.‫ﺒﻞ‬ ‫ا‬ ‫ﺟﺎﻧﺐ‬ ‫ﺗﻤﺮﻣﻦ‬ ‫ﺟﺴﻮر‬
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‫اﻟﻄﻮاﻗﻢ‬ ‫ﺸﺎﻃﺎت‬ ‫و‬ ‫اﻟﻄﺎﺋﺮات‬ ‫ﺣﺮﻛﺔ‬ ‫ﺟﺪوﻟﺔ‬ ‫ﻣﺜﻞ‬ ،‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ﺑﺎﻟﺸ‬ ‫ﺸﻄﺔ‬ ‫ﺟﺪوﻟﺔ‬
.‫اﳌﻄﺎرات‬
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.‫ﺎﺻﺔ‬ ‫ا‬ ‫اﳌﺆﺳﺴﺎت‬ ‫أو‬ ‫ﻮﻣﻴﺔ‬ ‫ا‬‫اﻛﺰ‬‫ﺮ‬‫اﳌ‬ ‫ﻧﺘﻈﺎر‬ ‫ﻃﻮاﺑ‬ ‫ﻣﺜﻞ‬ ، ‫اﻟﻄﻮاﺑ‬ ‫ﻧﺘﻈﺎر‬ ‫ات‬ ‫ﻓ‬ ‫ﺗﻘﻠﻴﺺ‬
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‫أو‬ ‫اﻟﺴﻔﻦ‬ ‫اﻧﺘﺎج‬ ‫ﺧﻄﻮط‬ ‫ﻣﺜﻞ‬ ‫ﻧﺘﺎج‬ ‫ﻊ‬‫ﺴﺮ‬ ‫و‬ ‫ﻠﻔﺔ‬ ‫اﻟﺘ‬ ‫ﺗﻘﻠﻴﺺ‬ ‫ﺪف‬ ‫ﻊ‬ ‫اﳌﺼﺎ‬ ‫واﻟﺘﺠﻤﻴﻊ‬ ‫ﻧﺘﺎج‬ ‫ﺧﻄﻮط‬ ‫ﺗﺼﻤﻴﻢ‬
.‫ات‬‫ﺮ‬‫اﻟﻄﺎﺋ‬‫أو‬ ‫اﻟﺴﻴﺎرات‬
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‫ﺣﻴﺚ‬ ‫ﻣﻦ‬ ‫ﻣﺜﻞ‬ ‫ﻖ‬‫اﻟﻄﺮ‬‫اﺧﺘﻴﺎر‬
‫ﻣﻦ‬ ‫ﻊ‬ ‫اﻟﺒﻀﺎ‬ ‫ﻟﺘﻮﺻﻴﻞ‬ ‫ﻣﺠﺘﻤﻌﺔ‬ ‫ﻮاﻧﺐ‬ ‫ا‬ ‫ﺬﻩ‬ ‫ﻞ‬ ‫ﻣﻦ‬ ‫أو‬ ‫ﻠﻔﺔ‬ ‫اﻟﺘ‬‫أو‬ ‫ﻣﺎن‬ ‫أو‬ ‫اﻟﺴﺮﻋﺔ‬
.‫ﺎﺋﻦ‬‫اﻟﺰ‬ ‫إ‬‫أو‬ ‫ﻊ‬ ‫اﻟﺘﻮز‬ ‫ﻧﻘﺎط‬ ‫إ‬ ‫ﻊ‬ ‫اﳌﺼﺎ‬
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.‫ﻮادث‬ ‫ا‬ ‫اﳌﺮوروﺗﻘﻠﻴﻞ‬ ‫ن‬ ‫وﺗﺤﺴ‬ ‫زدﺣﺎم‬ ‫ﻟﺘﻘﻠﻴﺺ‬ ‫ﺔ‬‫ر‬‫اﳌﺮو‬ ‫ﻧﻈﻤﺔ‬ ‫إدارة‬ ‫ﺎة‬ ‫اﳌﺤﺎ‬ ‫اﺳﺘﺨﺪام‬
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‫وﻛﻔﺎءة‬ ‫ﻮدة‬ ‫ا‬ ‫ن‬ ‫وﺗﺤﺴ‬ ‫ﻠﻔﺔ‬ ‫اﻟﺘ‬ ‫وﺗﻘﻠﻴﺺ‬ ‫ﺎح‬‫ر‬ ‫ﺎدة‬‫ز‬
.‫ﻧﺘﺎج‬
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.‫ﺎ‬ ‫وﻃﺎﻗ‬ ‫ﺎﺗﻒ‬ ‫اﻟ‬ ‫ﺷﺒﻜﺔ‬ ‫ﺎﻧﻴﺔ‬ ‫إﻣ‬ ‫ﺣﺪود‬ ‫ﺎﳌﺎت‬ ‫اﳌ‬ ‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫أﻛ‬ ‫ﻨﺎك‬ ‫ن‬‫ﻮ‬ ‫ﻳ‬ ‫ﺑﺤﻴﺚ‬ ‫ﺎﺗﻒ‬ ‫اﻟ‬ ‫اﺳﺘﺨﺪاﻣﺎت‬ ‫ﺗﻨﻈﻴﻢ‬
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.‫ﺎ‬ ‫وﻏ‬‫اﻟﻐﺎز‬ ‫ﺐ‬ ‫وأﻧﺎﺑ‬ ‫ﺪﻳﺪ‬ ‫ا‬ ‫واﻟﺴﻜﺔ‬ ‫ق‬‫واﻟﻄﺮ‬ ‫اﳌﻴﺎﻩ‬ ‫ﺎت‬ ‫ﺷﺒ‬ ‫وإدارة‬ ‫وﺗﻨﻔﻴﺬ‬ ‫وﺗﺨﻄﻴﻂ‬ ‫ﺗﺼﻤﻴﻢ‬
-
.‫اﻟﻌﺎﻣﻠﺔ‬ ‫ى‬‫ﻟﻠﻘﻮ‬ ‫ﻣﺜﻞ‬ ‫ﺳﺘﺨﺪام‬ ‫و‬ ‫ﺔ‬‫ﺸﺮ‬ ‫اﻟ‬ ‫اﳌﻮارد‬ ‫ﻃﺎﻗﺎت‬ ‫ﺗﻨﻈﻴﻢ‬
-
‫ا‬
‫ﻣﺜﻞ‬ ‫ﺳﺘﺨﺪام‬ ‫و‬ ‫ﺎب‬ ‫وﺧﻄﻂ‬ ‫ﺎة‬ ‫ﺑﺎﳌﺤﺎ‬ ‫ﺐ‬‫اﻟﺘﺪر‬ ‫اﻣﺞ‬‫ﺮ‬‫ﺑ‬ ‫وﺗﻨﻈﻴﻢ‬ ‫اﺗﻴﺠﻴﺎت‬ ‫ﺳ‬ ‫رﺳﻢ‬ ‫ﻣﺜﻞ‬ ‫ي‬‫اﻟﻌﺴﻜﺮ‬ ‫ﳌﺠﺎل‬
.‫ﺔ‬‫اﻟﻌﺴﻜﺮ‬‫واﻟﺬﺧﺎﺋﺮ‬ ‫ن‬‫ﻟﻠﻤﺆ‬
‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﻟﺒﺤﻮث‬ ‫اﻟﻌﺎﻣﺔ‬ ‫اﻟﺴﻤﺎت‬
-
.‫دﻗﻴﻖ‬ ‫ﻞ‬ ‫ﺸ‬ ‫ﺎ‬ ‫وﻃﺮﺣ‬ ‫ﻟﻠﻮاﻗﻊ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﺐ‬‫ﺗﻘﺮ‬
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.‫ﺎ‬ ‫ﺗﻔﺎﺻﻴﻠ‬ ‫ﻞ‬ ‫ﺑ‬ ‫ﻋﻠ‬ ‫ﻞ‬ ‫ﺸ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﺻﻴﺎﻏﺔ‬
-
.‫رﺎﺿﻴﺔ‬ ‫ﻋﻼﻗﺎت‬ ‫ﻞ‬ ‫ﺷ‬ ‫ﻋ‬ ‫ﺎ‬ ‫ﻌﺮﺿ‬ ‫ﻣﻨﺎﺳﺐ‬ ‫ﺎ‬‫ر‬ ‫ﻧﻤﻮذج‬ ‫ﻞ‬ ‫ﺷ‬ ‫ﻋ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﺻﻴﺎﻏﺔ‬
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‫اﻟﻮاﻗﻊ‬ ‫أرض‬ ‫ﻋ‬ ‫ﺎ‬ ‫ﻌﺬرﺗﺠﺮ‬ ‫إن‬ ‫ﺎة‬ ‫اﳌﺤﺎ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫ﺎ‬ ‫وﺗﺠﺮ‬ ‫ﺎ‬ ‫ﻟﻼﺧﺘﻴﺎرﻣ‬ ‫اﻟﻨﻤﻮذج‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫اﻟﺒﺪاﺋﻞ‬ ‫ﻣﻦ‬ ‫اﻟﻌﺪﻳﺪ‬ ‫إﻳﺠﺎد‬
.‫اراﳌﻨﺎﺳﺐ‬‫ﺮ‬‫اﻟﻘ‬ ‫ﻻﺗﺨﺎذ‬
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‫ﻣ‬ ‫ﻠﺔ‬ ‫ﻣﺸ‬ ‫ﺘﻨﺎ‬ ‫واﺟ‬ ‫ﻣﺎ‬ ‫إذا‬ ‫ى‬‫أﺧﺮ‬
ً
‫ﻣﺮة‬ ‫اﻟﻨﻤﺎذج‬ ‫ﺬﻩ‬ ‫ﺗﻄﺒﻴﻖ‬
.‫ﻤﺎﺛﻠﺔ‬
-
.‫ى‬‫ﺧﺮ‬ ‫اﳌﺠﺎﻻت‬ ‫ن‬ ‫اﳌﺨﺘﺼ‬ ‫اء‬ ‫ﺑﺎ‬ ‫ﺳﺘﻌﺎﻧﺔ‬
‫اﻟﻌﻠﻤﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫اﺳﺘﺨﺪام‬ ‫ﻋ‬ ‫أﻣﺜﻠﺔ‬
‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫أﺳﺎﻟﻴﺐ‬ ‫ﻌﺾ‬ ‫ﻋ‬ ‫أﻣﺜﻠﺔ‬

4. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
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‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
4
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‫ﻳﺘﻌﺬر‬ ‫ﺣﻴﻨﻤﺎ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﺴﺘﻔﻴﺪ‬ ‫و‬ ،‫ﺴﻴﺔ‬ ‫ﺋ‬‫ﺮ‬‫اﻟ‬ ‫ﺎ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫وﺗﻤﺜﻴﻞ‬ ‫اﻟﻮاﻗﻌﻴﺔ‬ ‫ﻊ‬‫اﳌﺸﺎر‬‫أو‬ ‫ﻞ‬ ‫اﳌﺸﺎ‬ ‫ﺗﻘﻠﻴﺪ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫ن‬‫ﻮ‬ ‫وﺗ‬ :‫ﺎة‬ ‫اﳌﺤﺎ‬
ً
‫وﺧﺎﺻﺔ‬ ،‫ة‬ ‫ﻛﺒ‬ ‫ﻣﺨﺎﻃﺮة‬ ‫ﻓﻴﮫ‬ ‫ن‬‫ﻮ‬ ‫ﻳ‬ ‫ﻗﺪ‬ ‫أو‬ ‫ﻟﻠﻐﺎﻳﺔ‬
ً
‫ﻠﻔﺎ‬ ‫وﻣ‬
ً
‫ﺻﻌﺒﺎ‬ ‫ن‬‫ﻮ‬ ‫و‬ ‫اﻟﻮاﻗﻊ‬ ‫أرض‬ ‫اﻟﻨﻈﺎم‬ ‫ﻋ‬ ‫اﻟﺘﺠﺎرب‬ ‫اء‬‫ﺮ‬‫إﺟ‬
‫اﳌﺤﺎ‬ ‫ﻮاﺳﻄﺔ‬‫و‬ .‫اﳌﻌﻘﺪة‬‫أو‬ ‫ة‬ ‫اﻟﻜﺒ‬ ‫ﻊ‬‫اﳌﺸﺎر‬
‫ﻋ‬ ‫ﻟﺘﻄﺒﻴﻘﮫ‬ ‫ﻣﺜﻞ‬ ‫ار‬‫ﺮ‬‫اﻟﻘ‬ ‫إ‬ ‫ل‬‫واﻟﻮﺻﻮ‬ ‫ﺎ‬ ‫وﺗﺤﻠﻴﻠ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫اﺳﺔ‬‫ر‬‫د‬ ‫ﻳﻤﻜﻦ‬ ‫ﺎة‬
.‫اﻟﻮاﻗﻊ‬ ‫أرض‬
-
‫واﳌﺎدﻳﺔ‬ ‫ﺔ‬‫ﺸﺮ‬ ‫اﻟ‬ ‫اﳌﻮارد‬ ‫واﺳﺘﺨﺪام‬ ‫اﻟﻌﻤﻞ‬ ‫ﺧﻄﻮات‬ ‫ﺗﻘﺴﻢ‬ ‫ﺣﻴﺚ‬ ‫ة‬ ‫اﻟﻜﺒ‬ ‫اﳌﺸﺎرﻊ‬ ‫ﺎ‬ ‫ﺴﺘﺨﺪﻣ‬ ‫و‬ :‫اﻟﺰﻣﻨﻴﺔ‬ ‫ﺪوﻟﺔ‬ ‫ا‬
‫اﳌﺴﺎ‬ ‫أﺳﻠﻮب‬ ‫ﺴﺘﺨﺪم‬ ‫و‬ ،‫ﻣﻔﺼﻠﺔ‬ ‫زﻣﻨﻴﺔ‬ ‫ل‬‫ﺟﺪاو‬ ‫ﻋ‬ ‫ﺑﺎﻻﻋﺘﻤﺎد‬
ً
‫زﻣﻨﻴﺎ‬ ‫واﳌﺎﻟﻴﺔ‬
ً
‫ﺟﺪا‬
ً
‫ﻣﻔﻴﺪة‬ ‫اﻟﺰﻣﻨﻴﺔ‬ ‫ﺪوﻟﺔ‬ ‫وا‬ ،‫ﺮج‬ ‫را‬
.‫ﻋﺎﻟﻴﺔ‬ ٍ‫ﺑﻜﻔﺎءة‬ ‫اﳌﺸﺮوع‬ ‫وﻹدارة‬ ‫ﻟﻠﻤﺸﺮوع‬ ‫ﺟﻤﺎﻟﻴﺔ‬ ‫اﳌﺪة‬ ‫ﻟﺘﻘﻠﻴﺺ‬
-
‫ﻟﻠﺘﺨﺰﻦ‬ ‫ﺎﻟﻴﻒ‬ ‫اﻟﺘ‬ ‫ﻟﺘﻘﻠﻴﺺ‬ ‫اﻟﺘﺨﺰﻦ‬ ‫ﻧﻈﻢ‬ ‫ﺑﺘﺼﻤﻴﻢ‬ ‫ﺘﻢ‬ ‫واﻟﺬي‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﻓﺮوع‬ ‫ﻣﻦ‬ ‫ﻓﺮع‬ ‫ﻮ‬ ‫و‬ :‫ﻦ‬‫اﻟﺘﺨﺰ‬ ‫ﻧﻈﻢ‬
‫ﺬا‬ ‫و‬ ،‫اﳌﻨﺎﺳﺐ‬ ‫اﻟﻮﻗﺖ‬ ‫ن‬‫ﻟﻠﺰﻮ‬ ‫اﳌﻨﺘﺞ‬ ‫ل‬‫وﺻﻮ‬ ‫ﻣﻦ‬ ‫ﻟﻠﺘﺄﻛﺪ‬ ‫وﻛﺬﻟﻚ‬
‫ﻨﺪﺳﺔ‬ ‫ﺑﺎﻟ‬ ‫ﻳﺮﺗﺒﻂ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﻣﻦ‬ ‫اﻟﻔﺮع‬
.‫اﻟﺼﻨﺎﻋﻴﺔ‬
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‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫وذﻟﻚ‬ ،‫اﻟﻄﺎﺑﻮر‬ ‫ﻧﺘﻈﺎر‬ ‫ﻣﺪة‬ ‫ﻣﻦ‬ ‫اﻟﺘﻘﻠﻴﻞ‬ ‫ﺎ‬ ‫ﺪﻓ‬ ‫و‬ ، ‫اﻟﻄﻮاﺑ‬ ‫ﻧﻈﺮﺔ‬
ً
‫أﻳﻀﺎ‬ ‫ﺴ‬ ‫و‬ :‫ﻧﺘﻈﺎر‬ ‫ﺻﻔﻮف‬ ‫ﻧﻤﺎذج‬
‫ات‬‫ر‬‫وإﺷﺎ‬ ‫واﳌﻄﺎﻋﻢ‬ ‫اﻟﻮﻗﻮد‬ ‫ﻛﻤﺤﻄﺎت‬ ‫ﻣﺎﻛﻦ‬ ‫ﻣﺨﺘﻠﻒ‬ ‫ﺴﺘﺨﺪم‬‫و‬ ‫اﻟﺬروة‬ ‫ﻈﺎت‬
ً
‫وﺧﺼﻮﺻﺎ‬ ‫ﺪﻣﺔ‬ ‫ا‬ ‫ﻛﻔﺎءة‬ ‫ﺎدة‬‫ز‬
‫اﳌ‬
‫ﺧﺪﻣﺎت‬ ‫ﻋ‬ ‫ل‬‫ﺼﻮ‬ ‫ا‬ ‫ﻳﻤﻜﻦ‬ ‫ﺔ‬‫اﻟﻨﻈﺮ‬ ‫ﺬﻩ‬ ‫ﺘﻄﺒﻴﻖ‬‫و‬ ‫ﺎة‬ ‫اﳌﺤﺎ‬ ‫أﺳﻠﻮب‬ ‫اﻟﻨﻤﺎذج‬ ‫ﺬﻩ‬ ‫ﺴﺘﺨﺪم‬‫و‬ .‫ﺎ‬ ‫وﻏ‬ ‫ﺮورواﻟﺒﻨﻮك‬
.‫أﻗﻞ‬ ‫ﻠﻔﺔ‬ ‫وﺗ‬ ‫أﻗﻞ‬ ‫ﺑﻮﻗﺖ‬ ‫أﻓﻀﻞ‬ ‫ﻞ‬ ‫ﺸ‬ ‫ن‬‫ﻟﻠﺰﻮ‬ ‫ﻣﺮﺿﻴﺔ‬
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‫ﻓﻴﺼﺒﺢ‬ ‫ﺑﺨﻄﻮط‬ ‫ﺎ‬ ‫ﺑﻴ‬ ‫ﻓﻴﻤﺎ‬ ‫ﺗﺮﺗﺒﻂ‬ ‫ﻋﻘﺪ‬ ‫إ‬ ‫ﻠﮫ‬ ‫ﺑﺘﺤﻮ‬ ‫اﳌﺸﺮوع‬ ‫ﺗﺤﻠﻴﻞ‬ ‫اﻟﻨﻤﺎذج‬ ‫ﺬﻩ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫ﺘﻢ‬‫و‬ :‫ﺎت‬ ‫اﻟﺸﺒ‬ ‫ﻧﻤﺎذج‬
‫ﻋﺒﺎر‬ ‫اﳌﺸﺮوع‬
‫ﺬﻩ‬ ‫اﺳﺘﺨﺪام‬ ‫ﻣﺜﻞ‬ .‫ﻗﺼﺮ‬ ‫ﻖ‬‫اﻟﻄﺮ‬ ‫ﺑﺎﺗﺨﺎذ‬ ‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫إ‬ ‫ل‬‫اﻟﻮﺻﻮ‬ ‫ﺎ‬ ‫ﺧﻼﻟ‬ ‫ﻣﻦ‬ ‫ﻟﻴﺘﻢ‬ ‫ﺷﺒﻜﺔ‬ ‫ﻋﻦ‬ ‫ة‬
.‫ق‬‫اﻟﻄﺮ‬ ‫ﻣﻦ‬ ‫ﺷﺒﻜﺔ‬ ‫ﻋ‬ ‫ن‬ ‫ﺘ‬ ‫ﻣﺪﻳ‬ ‫ن‬ ‫ﺑ‬ ‫ﻖ‬‫ﻃﺮ‬‫ﻷﻗﺼﺮ‬ ‫ل‬‫ﻟﻠﻮﺻﻮ‬ ‫ﻘﺔ‬‫اﻟﻄﺮ‬
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.‫ﺎ‬ ‫وﻏ‬ ‫واﻟﺘﺨﺼﻴﺺ‬ ‫اﻟﻨﻘﻞ‬ ‫ﻛﻨﻤﻮذج‬ ،‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﻧﻤﺎذج‬ ‫ﻣﻦ‬ ‫ى‬‫أﺧﺮ‬ ‫أﻧﻮاع‬ ‫ﺑﺎﻟﻄﺒﻊ‬ ‫ﻨﺎك‬ ‫و‬
‫وﻓﻦ‬ ‫ﻋﻠﻢ‬ ‫اﻟﻌﻠﻤﻴﺎت‬ ‫ﺑﺤﻮث‬
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‫ﺣﺼﺎﺋﻴﺔ‬ ‫واﻟﺘﺤﻠﻴﻼت‬ ‫ﺴﺎﺑﺎت‬ ‫ا‬ ‫ﺴﺘﺨﺪم‬ ‫و‬ ‫ﺎﺿﻴﺔ‬‫اﻟﺮ‬ ‫ﺳﺎﻟﻴﺐ‬ ‫ﺗﻮﻓﺮ‬ ‫ﺎ‬ ‫ﻷ‬ ‫ﻋﻠﻢ‬ ،‫وﻓﻦ‬ ‫ﻋﻠﻢ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬
‫وﻛﺬﻟﻚ‬ ‫ﺎ‬‫ر‬ ‫ﻟﻨﻤﻮذج‬ ‫ﺎ‬ ‫ﻠ‬‫وﺗﺤﻮ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﺸﺎف‬ ‫اﻛ‬ ‫ﻋ‬ ‫اﻟﻘﺪرة‬ ‫ﻋ‬ ‫ﻌﺘﻤﺪ‬ ‫ﺎ‬ ‫ﻷ‬ ‫ﻓﻦ‬ ‫و‬ ،‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ﺑﺎﻟﺸ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﻞ‬
‫اﳌﻼ‬‫ار‬‫ﺮ‬‫اﻟﻘ‬ ‫واﺗﺨﺎذ‬ ‫اﻟﻨﻤﻮذج‬ ‫ﺬا‬ ‫ﺗﺤﻠﻴﻞ‬ ‫ﻋ‬ ‫اﻟﻘﺪرة‬ ‫ﻋ‬
.‫ﻋﺪة‬ ‫ات‬‫ر‬‫ﺧﻴﺎ‬ ‫ن‬ ‫ﺑ‬ ‫ﻣﻦ‬ ‫ﺋﻢ‬
-
‫ﻣﺜﻼ‬
‫ﺗﻢ‬ ‫ﺣﻴﺚ‬ ،‫ﺴﻴﻄﺔ‬ ‫إﺑﺪاﻋﻴﺔ‬ ‫ﺑﻔﻜﺮة‬ ‫ﺣﻠﮫ‬ ‫ﺗﻢ‬ ‫واﻟﺬي‬ ‫ﺎﺋﻴﺔ‬‫ﺮ‬ ‫اﻟﻜ‬ ‫اﳌﺼﺎﻋﺪ‬ ‫اﻟﻨﺎس‬ ‫ﺐ‬ ‫ﻳﺼ‬ ‫اﻟﺬي‬ ‫اﳌﻠﻞ‬ ‫ﻠﺔ‬ ‫ﳌﺸ‬‫اﻧﻈﺮ‬
،‫ﺎ‬ ‫ﻓ‬ ‫ﻢ‬ ‫أﻧﻔﺴ‬ ‫ﺔ‬ ‫ﺑﺮؤ‬ ‫اﳌﺼﻌﺪ‬‫ﻣﺴﺘﺨﺪﻣﻮ‬ ‫ﺸﻐﻞ‬ ‫ﻳ‬ ‫ﺣ‬ ‫اﻟﻌﺎﻟﻢ‬ ‫ل‬‫ﺣﻮ‬ ‫اﳌﺼﺎﻋﺪ‬ ‫ﻞ‬ ‫وأﺻﺒﺤﺖ‬ ‫ة‬ ‫ﻛﺒ‬ ‫آة‬‫ﺮ‬‫ﻣ‬ ‫اﺳﺘﺨﺪام‬
-
‫ﺣ‬
‫ﻧﻔﺴﮫ‬ ‫ﺳﺘﺎذ‬
‫ﺣﻴﻨﻤﺎ‬
‫ﻳﻜ‬‫او‬ ‫ﺴﺘﻌﺮض‬
‫ﻋﻠﻤﻴﺔ‬ ‫ﻣﺎدة‬ ‫ﺘﺐ‬
‫ﺧﻄﻄﺖ‬ ‫ﺣﻴﻨﻤﺎ‬ ‫وذﻟﻚ‬ ،
ً
‫ﻓﻌﻠﻴﺎ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫اﺳﺘﺨﺪم‬ ‫ﻓﻘﺪ‬
‫ﻟﻜﺘﺎﺑﺔ‬
ً
‫ﻣﺴﺒﻘﺎ‬
‫ﺸﻮر‬ ‫ﻣ‬ ‫او‬ ‫ﻣﻘﺎل‬
‫اﻟﺬي‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺤﻮث‬ ‫ﻒ‬‫ﻌﺮ‬ ‫ﺣ‬ ،‫ﻣﺜﻞ‬ ‫ار‬‫ﺮ‬‫اﻟﻘ‬ ‫واﺗﺨﺬت‬ ‫ات‬‫ر‬‫ﺧﻴﺎ‬ ‫ﻋﺪة‬ ‫واﺳﺘﻌﺮض‬
‫ﺘﮫ‬ ‫ﻛﺘ‬
‫اﻟﺒﺪاﻳﺔ‬
‫ﻳﻤﻜ‬ ‫ﻣﺎ‬ ‫ﺑﺄﻓﻀﻞ‬ ‫اﻟﻔﻜﺮة‬ ‫ﺗﺼﻠﻚ‬ ‫ﻲ‬ ‫اﳌﺨﺘﻠﻔﺔ‬ ‫ﻒ‬‫اﻟﺘﻌﺎر‬ ‫ﻣﻦ‬ ‫اﻟﻜﺜ‬ ‫ن‬ ‫ﺑ‬ ‫ﻣﻦ‬ ‫اﺧﺘﻴﺎرﻩ‬ ‫ﺗﻢ‬ ‫ﻗﺪ‬ ،
‫ﻦ‬
‫أﻗﻞ‬ ،
! ْ
‫اﻟﻮﻗﺖ‬ ‫ﻧﻔﺲ‬ ‫وﻣﻨﻚ‬ ّ
ِ‫ﻣ‬ ،‫ﻣﻤﻜﻦ‬ ‫ﺪ‬ ‫وﺟ‬ ‫وﻗﺖ‬

5. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
5
‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬
LinearProgramming
‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬
Linear programming
‫ﺦ‬‫ﺗﺎر‬ ‫ﻌﻮد‬ ‫و‬ ،‫ات‬‫ر‬‫ا‬‫ﺮ‬‫اﻟﻘ‬ ‫اﺗﺨﺎذ‬ ‫ﻣﺠﺎل‬
ً
‫ﺷﻴﻮﻋﺎ‬ ‫ﻛ‬ ‫ﺳﻠﻮب‬ ‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﺪ‬ّ‫ﻌ‬
ُ
‫ﻋﺎم‬ ‫إ‬ ‫ﺎ‬ ‫إﻳﺠﺎد‬
١٩٤٧
،‫ار‬‫ﺮ‬‫اﻟﻘ‬ ‫ﺘﺨﺬ‬ُ‫ﻣ‬ ‫ﻮاﺟﮫ‬
ُ
‫ﺗ‬ ‫اﻟ‬ ‫ﻞ‬ ‫اﳌﺸﺎ‬ ‫ﻞ‬ ٍ
‫ﺴﺘﺤﺪث‬ُ‫ﻣ‬ ٍ
‫ﻛﺄﺳﻠﻮب‬ ‫ﺎ‬ ‫ﺑﺈدﺧﺎﻟ‬ ‫ج‬ ‫داﻧ‬ ‫ﺟﻮرج‬ ‫اﻟﻌﺎﻟﻢ‬ ‫ﻗﺎم‬ ‫ﺣﻴﺚ‬ ‫م‬
‫ﻳﻤﻜﻨﻨﺎ‬ ‫ذﻟﻚ‬ ‫ﻋ‬ ً‫ﻨﺎء‬‫و‬
‫أﺳﻠ‬ ‫ﻋﻦ‬
ٌ
‫ة‬‫ر‬‫ﻋﺒﺎ‬ ‫ﺎ‬ ّ‫ﺑﺄ‬ ‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻒ‬‫ﻌﺮ‬
ِ
‫ﻟﻐﺎﻳﺎت‬ ‫ﺴﺘﺨﺪم‬ُ
ٍ ‫ﺎ‬‫ر‬ ٍ
‫ﻮب‬
‫د‬‫ر‬‫اﳌﻮا‬ ‫اﺳﺘﺨﺪام‬ ‫اﳌﻄﺮوﺣﺔ‬ ‫اﻟﺒﺪاﺋﻞ‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ن‬ ‫ﺑ‬ ‫ﻣﻦ‬ ‫ﻣﺜﻞ‬ ‫ار‬‫ﺮ‬‫اﻟﻘ‬ ‫واﺗﺨﺎذ‬ ‫اﻟﺘﺨﻄﻴﻂ‬
.‫ﺎن‬ ‫ﻣ‬ ‫ﻗﺪر‬ ‫ﻠﻔﺔ‬ ‫اﻟﺘ‬ ‫ﻗﻴﻤﺔ‬ ‫وﺗﺨﻔﻴﺾ‬ ،‫ﻌﻈﻴﻤﮫ‬‫و‬ ‫ﺢ‬ ّ‫اﻟﺮ‬ ‫ﺎدة‬‫ﻟﺰ‬
ً
‫ﺳﻌﻴﺎ‬ ‫ﺮة‬
ّ
‫اﳌﺘﻮﻓ‬
‫دور‬ ‫ﻟﺘﻌﻈﻴﻢ‬ ‫ﺆدﻳﺔ‬
ُ
‫اﳌ‬ ‫ﻞ‬ ‫اﳌﺸﺎ‬ ِ‫ﺔ‬ ‫ﻣﻌﺎ‬
ً
‫ﻤﺎ‬ ‫ﻣ‬
ً
‫دورا‬ ‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﺗﻠﻌﺐ‬
‫ﻣﺎ‬ ‫ﻣﺠﺎل‬ ‫ﺎ‬ ‫ﺗﺼﻐ‬‫أو‬ ‫ﺪاف‬
‫وذﻟﻚ‬
‫ﺑﺎﻻﻋﺘﻤ‬
‫ﻋ‬ ‫ﺎد‬
‫ﺘﺨﺬ‬ ُ‫ﻣ‬ ‫ﺪﻋﻢ‬ِ‫ﻟ‬ ِ‫ﻤﻴﺔ‬ ِ‫ﻏﺎﻳﺔ‬ ٌ
‫أﺳﻠﻮب‬ ‫ﺎ‬ ّ‫أ‬ ‫ﻋ‬ ‫ﺎ‬ ‫وﺻﻔ‬ ‫ﻤﻜﻨﻨﺎ‬ُ‫ﻳ‬ ‫ﻛﻤﺎ‬ ،‫اﻟﺔ‬ ّ‫اﻟﺪ‬ ‫ات‬ ‫ﺘﻐ‬
ُ
‫اﳌ‬ ‫ﻣﻦ‬ ٍ‫ﻋﺪد‬ ‫ﻋ‬ ٍ‫ﻣﻔﺮوﺿﺔ‬ ‫ﻗﻴﻮد‬ ‫ﻣﻦ‬‫ﻳﺘﻮﻓﺮ‬ ‫ﻣﺎ‬
.‫اﻟﻌﻠﻤﻴﺔ‬ ‫ق‬‫اﻟﻄﺮ‬ ‫إ‬ ‫ﻨﺎد‬ ‫ﺑﺎﻻﺳ‬ ‫ﻴﺢ‬ ‫واﻟ‬ ‫ﻣﺜﻞ‬ ‫ار‬‫ﺮ‬‫اﻟﻘ‬ ‫اﺗﺨﺎذ‬ ‫ﻣﻦ‬ ‫اروﺗﻤﻜﻴﻨﮫ‬‫ﺮ‬‫اﻟﻘ‬
‫ﻌﺒ‬
‫ﻣﺠﺔ‬ ‫اﻟ‬
‫ﻌ‬
‫وﺗﺤﻘ‬ ‫ﻟﺒﻠﻮغ‬ ‫ﻣﺎ‬ ‫ﻣﻮﺿﻮع‬ ‫أو‬ ‫ﻣﺴﺄﻟﺔ‬ ‫ﻞ‬ ‫ﺧﻄﻮات‬ ‫وﺿﻊ‬
‫ﯿ‬
‫ﻖ‬
‫ﻣﻌ‬ ‫ﺪف‬
،‫ن‬
‫ﻌﺒ‬ ‫أﻣﺎ‬
‫ﺧﻄ‬
‫ﯿ‬
‫ﺔ‬
‫ﻓ‬
‫ﯿ‬
‫ﻌ‬
‫اض‬ ‫اﻓ‬
‫ﻐ‬
‫ﺧﻄ‬ ‫ﺑﺼﻮرة‬ ‫ﺎ‬ ‫اﺳ‬‫ر‬‫ﺑﺪ‬ ‫ﻧﻘﻮم‬ ‫اﻟ‬ ‫ﺮة‬ ‫اﻟﻈﺎ‬
‫ﯿ‬
‫ﺔ‬
‫ﻣﺴﺘﻘ‬ ‫ﺧﻂ‬ ‫ﻞ‬ ‫ﺷ‬ ‫)ﻋ‬
‫ﯿ‬
‫ﻢ‬
‫(وﻛﺜ‬
‫ا‬
‫ﻣﺎ‬
‫ﺴﺘﺨﺪم‬
‫ﻟﺘﻘﺮ‬ ‫اض‬ ‫ﻓ‬ ‫ﺬا‬
‫ﺐ‬
‫اﻟﻮاﻗﻊ‬
‫ﺻ‬ ‫إ‬
‫ﯿ‬
‫ﺎﻏﺔ‬
‫ر‬
‫ﺎﺿ‬
‫ﯿ‬
‫ﺔ‬
‫ﺗﺠﺪر‬ ‫وﻣﻤﺎ‬ .‫ﻠﺔ‬ ‫ﺳ‬
‫ﺷﺎرة‬
‫إﻟ‬
‫ﯿ‬
‫ﮫ‬
‫ا‬ ‫أن‬ ‫ﻮ‬
‫ﻟﻐﺎ‬
‫ﯾ‬
‫ﺔ‬
‫ﺗﻄﺒ‬ ‫ﻣﻦ‬
‫ﯿ‬
‫ﻖ‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫أﺳﻠﻮب‬
‫ﯿ‬
‫ﺔ‬
‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻧﻤﻮذج‬ ‫ﺣﻞ‬ ‫إ‬ ‫ل‬‫اﻟﻮﺻﻮ‬
‫ﻄ‬ ‫ا‬
‫ﯿ‬
‫ﺔ‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫)وﻧﻤﻮذج‬
‫ﯿ‬
‫ﺔ‬
‫واﳌﺘﺒﺎ‬ ‫اﳌﻌﺎدﻻت‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻋﻦ‬ ‫ﻋﺒﺎرة‬‫ﻮ‬
‫ﯾ‬
‫ﻨﺎت‬
‫اﳌﻌﺎدﻻت‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻞ‬ ‫ﻟ‬ ‫أن‬ ‫ﺗ‬ ‫وﻻ‬ ،
‫ﻣﻌﺎدﻻت‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬ ‫ﻣﺎ‬ ‫وﻋﺎدة‬ ،‫ﺣﻼ‬
‫آﻧ‬
‫ﯿ‬
‫ﺔ‬
‫ا‬
‫ل‬‫ﻠﻮ‬
‫إ‬
‫ﯾ‬
‫ﺠﺎد‬
‫ﻗ‬
‫ﯿ‬
‫ﻢ‬
‫اﳌﺘﻐ‬
،‫ات‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻧﻤﻮذج‬ ‫ﺣﻞ‬ ‫ﺣﺎﻟﺔ‬ ‫و‬
‫ﯿ‬
‫ﺔ‬
‫إ‬ ‫إ‬ ‫ﺴ‬ ‫داﺋﻤﺎ‬
‫ﯾ‬
‫ﺠﺎد‬
‫ﻞ‬ ‫ا‬
‫أﻧﻮاع‬ ‫ﺛﻼث‬ ‫ﻋ‬ ‫ل‬‫ﻠﻮ‬ ‫ا‬ ‫ن‬‫ﻮ‬ ‫وﺗ‬ ‫ﻣﺜﻞ‬
-
‫إﻟ‬ ‫ل‬‫اﻟﻮﺻﻮ‬ ‫ﻣﻤﻜﻦ‬ ‫ﺣﻞ‬‫ﻮ‬ ‫و‬ :‫ﻞ‬ ‫ا‬
‫ﯿ‬
‫ﮫ‬
‫أ‬
‫ﯾ‬
‫ﺔ‬
.‫اﳌﻌﺎدﻻت‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬
-
‫اﻟﺬي‬ ‫ﻞ‬ ‫ا‬ ‫ﻮ‬ ‫و‬ :‫اﳌﻤﻜﻦ‬ ‫ﻞ‬ ‫ا‬
‫ﯾ‬
‫ﻤﻜﻦ‬
‫إ‬
‫ﯾ‬
‫ﺠﺎدﻩ‬
‫ﻞ‬ ‫ا‬ ‫ﺬا‬ ‫و‬ ‫و‬ ‫ﺎﻟﺔ‬ ‫ا‬ ‫ﻞ‬ ‫ا‬ ‫إ‬ ‫اﻟﺘﻮﺻﻞ‬ ‫ﻌﺪ‬
‫ﯾ‬
‫ﺤﻘﻖ‬
‫اﻟﻘ‬
‫ﯿ‬
‫ﻮد‬
‫ﺎﻓﺔ‬
.‫ﻋﺎم‬ ‫ﻞ‬ ‫ﺸ‬
-
‫اﻟﺬي‬ ‫ﻞ‬ ‫ا‬‫ﻮ‬ ‫و‬ :‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬
‫ﯾ‬
‫ﻤﻜﻦ‬
‫إ‬
‫ﯾ‬
‫ﺠﺎدﻩ‬
‫ﻞ‬ ‫ا‬ ‫ﺬا‬ ‫و‬ ،‫اﳌﻤﻜﻦ‬ ‫ﻞ‬ ‫ا‬ ‫إ‬ ‫اﻟﺘﻮﺻﻞ‬ ‫ﻌﺪ‬
‫ﯾ‬
‫ﺤﻘﻖ‬
‫اﻟﻘ‬
‫ﯿ‬
‫ﻮد‬
‫داﻟﺔ‬ ‫ﺑﻮﺟﻮد‬ ‫ﺎﻓﺔ‬
.‫ﺪف‬ ‫اﻟ‬
-
‫ﺬا‬ ‫و‬
‫اﻟﺼﺪد‬
‫ﯾ‬
‫ﺠﺐ‬
‫ﻻ‬ ‫اﳌﻤﻜﻦ‬ ‫ﻞ‬ ‫ا‬ ‫أن‬ ‫ﻣﻦ‬ ‫اﻟﺘﺄﻛﺪ‬
‫ﯾ‬
‫ﺘﺤﻘﻖ‬
‫وﻻ‬ ،‫ﻞ‬ ‫ا‬ ‫وﺟﻮد‬ ‫ﻌﺪ‬
‫ﯾ‬
‫ﻤﻜﻦ‬
‫ﺗﺤﻘ‬
‫ﯿ‬
‫ﻖ‬
‫ﻞ‬ ‫ا‬
‫ﻣﺜﻞ‬
‫أن‬ ‫ﻌﺪ‬ ‫إﻻ‬
‫ﯾ‬
‫ﺘﺤﻘﻖ‬
.‫اﳌﻤﻜﻦ‬ ‫ﻞ‬ ‫ا‬
‫ﻣﺘﻄﻠﺒﺎت‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻧﻤﻮذج‬ ‫وﻓﺮوض‬
‫ﯿ‬
‫ﺔ‬
:
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫اﺳﺘﺨﺪام‬ ‫ﻣﺘﻄﻠﺒﺎت‬
‫ﯿ‬
‫ﺔ‬
:
-
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻠﺔ‬ ‫ﻣﺸ‬ ‫ﺗﺘﻄﻠﺐ‬
‫ﯿ‬
‫ﺔ‬
‫أﺳﺎﺳ‬ ‫ﺧﺼﺎﺋﺺ‬ ‫ﺧﻤﺲ‬
‫ﯿ‬
‫ﺔ‬

6. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
6
o
‫ﺗﺤ‬
‫ﺪ‬
‫ﯾ‬
‫ﺪ‬
‫ﺪف‬ ‫اﻟ‬
‫ﻟﺘﺤﻘ‬ ‫ﺴ‬ ‫ﻣﺎ‬ ‫أي‬ :
‫ﯿ‬
‫ﻘﮫ‬
‫ز‬ ‫إﻣﺎ‬‫ﻮ‬ ‫و‬
‫ﺎدة‬
‫ﺗﻘﻠ‬‫أو‬ ‫رﺎح‬
‫ﯿ‬
‫ﻞ‬
‫ﺑﺼ‬ ‫ﻋﻨﮫ‬ ‫ﻣﻌ‬ ،‫ﻠﻔﺔ‬ ‫اﻟ‬
‫ﯿ‬
‫ﻐﺔ‬
‫ر‬
‫ﺎﺿ‬
‫ﯿ‬
‫ﺔ‬
‫ﯾ‬
‫ﻄﻠﻖ‬
‫ﻋﻠ‬
‫ﺎ‬
‫اﻟ‬ ‫داﻟﺔ‬
: ‫اﻟﺘﺎ‬ ‫ﻞ‬ ‫ﺑﺎﻟﺸ‬ ‫ﺗﺼﺎغ‬ ‫ﺣﻴﺚ‬ ‫ﺪف‬
MinZ 2 x  3 ‫اﻟﺘﻘﻠﻴﻞ‬ ‫ﺣﺎﻟﺔ‬
MaxZ 2 x 3y ‫اﻟﺘﻌﻈﻴﻢ‬ ‫ﺣﺎﻟﺔ‬
o
:‫اﻟﺒﺪاﺋﻞ‬ ‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫ﺗﻮﻓ‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﺴﺘﺨﺪم‬
‫ﯿ‬
‫ﺔ‬
‫ﻟﺪ‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬ ‫ﻋﻨﺪﻣﺎ‬
‫ﯾ‬
‫ﻨﺎ‬
‫دا‬ ‫ﻻ‬ ً ‫ﺎن‬ ‫ﻓﺈذا‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﻞ‬ ‫ﺑﺪاﺋﻞ‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻻﺳﺘﺨﺪام‬
‫ﯿ‬
‫ﺔ؛‬
‫ﺑﺪ‬ ‫ﻨﺎك‬
‫ﯾ‬
‫ﻞ‬
‫إذا‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﻞ‬ ‫واﺣﺪ‬
o
‫ﻣﺤﺪود‬
‫ﯾ‬
‫ﺔ‬
‫اﳌﻮارد‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻻﺳﺘﺨﺪام‬ ‫ﻧﺤﺘﺎج‬ :
‫ﯿ‬
‫ﺔ‬
‫ﺸﺮ‬ ‫اﻟ‬ ‫ﺎﳌﻮارد‬ (‫)ﻧﺎدرة‬ ‫ﻣﺤﺪدة‬ ‫اﳌﻮارد‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬ ‫ﻋﻨﺪﻣﺎ‬
‫ﺔ‬
،
‫أو‬
‫ﻟﺘﺤﻘ‬ ‫ﺷﺮوط‬ ‫ﺑﻤﺜﺎﺑﺔ‬ ‫و‬.‫ﻻت‬ ‫اﺷﺘﻐﺎل‬ ‫ﺳﺎﻋﺎت‬‫أو‬ ،‫اﳌﻮاد‬
‫ﯿ‬
‫ﻖ‬
‫ﻟﺪ‬ ‫ﺎن‬ ‫ﻓﺈذا‬ ،‫ﺪف‬ ‫اﻟ‬
‫ﯾ‬
‫ﻨﺎ‬
400
‫اﻟﻘﺴﻢ‬ ‫ﺳﺎﻋﺔ‬
‫ل‬‫و‬
‫ﻟﺴﺎﻋﺘ‬ ‫ﻧﺤﺘﺎج‬ ‫وﻛﻨﺎ‬
‫ن‬
‫ﻹ‬ ‫ﺳﺎﻋﺎت‬ ‫وﺛﻼﺛﺔ‬ ‫ل‬‫و‬ ‫اﳌﻨﺘﻮج‬ ‫ﻹﻧﺘﺎج‬
‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﺬﻩ‬ ‫ﻋﻦ‬ ‫ﻌ‬ ‫ﻲ‬ ‫اﻟﺜﺎ‬ ‫اﳌﻨﺘﺞ‬ ‫ﻧﺘﺎج‬
‫ﺗﻴﺔ‬ ‫ﺑﺎﳌﻌﺎدﻟﺔ‬
+ ≤
o
:‫ﺧﻄﻴﺔ‬ ‫ﻋﻼﻗﺔ‬ ‫وﺟﻮد‬
‫ان‬
‫ﻄ‬ ‫ا‬
‫ﯿ‬
‫ﺔ‬
‫ﻣﺠﺔ‬ ‫اﻟ‬
‫ﯾ‬
‫ﺠﺐ‬
‫اﻟﻘ‬ ‫و‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﺗﺘﻮﻓﺮ‬ ‫أن‬
‫ﯿ‬
‫ﻮد‬
،(‫)اﳌﻮارد‬
‫ﺑﺤ‬
‫ﯿ‬
‫ﺚ‬
‫أ‬
‫ن‬
‫ﻐ‬ ‫أي‬
‫ﻛﻤ‬
‫ﯿ‬
‫ﺎت‬
‫ﻧﺘﺎج‬
‫ﯾ‬
‫ﺆدي‬
‫ز‬ ‫إ‬
‫ﺎدة‬
‫ﺗﻘﻠ‬ ‫أو‬ ‫رﺎح‬
‫ﯿ‬
‫ﻞ‬
‫ﻠ‬ ‫اﻟﺘ‬
‫ﯿ‬
‫ﻒ‬
‫ﺧﻄﻲ‬ ‫ﻞ‬ ‫ﺸ‬
(‫)ﻃﺮدي‬
‫ز‬ ‫ﻣﻊ‬
‫ﺎدة‬
‫ﻛﻤ‬
‫ﯿ‬
‫ﺔ‬
‫ز‬ ‫ﻣﻊ‬ ‫ﺧﻄﻲ‬ ‫ﻞ‬ ‫ﺸ‬ ‫ﻨﻔﺬ‬ ‫ﺴ‬ ‫اﳌﻮارد‬ ‫وﻛﺬﻟﻚ‬ ،‫ﻧﺘﺎج‬
‫ﺎدة‬
‫ﻛﻤ‬
‫ﯿ‬
‫ﺔ‬
‫ﻧﺘﺎج؛‬
o
‫اﻟﻘ‬
‫ﯿ‬
‫ﻮد‬
‫ﻏ‬
‫اﻟﺴﺎﻟﺒﺔ‬
‫اﻟﺸﺮط‬ ‫ﺬا‬ ‫إن‬ :
‫ﯾ‬
‫ﻠ‬
‫ﻓﺮﺿ‬ ‫إﺣﺪى‬
‫ﯿ‬
‫ﺎت‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬
‫ﯿ‬
‫ﺔ‬
‫اﻟﺴﻠﺒ‬ ‫ﻋﺪم‬ ‫ﺷﺮط‬‫ﻮ‬ ‫و‬
‫ﯿ‬
‫ﺔ‬
.
‫وﻟﺬﻟﻚ‬
‫ﻻ‬
‫ﯾ‬
‫ﻤﻜﻦ‬
‫أن‬
‫ﯾ‬
‫ن‬‫ﻮ‬
‫اﻟﻘ‬ ‫أﺣﺪ‬
‫ﯿ‬
‫ﻮد‬
‫ﯾ‬
‫ﺘﺞ‬
‫ﻣﺘﻐ‬
‫ات‬
+ ≤ −

7. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
7
‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﺗﻄﺒﻴﻖ‬ ‫ﻣﺠﺎﻻت‬
:
١
-
،‫اﳌﺨﺮﺟﺎت‬ ‫ﻣﻦ‬
ّ
‫ﻛﻼ‬ ‫ﺸﻤﻞ‬‫و‬ ،‫ﻧﺘﺎج‬ ‫ﺗﺨﻄﻴﻂ‬
٢
-
.‫ﺎدﺗﮫ‬ ‫وز‬ ‫ﺢ‬ ّ‫اﻟﺮ‬ ‫ﻌﻈﻴﻢ‬
َ
‫و‬ ،‫ﻧﺘﺎج‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬ ‫وﺗﺨﻔﻴﺾ‬
٣
-
.‫ﻟﻠﻤﻨﺘﺠﺎت‬ ‫ﻣﺜﻞ‬ ‫ﻞ‬
ّ
‫اﻟﺸ‬ ‫ﺤﺪﻳﺪ‬
َ
‫ﺗ‬
٤
-
.‫ﺪﻣﺎت‬ ‫وا‬ ‫اﳌﻨﺘﺠﺎت‬ ‫ﺗﺼﻤﻴﻢ‬ ِ‫ﻠﺔ‬ ‫ﳌﺸ‬ ‫ل‬‫ﺣﻠﻮ‬ ‫إﻳﺠﺎد‬
٥
-
.‫ﻧﺘﺎج‬ ‫و‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﻟﻨﻈﺎم‬ ‫ﺪﺧﻼت‬
ُ
‫ﻋﻨﺎﺻﺮاﳌ‬ ‫ﺗﺨﻄﻴﻂ‬
٦
-
.‫ﻊ‬ ‫واﻟﺘﻮز‬ ‫ﻘﻞ‬ّ‫اﻟﻨ‬ ِ
‫ﳌﺸﻜﻼت‬ ٍ
‫ل‬‫ﺣﻠﻮ‬ ‫إﻳﺠﺎد‬
٧
-
.‫ﺎ‬ ‫ﺑﻴ‬ ‫ﻣﻦ‬ ‫ﻣﺜﻞ‬ ‫واﺧﺘﻴﺎر‬ ‫ات‬‫ر‬‫ﺜﻤﺎ‬ ‫ﺳ‬ ‫ﺗﺨﻄﻴﻂ‬ ‫ﻠﺔ‬ ‫ﺸ‬ ِ‫ﳌ‬ ‫ل‬‫ﻠﻮ‬ ‫ا‬ ‫ﻣﻦ‬ ٍ‫ﻣﺠﻤﻮﻋﺔ‬ ‫وﺿﻊ‬
‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫اﺳﺘﺨﺪام‬ ‫ﺷﺮوط‬
-
.‫ﻤﻴﺔ‬
َ
‫اﻟﻜ‬ ‫ﺣﻴﺚ‬ ‫ﻣﻦ‬ ‫دارة‬ ‫ﻞ‬َ‫ﺒ‬ِ‫ﻗ‬ ‫ﻣﻦ‬ ‫ﺎ‬ ‫ﺗﺤﻘﻴﻘ‬‫اﳌﺮﺟﻮ‬ ‫ﺪاف‬ ‫ﺗﺤﺪﻳﺪ‬ ‫ﺔ‬
ّ
‫اﻟﺪﻗ‬
-
‫ﻋ‬‫أو‬ ‫ﻳﺠﺎﺑﻴﺔ‬ ‫ﺷﺮوط‬‫ﺗﻮﻓﺮ‬ ‫ﺿﺮورة‬ ‫ﻣﻊ‬ ‫ات‬ ‫ﻣﺘﻐ‬ ‫ﻣﻦ‬ ‫ﻠﺔ‬ ‫ﺸ‬
ُ
‫اﳌ‬ ‫ﻌﺎد‬ ‫أ‬ ‫ن‬ ‫ﺑ‬ ٍ‫ﺧﻄﻴﺔ‬ ٍ‫ﻋﻼﻗﺔ‬ ‫وﺟﻮد‬
.‫اﻟﺴﻠﺒﻴﺔ‬ ‫ﻏ‬ ‫ﻗﻞ‬
-
.‫اﳌﺘﺎﺣﺔ‬ ‫اﳌﻮارد‬ ‫ﺪرة‬
ُ
‫ﻧ‬
‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫اﺳﺘﺨﺪام‬ ‫ﺧﻄﻮات‬
-
.‫ﺎ‬ ‫وﺻﻴﺎﻏ‬ ‫ﺑﺪﻗﺔ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﺗﺤﺪﻳﺪ‬
-
.‫واﳌﻌﺎدﻻت‬ ‫اﳌﺘﺒﺎﻳﻨﺎت‬ ‫ﻋ‬ ‫ﺑﺎﻻﻋﺘﻤﺎد‬ ‫ﺑﺪﻗﺔ‬ ِ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﻋﻦ‬ ‫ﻳﻜﺸﻒ‬ ٍ ‫ﺎ‬‫ر‬ ٍ
‫ﻧﻤﻮذج‬ ‫ﻨﺎء‬ ‫ﺑ‬ ‫ﺮوع‬
‫ﱡ‬
‫اﻟﺸ‬
-
.‫اﳌﻄﺮوﺣﺔ‬ ‫ﻠﺔ‬ ‫ﻟﻠﻤﺸ‬ ‫ﺎ‬ ّ‫اﻟﺮ‬ ‫اﻟﻨﻤﻮذج‬ ‫ﻣﻦ‬ ّ
ٍ
‫ﺣﻞ‬ ‫إﻳﺠﺎد‬
‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫أﺳﺎﻟﻴﺐ‬
‫ﻄﻴﺔ‬
‫ﻣﺮﺗﺪة‬ ‫ﺗﻐﺬﯾﺔ‬
‫ﻣﺨﺮﺟﺎت‬
‫ﻣﺤﺪدة‬ ‫ﺳﯿﺎﺳﺎت‬
‫ﻣﻨﺘﺠﺎت‬
‫ﻋﻤﻠﯿﺎت‬
‫اﻟﺒﺮﻣﺠﺔ‬ ‫ﻧﻤﻮذج‬
‫اﻟﺨﻄﯿﺔ‬
‫ﻣﺪﺧﻼت‬
‫ﻣﺨﺘﻠﻔﺔ‬ ‫ﻣﻮارد‬
‫ﻣﺘﻌﺪدة‬ ‫ﻗﯿﻮد‬
‫اﻟﺤﺴﺎﺳﯿﺔ‬ ‫ﺗﺤﻠﯿﻞ‬
‫اﻟﮭﺪف‬ ‫ﺗﺤﻘﻖ‬
‫اﻟﻤﺜﻠﻰ‬
)
‫وأدﻧﻰ‬ ‫أﻋﻈﻢ‬
(
‫ﻧﻈﺎم‬ ‫ﺿﻤﻦ‬ ‫اﻟﺨﻄﯿﺔ‬ ‫اﻟﺒﺮﻣﺠﺔ‬ ‫ﻟﻤﺸﻜﻠﺔ‬ ‫اﻟﻌﺎم‬ ‫اﻹطﺎر‬ ‫وﺿﻊ‬

8. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
8
-
.‫ﻲ‬ ‫اﻟﺒﻴﺎ‬ ُ
‫ﺳﻠﻮب‬
-
.‫اﻟﺴﻤﺒﻠﻜﺲ‬ ُ
‫أﺳﻠﻮب‬
-
.‫اﻟﻨﻘﻞ‬ ُ
‫أﺳﻠﻮب‬
-
.‫ﺨﺼﻴﺺ‬ّ‫اﻟﺘ‬ ُ
‫أﺳﻠﻮب‬
‫ﺻ‬
‫ﯿ‬
‫ﺎﻏﺔ‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻧﻤﻮذج‬ ‫ﺑﻨﺎء‬‫أو‬
‫ﯿ‬
‫ﺔ‬
:
‫ﺻ‬ ‫إن‬
‫ﯿ‬
‫ﺎﻏﺔ‬
‫إدار‬ ‫ﻠﺔ‬ ‫ﻣﺸ‬
‫ﺔ‬
‫ﻣﻌ‬
‫ﯿ‬
‫ﻨﺔ‬
‫ﺧﻄ‬ ‫ﺑﺮﻣﺠﺔ‬ ‫ﻣﺴﺄﻟﺔ‬ ‫ﻞ‬ ‫ﺸ‬
‫ﯿ‬
‫ﺔ‬
‫ﺗﻄﻮ‬ ‫ﺳﺎﺑﻘﺎ‬ ‫أﺷﺮﻧﺎ‬ ‫ﻛﻤﺎ‬ ‫ﺗﻘﺘ‬
‫ﺮ‬
‫ر‬ ً ‫ﻧﻤﻮذج‬
‫ﯾ‬
‫ﺎ‬
‫ﯾ‬
‫ﻤﺜﻞ‬
‫ﺎ‬ ‫ا‬
‫أو‬ ‫ﻟﺔ‬
‫دار‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬
،‫ﺔ‬
‫ﻓﺈﻧﮫ‬ ‫ﺬا‬ ‫و‬
‫ﯾ‬
‫ﺠﺐ‬
ً
‫ﻤﺎ‬ ‫ﻓ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫أو‬ ‫ي‬‫دار‬ ‫اﳌﻮﻗﻒ‬ ‫ﻢ‬ ‫ﻓ‬
‫دﻗ‬
‫ﯿ‬
ً
‫ﻘﺎ‬
‫ﺻ‬ ‫إن‬ ،‫ﺎ‬ ‫ﻠ‬ ‫و‬ ‫ﻄﻮة‬ ‫ا‬ ‫و‬
‫ﯿ‬
‫ﺎﻏﺔ‬
‫ﻧ‬
‫ﻤﻮذج‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬
‫ﯿ‬
‫ﺔ‬
‫ﯾ‬
‫ﻤﻜﻦ‬
‫ﺧﻄﻮاﺗ‬ ‫ﺗﺠﻤﻞ‬ ‫أن‬
‫ﮫ‬
:‫ﻲ‬ ‫ﺑﺎﻵ‬
-
‫واﻟﺪﻗ‬ ‫ﺎﻣﻞ‬ ‫اﻟ‬ ‫ﻢ‬ ‫اﻟﻔ‬
‫ﯿ‬
‫ﻖ‬
‫دار‬ ‫ﻠﺔ‬ ‫ﻟﻠﻤﺸ‬
‫ﺔ‬
‫اﻟ‬
‫ﯾ‬
‫ﺎ‬ ‫ﻮاﺟ‬
‫اﳌﺪ‬
‫ﯾ‬
‫ﺮ؛‬
-
‫ﯿ‬
‫ﺺ‬
‫واﻟﻘ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬
‫ﯿ‬
‫ﻮد‬
‫اﳌﺤﺪدة؛‬
-
‫ﺗﺤﺪ‬
‫ﯾ‬
‫ﺪ‬
‫ﻣﺘﻐ‬
‫ات‬
‫ار؛‬‫ﺮ‬‫اﻟﻘ‬
-
-
‫ﻣﺘﻐ‬ ‫اﺳﺘﺨﺪام‬
‫ات‬
‫اﻟﺮ‬ ‫ات‬ ‫اﻟﻌ‬ ‫ﻛﺘﺎﺑﺔ‬ ‫اﻟﻘﺮار‬
‫ﺎﺿ‬
‫ﯿ‬
‫ﺔ‬
‫واﻟﻘ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﻣﻦ‬ ‫ﻞ‬ ‫ﻟ‬
‫ﯿ‬
‫ﻮد‬
.
‫ﺻ‬
‫ﯿ‬
‫ﺎﻏﺔ‬
‫اﻟﺮ‬ ‫اﻟﻨﻤﻮذج‬
‫ﺎ‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫ﻟﻠ‬
‫ﯿ‬
‫ﺔ‬
:
‫ﻣﻦ‬
‫ﺻ‬ ‫اﺟﻞ‬
‫ﯿ‬
‫ﺎﻏﺔ‬
‫ﻄ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻧﻤﻮذج‬
‫ﯿ‬
‫ﺔ‬
‫ﯾ‬
‫ﺠﺐ‬
‫ﺳﺎﺳ‬ ‫اﻟﻌﻨﺎﺻﺮ‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺎت‬ ‫ﺗﻮﻓﺮﺛﻼث‬
‫ﯿ‬
‫ﺔ‬
: ‫و‬
-
‫ﺗﺤﺪ‬
‫ﯾ‬
‫ﺪ‬
‫ﻛﻤ‬ ‫ﺑﺼﻮرة‬ ‫ﺪف‬ ‫اﻟ‬
‫ﯿ‬
‫ﺔ‬
:
‫ﻌ‬
‫ﻌﻈ‬ ‫اﳌﻄﻠﻮب‬ ‫اﻟﺪاﻟﺔ‬ ‫ﻋﻨﺪ‬ ‫ﻋﺒﺎرة‬ ‫و‬ ‫ﺪف‬ ‫اﻟ‬ ‫ﺑﺪاﻟﺔ‬ ‫ﻋﻨﮫ‬
‫ﯿ‬
‫ﺎ‬ ‫ﻤ‬
‫ﺗﺪﻧ‬‫أو‬
‫ﯿ‬
‫ﺎ‬
‫ﻋﺎد‬ ‫و‬
‫ﻣﺎ‬ ‫ة‬
‫ن‬‫ﻮ‬ ‫ﺗ‬
‫ﺻﻮرة‬
‫ﻧﻘﺪ‬
‫ﯾ‬
‫ﺔ‬
‫ﻃﺒ‬ ‫أو‬
‫ﯿ‬
‫ﻌ‬
‫ﯿ‬
‫ﺔ‬
‫و‬
‫ﺘﻮﻗﻒ‬
‫ﻃﺒ‬ ‫ﻋ‬ ‫ذﻟﻚ‬
‫ﯿ‬
‫ﻌﺔ‬
‫ﺗﺤﻠ‬ ‫ﺔ‬‫اﳌﻄﻠﻮ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬
‫ﯿ‬
‫ﺎ‬ ‫ﻠ‬
‫و‬
‫ﺠﺐ‬
‫أن‬
‫ﯾ‬
‫ن‬‫ﻮ‬
‫ﺑﺎﻹ‬
‫ﺎن‬ ‫ﻣ‬
‫ﻛﺄن‬
‫ﯾ‬
‫ن‬‫ﻮ‬
‫ﺗﺤﻘ‬ ‫ﺪف‬ ‫اﻟ‬
‫ﯿ‬
‫ﻖ‬
‫ﻣﺎ‬ ‫اﻛ‬
‫ﯾ‬
‫ﻤﻜﻦ‬
‫ﺗﺄﻣ‬ ‫أو‬ ‫ﺢ‬‫اﻟﺮ‬ ‫ﻣﻦ‬
‫ن‬
‫ﻣﺎ‬‫اﺻﻐﺮ‬
‫ﯾ‬
‫ﻤﻜﻦ‬
‫ﻣﻦ‬
‫اﻟﺘﻌﺒ‬
‫ﻛﻤ‬ ‫ﺪف‬ ‫اﻟ‬ ‫ﻋﻦ‬
‫ﯿ‬
‫ﺎ‬
‫ت‬
‫ﻠﻔﺔ‬ ‫اﻟ‬
‫ﺗ‬ ‫أو‬
‫ﻮﻓ‬
‫ﻣﺎ‬ ‫أﻋﻈﻢ‬
‫ﯾ‬
‫ﻤﻜﻦ‬
‫ﺪ؛‬ ‫وا‬ ‫اﻟﻮﻗﺖ‬ ‫ﻣﻦ‬
-
‫ﺗﺤﺪ‬
‫ﯾ‬
‫ﺪ‬
‫اﻟﻘ‬
‫ﯿ‬
‫ﻮد‬
:
‫ﯾ‬
‫ﺠﺐ‬
‫ﻛﻤﺎ‬ ،‫ﻣﺤﺪدة‬ ‫اﳌﺘﺎﺣﺔ‬ ‫اﳌﻮارد‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬ ‫أن‬
‫ﯾ‬
‫ﺠﺐ‬
‫ﻟﻠﻘ‬ ‫ﻗﺎﺑﻠﺔ‬ ‫اﳌﻮارد‬ ‫ﺗﻠﻚ‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬ ‫أن‬
‫ﯿ‬
‫ﺎس‬
‫و‬
‫ﺘﻢ‬
‫اﻟﺘﻌﺒ‬
‫ﺎ‬ ‫ﻋ‬
‫ﺑﺼ‬
‫ﯿ‬
‫ﻐﺔ‬
‫ر‬
‫ﺎﺿ‬
‫ﯿ‬
‫ﺔ‬
‫ﻞ‬ ‫ﺷ‬ ‫ﻋ‬
‫ﻣﺘﺒﺎﻳﻨﺎت‬
‫ﺧﻠ‬‫أو‬ ،‫ﻣﻌﺎدﻻت‬‫أو‬
‫ﯿ‬
‫ﻂ‬
‫ﺴ‬‫و‬ ‫ﺎ‬ ‫ﻣ‬
‫ﯾ‬
‫ﺎﻟﻘ‬
‫ﯿ‬
‫ﻮد‬
‫اﻟ‬
‫ﯿ‬
‫ﻠ‬
‫ﯿ‬
‫ﺔ؛‬
-
‫اﻟﺴﻠﺒ‬ ‫ﻋﺪم‬ ‫ﺷﺮط‬
‫ﯿ‬
‫ﺔ‬
:
‫إذ‬
‫ﯾ‬
‫ﺠﺐ‬
‫اﳌﺘﻐ‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬ ‫أن‬
‫ات‬
‫ار‬‫ﺮ‬‫اﻟﻘ‬
‫ﺔ‬
‫ﻗ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬
‫ﯿ‬
‫ﺪ‬
‫ﻣﺘﻐ‬ ‫اﺳﺔ‬‫ر‬‫اﻟﺪ‬
‫ات‬
‫ﺻﻔﺮ‬ ‫أو‬ ‫ﻣﻮﺟﺒﺔ‬
‫ﺔ‬
‫وﻏ‬
.‫ﺳﺎﻟﺒﺔ‬
‫و‬
‫ﻤﻜﻦ‬
‫اﻟﺼ‬ ‫وﺿﻊ‬
‫ﯿ‬
‫ﻐﺔ‬
‫ﻣﺠﺔ‬ ‫ﻟﻠ‬ ‫اﻟﻌﺎﻣﺔ‬
( ) =
:
∑ ∑ (≤, =, ≥)

9. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
9
≥ 0
‫أن‬ ‫إذ‬
:
j
,c
i
,b
ij
a
‫ﺛﻮ‬
‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﺳﻴﺎق‬ ‫ﻣﻦ‬ ‫ﺗﺤﺪد‬ ‫اﺑﺖ‬
Z
‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬
j
X
‫ات‬ ‫اﳌﺘﻐ‬
‫ﺎ‬ ‫ﺸﺄ‬ ‫اﻟﻘﺮار‬ ‫اﺗﺨﺎذ‬ ‫اﳌﻄﻠﻮب‬
i
b
‫اﳌﺤﺪدة‬ ‫اﳌﻮارد‬ ‫ﺗﻤﺜﻞ‬
ij
a
‫اﻟﻨﻮع‬ ‫ﻣﻦ‬ ‫اﳌﺤﺪدة‬ ‫اﳌﻮارد‬ ‫ﻛﻤﻴﺔ‬ ‫ﺗﻤﺜﻞ‬
i
‫ﺸﺎط‬ ‫اﻟ‬ ‫وﺣﺪات‬ ‫ﻣﻦ‬ ‫وﺣﺪة‬ ‫ﻞ‬ ‫ﻟ‬ ‫ﺎ‬ ‫ﺗﺨﺼﻴﺼ‬ ‫واﻟﻼزم‬
j
j
C
‫اﳌﻮرد‬ ‫ﺗﺨﺼﻴﺺ‬ ‫ﻋﻦ‬ ‫اﻟﻨﺎﺗﺠﺔ‬ ‫ﻠﻔﺔ‬ ‫اﻟﺘ‬‫أو‬ ‫ﺢ‬‫اﻟﺮ‬ ‫ﺗﻤﺜﻞ‬
i
‫ﺸﺎط‬ ‫اﻟ‬ ‫ﻣﻦ‬ ‫واﺣﺪة‬ ‫وﺣﺪة‬ ‫ﻹﻧﺘﺎج‬
j
‫ﻦ‬‫ﺗﻤﺮ‬
‫ﻧﻮﻋ‬ ‫ﺎت‬ ‫اﻟﺸﺮ‬ ‫إﺣﺪى‬ ‫ﺘﺞ‬ ‫ﺗ‬
‫ن‬
‫ﻧﻮع‬ ،‫اﻟﺴﻠﻊ‬ ‫ﻣﻦ‬
A
‫وﻧﻮع‬
B
‫ﻣﺮﺣﻠﺔ‬ ‫ﻞ‬ ‫اﺣﻞ‬‫ﺮ‬‫ﻣ‬ ‫ﺛﻼث‬ ‫ﻋ‬ ‫ﺳﻠﻌﺔ‬ ‫ﻞ‬ ‫ﺗﺼﻨﻊ‬،
‫ﺗﺼ‬ ‫ﺎن‬ ‫ﻓﺈذا‬ ،‫اﻟﺸﺮﻛﺔ‬ ‫اﳌﻮﺟﻮدة‬ ‫اﻟﺜﻼﺛﺔ‬ ‫ﻗﺴﺎم‬ ‫اﺣﺪ‬
‫ﯿ‬
‫ﻊ‬
‫اﻟﺴﻠﻌﺔ‬
A
‫ﯾ‬
‫ﺤﺘﺎج‬
‫ﺳﺎﻋﺘ‬ ‫إ‬
‫ن‬
‫ﻋﻤﻞ‬
‫اﻟ‬ ‫اﻟﻘﺴﻢ‬ ‫ﻋﻤﻞ‬ ‫ﺳﺎﻋﺎت‬ ‫ﻊ‬‫وأر‬ ‫ﻲ‬ ‫اﻟﺜﺎ‬ ‫اﻟﻘﺴﻢ‬ ‫ﻋﻤﻞ‬ ‫وﺳﺎﻋﺔ‬ ‫ل‬‫و‬ ‫اﻟﻘﺴﻢ‬
‫ﺜﺎﻟﺚ‬
‫و‬
‫ﺤﺘﺎج‬
‫ﺗﺼ‬
‫ﯿ‬
‫ﻊ‬
‫اﻟﺴﻠﻌﺔ‬
B
‫ﺳﺎﻋﺘ‬ ‫إ‬
‫ن‬
‫ل‬‫و‬ ‫اﻟﻘﺴﻢ‬ ‫اﳌﺘﺎﺣﺔ‬ ‫اﻟﻌﻤﻞ‬ ‫ﺳﺎﻋﺎت‬ ‫ﻋﺪد‬ ‫أن‬ ‫ﻛﻤﺎ‬ ‫ﻗﺴﻢ‬ ‫ﻞ‬ ‫ﻋﻤﻞ‬
١٦٠
‫أﺳﺒﻮﻋ‬ ‫ﻋﻤﻞ‬ ‫ﺳﺎﻋﺔ‬
‫ﯿ‬
‫ﺎ‬
‫ﻲ‬ ‫اﻟﺜﺎ‬ ‫اﻟﻘﺴﻢ‬ ‫و‬
١٢٠
‫أﺳﺒﻮﻋ‬ ‫ﻋﻤﻞ‬ ‫ﺳﺎﻋﺔ‬
‫ﯿ‬
‫ﺎ‬
‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﻘﺴﻢ‬ ‫و‬
٢٨٠
‫ﺳﺎ‬
‫أﺳﺒﻮﻋ‬ ‫ﻋﻤﻞ‬ ‫ﻋﺔ‬
‫ﯿ‬
‫ﺎ‬
‫اﻟﻮﺣﺪ‬ ‫ﺢ‬‫ر‬ ‫ﺎن‬ ‫ذا‬ ‫وا‬
‫ة‬
‫اﻟﺴﻠﻌﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻮاﺣﺪة‬
A
‫ﻮ‬
٢
‫ﺟﻨﻴﮫ‬
‫اﻟﺴﻠﻌﺔ‬ ‫وﻣﻦ‬
B
‫ﻮ‬
٣
‫ﺟﻨﻴﮫ‬
.
:‫اﳌﻄﻠﻮب‬
‫ﺧﻄ‬ ‫ﺑﺮﻣﺠﺔ‬ ‫ﻧﻤﻮذج‬
‫ﯿ‬
‫ﺔ‬
‫ﻟﺘﺤﺪ‬
‫ﯾ‬
‫ﺪ‬
‫اﻟﺴﻠﻌﺘ‬ ‫ﻣﻦ‬ ‫ﻣﺜﻞ‬ ‫ﻧﺘﺎج‬ ‫ﻢ‬
‫ن‬
‫أ‬ ‫ﻋ‬ ‫ل‬‫ﺼﻮ‬ ‫ﻮا‬ ‫اﻟﺸﺮﻛﺔ‬ ‫ﺪف‬ ‫ﺎن‬ ‫إذا‬
‫أ‬ ‫ﻋﺎﺋﺪ‬ ‫ﻛ‬
‫ر‬
‫ﺎح‬
‫ﻣﻤﻜﻦ‬
.
‫ﻞ‬ ‫ا‬
‫ﺗﻜﻮ‬
‫ﻦ‬
:‫اﻟﻨﻤﻮذج‬
‫ﺗﺤﺪ‬
‫ﯾ‬
‫ﺪ‬
‫اﳌﺘﻐ‬
‫ات‬
‫واﻟﺘﻌﺒ‬ ‫ﻮﻟﺔ‬ ‫اﳌﺠ‬
‫ﺟ‬ ‫ﺑﺮﻣﻮز‬ ‫ﺎ‬ ‫ﻋ‬
‫ﯾ‬
،‫ﺔ‬
:‫وﻟﺬﻟﻚ‬
-
‫ﻧﻔﺮض‬
‫اﻟﺴﻠﻌﺔ‬ ‫ﻣﻦ‬ ‫اﳌﻨﺘﺠﺔ‬ ‫اﻟﻮﺣﺪات‬ ‫ﻋﺪد‬
A
‫ﻮ‬
X1
.
-
‫ﻧﻔﺮض‬
‫اﻟﺴﻠﻌﺔ‬ ‫ﻣﻦ‬ ‫اﳌﻨﺘﺠﺔ‬ ‫اﻟﻮﺣﺪات‬ ‫ﻋﺪد‬
B
‫ﻮ‬
X2
.
‫ﺗﺤﺪ‬
‫ﯾ‬
‫ﺪ‬
‫اﻟﻘ‬
‫ﯿ‬
‫ﻮد‬
‫اﻟﺘﻌﺒ‬‫و‬
‫ﺎت‬ ‫ا‬ ‫ﻣ‬‫أو‬ ‫ﺑﻤﻌﺎدﻻت‬ ‫ﺎ‬ ‫ﻋ‬
‫واﻟﻘ‬
‫ﯿ‬
‫ﻮد‬
‫ﻨﺎ‬
‫ﻟﻠﺘﺼ‬ ‫اﻟﻼزم‬ ‫اﻟﻮﻗﺖ‬ ‫أن‬
‫ﯿ‬
‫ﻊ‬
‫و‬ ‫ﻣﺤﺪود‬ ‫ﻗﺴﻢ‬ ‫ﻞ‬
‫ﺠﺐ‬
،‫ﺪ‬ ‫ا‬ ‫ﺬا‬ ‫ﺗﺠﺎوز‬ ‫ﻧﺘﺠﻨﺐ‬ ‫أن‬
‫ﻻﺣﻆ‬
‫ﻟﻠﺘﺼ‬ ‫اﻟﻼزم‬ ‫اﻟﻮﻗﺖ‬ ‫أن‬
‫ﯿ‬
‫ﻊ‬
‫ﯾ‬
‫ﺘﻮﻗﻒ‬
‫ﻋ‬
‫اﻟﻜﻤ‬
‫ﯿ‬
‫ﺔ‬
‫اﻟﺴﻠﻌﺔ‬ ‫ﻣﻦ‬ ‫اﳌﻨﺘﺠﺔ‬
A
‫اﻟﺴﻠﻌﺔ‬‫و‬
B
.

10. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
10
‫ﺴﺒﺔ‬ ‫ﺑﺎﻟ‬
‫ﻟﻠﺘﺼ‬ ‫اﻟﻼزم‬ ‫اﻟﻮﻗﺖ‬ :‫ل‬‫و‬ ‫ﻟﻠﻘﺴﻢ‬
‫ﯿ‬
‫ﻊ‬
‫اﻟﺴﻠﻌﺔ‬ ‫ﻣﻦ‬ ‫اﳌﻨﺘﺠﺔ‬ ‫اﻟﻮﺣﺪات‬ ‫)ﻋﺪد‬ = (‫)اﳌﺘﺎح‬
A
*
(
‫ﻟﺘﺼ‬ ‫اﻟﻼزم‬ ‫)اﻟﻮﻗﺖ‬
‫ﯿ‬
‫ﻊ‬
‫اﻟﺴﻠﻌﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻮاﺣﺪة‬ ‫اﻟﻮﺣﺪة‬
A
‫اﻟﻮﺣﺪات‬ ‫)ﻋﺪد‬+ (
‫اﻟﺴﻠﻌﺔ‬ ‫ﻣﻦ‬ ‫اﳌﻨﺘﺠﺔ‬
B
‫*)اﻟﻮﻗﺖ‬ (
‫اﻟﻼزم‬
‫ﻟﺘﺼ‬
‫ﯿ‬
‫ﻊ‬
‫اﻟﺴﻠﻌﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻮاﺣﺪة‬ ‫اﻟﻮﺣﺪة‬
B
‫)و‬،
‫ﺠﺐ‬
‫ﻻ‬ ‫أن‬
‫ﯾ‬
‫ﺘﺠﺎوز‬
‫اﻟﻘﺴﻢ‬ ‫اﳌﺘﺎﺣﺔ‬ ‫اﻟﻌﻤﻞ‬ ‫اﻟﺴﺎﻋﺎت‬ ‫ﻋﺪد‬
‫ل‬‫و‬
‫ﺗ‬ ‫ﺔ‬ ‫ا‬ ‫اﳌ‬ ‫وﻛﻤﺎ‬
‫ﯿ‬
‫ﺔ‬
:
2 + 2 ≤ 160
‫اﻟﻄﺮ‬ ‫ﻨﻔﺲ‬ ‫و‬
‫ﻘﺔ‬
‫ﻟﻠﻘﺴﻤ‬ ‫ﺴﺒﺔ‬ ‫ﺑﺎﻟ‬
‫ن‬
‫أ‬ ‫واﻟﺜﺎﻟﺚ‬ ‫ﻲ‬ ‫اﻟﺜﺎ‬
‫ﯾ‬
‫ﻀﺎ‬
‫ﺗ‬ ‫ﺎت‬ ‫ا‬ ‫اﳌ‬ ‫وﻛﻤﺎ‬
‫ﯿ‬
‫ﺔ‬
:
‫ﺴﺒﺔ‬ ‫ﺑﺎﻟ‬
:‫ﻲ‬ ‫اﻟﺜﺎ‬ ‫ﻟﻠﻘﺴﻢ‬
+ 2 ≤ 120
‫ﺴﺒﺔ‬ ‫ﺑﺎﻟ‬
:‫اﻟﺜﺎﻟﺚ‬ ‫ﻟﻠﻘﺴﻢ‬
+ 2 ≤ 120
‫ﻻ‬ ‫اﳌﻨﺘﺠﺔ‬ ‫اﻟﻮﺣﺪات‬ ‫ﻋﺪد‬ ‫وﻷن‬
‫ﯾ‬
‫ﻤﻜﻦ‬
‫أن‬
‫ﯾ‬
‫ن‬‫ﻮ‬
:‫ﻲ‬ ‫اﻟﻨﺤﻮ‬ ‫وﻋ‬ ،‫ﺳﺎﻟﺒﺎ‬
, ≥
‫ﺗﺤﺪ‬
‫ﯾ‬
‫ﺪ‬
:‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬
MaxZ=2A+3B
‫اﻟﻜﻤ‬ ‫اﻧﺘﺎج‬ ‫إ‬ ‫ﺪف‬ ‫و‬
‫ﯿ‬
‫ﺎت‬
‫ﻣﻦ‬ ‫اﳌﺜ‬
‫ن‬ ‫اﳌﻨﺘﺠ‬
A,B
‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﺗﺠﻌﻞ‬ ‫اﻟ‬
Z
‫ﻣﺎ‬ ‫اﻛ‬
‫ﯾ‬
‫ﻤﻜﻦ‬
Maximize
‫وداﺋﻤﺎ‬
‫اﻟﺘﺎ‬ ‫ﻞ‬ ‫ﺑﺎﻟﺸ‬ ‫ﻄﻲ‬ ‫ا‬ ‫ﻧﺎﻣﺞ‬ ‫اﻟ‬ ‫ن‬‫ﻟﻴﻜﻮ‬
Max Z=2A+3B
S.To:
2 + 2 ≤ 160
+ 2 ≤ 12
4 + 2 ≤ 280
, ≥
‫ﻲ‬ ‫ذا‬ ‫ﻢ‬‫ﺗﻘﻮ‬
SelfEvaluation
‫ﻋﺼ‬ ‫ﻣﻦ‬ ‫أﻧﻮاع‬ ‫ﺛﻼث‬ ‫ﺎت‬‫اﻟﺸﺮ‬ ‫إﺣﺪى‬ ‫ﺘﺞ‬ ‫ﺗ‬
‫ﻣﺼﻨﻌ‬ ‫اﻟﻔﻮاﻛﮫ‬
‫ﯿ‬
‫ن‬
A
‫و‬
B
:‫ﻲ‬ ‫ﺎﻵ‬ ‫ﺗﻘﺪر‬ ‫اﻟﻴﻮم‬ ‫ﻧﺘﺎج‬ ‫ﻛﻤﻴﺎت‬ ‫وأن‬

11. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
11
‫اﻟﻌﺼ‬ ‫ﻧﻮع‬
‫اﳌﻨﺘﺞ‬
A
/
‫ﻟ‬
‫اﳌﻨﺘﺞ‬
B
/
‫ﻟ‬
1
١٥٠٠
١٥٠٠
2
٣٠٠٠
١٠٠٠
3
٢٠٠٠
٥٠٠٠
‫ﺎﻧﺖ‬
‫أن‬ ‫اﳌﺘﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫أن‬ ‫ق‬‫ﻟﻠﺴﻮ‬ ‫اﺳﺔ‬‫ر‬‫د‬ ‫ﺮت‬ ‫أﻇ‬ ‫ﻗﺪ‬
‫ﯾ‬
‫ن‬‫ﻮ‬
‫ﺮ‬ ‫ﺷ‬ ‫ﻃﻠﺐ‬ ‫ﻨﺎك‬
‫اﻏﺴﻄﺲ‬
‫ﯾ‬
‫ﻘﺪر‬
‫ـ‬‫ﺑ‬
٢٠٠٠٠
‫ﻟ‬
‫و‬ ‫ل‬‫و‬ ‫اﻟﻨﻮع‬ ‫ﻣﻦ‬
٤٠٠٠٠
‫و‬ ‫ﻲ‬ ‫اﻟﺜﺎ‬ ‫اﻟﻨﻮع‬ ‫ﻣﻦ‬
٤٤٠٠٠
‫ﺸﻐ‬ ‫ﻠﻔﺔ‬ ‫ﻓﺈن‬ ‫وﻛﺬﻟﻚ‬ ،‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﻨﻮع‬ ‫ﻣﻦ‬
‫ﯿ‬
‫ﻞ‬
‫اﳌﺼﻨﻊ‬
A
٦٠٠
‫ﻧﻘﺪ‬ ‫وﺣﺪة‬
‫ﯾ‬
‫ﺔ‬
‫اﻟ‬
‫ﯿ‬
‫ﻮم‬
‫و‬
٤٠٠
‫ﻧﻘﺪ‬ ‫وﺣﺪة‬
‫ﯾ‬
‫ﺔ‬
‫ﻟﻠﻤﺼﻨﻊ‬
B
.
‫اﳌﻄﻠﻮب‬
‫ﺗﺤﺪ‬ :
‫ﯾ‬
‫ﺪ‬
‫ﻋﺪد‬
‫ﯾ‬
‫ﺎم‬
‫اﻟ‬
‫ﺎ‬ ‫ﺸﺘﻐﻠ‬
‫اﳌﺼﻨﻌ‬ ‫ﻣﻦ‬ ‫ﻛﻼ‬
‫ن‬
‫ﺮ‬ ‫ﺷ‬ ‫اﳌﺘﻮﻗﻊ‬ ‫ق‬‫اﻟﺴﻮ‬ ‫ﺑﻄﻠﺐ‬ ‫ﻟﻠﻮﻓﺎء‬
‫اﻏﺴﻄﺲ‬
‫ﻣﻊ‬
‫ﺗﺪﻧ‬
‫ﯿ‬
‫ﺔ‬
‫ﺎﻟ‬ ‫اﻟﺘ‬
‫ﯿ‬
‫ﻒ‬
‫)ﺻ‬ ‫ﻣﻤﻜﻦ‬ ‫ﺣﺪ‬ ‫ﻰ‬ ‫أد‬ ‫إ‬
‫ﯿ‬
‫ﺎﻏﺔ‬
. ‫اﳌﺼﻔﻮ‬ ‫ﻞ‬ ‫ﺑﺎﻟﺸ‬ ‫ﻄﻲ‬ ‫ا‬ ‫ﻧﺎﻣﺞ‬ ‫اﻟ‬ ‫وﻛﺘﺎﺑﺔ‬ ،(‫اﳌﺴﺄﻟﺔ‬
‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻧﻤﺎذج‬ ‫ﺣﻞ‬ ‫ﻃﺮق‬
‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻧﻤﺎذج‬ ‫ﻞ‬ ‫ﺘﺎن‬ ‫اﺳﺎﺳ‬ ‫ﻘﺘﺎن‬‫ﻃﺮ‬ ‫ﻨﺎك‬
١
-
‫اﻟﺒﻴﺎﻧﻴﺔ‬ ‫اﻟﻄﺮﻗﺔ‬
٢
-
‫ﺴﻴﻄﺔ‬ ‫اﻟ‬ ‫ﻘﺔ‬‫اﻟﻄﺮ‬
simplex
ً
‫اوﻻ‬
‫اﻟﺒﻴﺎﻧﻴﺔ‬ ‫ﻘﺔ‬‫اﻟﻄﺮ‬ /
١
-
‫ﻓﻘﻂ‬ ‫ن‬ ‫اﺛﻨ‬ ‫ﻳﻦ‬ ‫ﻣﺘﻐ‬ ‫ﻋ‬ ‫ي‬‫ﺗﺤﺘﻮ‬ ‫واﻟ‬ ‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻞ‬ ‫ﻣﺸﺎ‬ ‫ﻞ‬ ‫ﻘﺔ‬‫اﻟﻄﺮ‬ ‫ﺬﻩ‬ ‫ﺗﺼ‬
٢
-
‫ﺑﺎﻹﺷﺎرة‬ ‫ﻣﻘﻴﺪة‬ ‫ﻏ‬‫او‬ ‫ﻣﻘﻴﺪة‬ ‫ات‬ ‫اﳌﺘﻐ‬ ‫ﺎﻧﺖ‬ ‫اذا‬ ‫ﻘﺔ‬‫اﻟﻄﺮ‬ ‫ﺬﻩ‬ ‫ﺴﺘﺨﺪم‬
‫ﻣﻌ‬ ‫ﻛﻔﻮءة‬ ‫ﻏ‬ ‫ﻘﺔ‬‫ﻃﺮ‬ ‫ﺎ‬ ‫ا‬ ‫دﻗﻴﻘﺔ‬ ‫ﻧﺘﺎﺋﺞ‬ ‫ﻌﻄﻲ‬ ‫واﻟ‬ ‫ﺴﻴﻄﺔ‬ ‫اﻟ‬ ‫ق‬‫اﻟﻄﺮ‬ ‫ﻣﻦ‬ ‫ﻘﺔ‬‫اﻟﻄﺮ‬ ‫ﺬﻩ‬ ‫ﻌﺘ‬‫و‬
‫اﻟ‬ ‫ﻣﺸﻜﻼت‬ ‫ﺔ‬ ‫ﺎ‬
‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬
‫اﻟﻌﻤﻠﻴﺔ‬ ‫ﻴﺎة‬ ‫ا‬
‫ﻞ‬ ‫ا‬ ‫ﺧﻄﻮات‬
١
-
‫ل‬‫ﻧﺤﻮ‬
‫ﻣﺘﺒﺎﻳﻨﺎت‬
‫ﻣﻌﺎدﻻت‬ ‫ا‬ ‫ﻣﺘﺒﺎﻳﻨﺎت‬ ‫ﻣﻦ‬ ‫اﻟﻘﻴﻮد‬
٢
-
،‫ﺧﺮ‬ ‫ﻟﻠﻤﺘﻐ‬ ‫ﺴﺒﺔ‬ ‫ﺑﺎﻟ‬ ‫ذﻟﻚ‬ ‫ﻧﻜﺮر‬ ‫ﺛﻢ‬ ،‫ﻲ‬ ‫اﻟﺜﺎ‬ ‫اﳌﺘﻐ‬ ‫ﻗﻴﻤﺔ‬ ‫اج‬‫ﺮ‬‫ﻻﺳﺘﺨ‬‫ﺻﻔﺮ‬ ‫ﺑﻘﻴﻤﺔ‬ ‫اﻟﻮاﺣﺪة‬ ‫اﳌﻌﺎدﻟﺔ‬ ‫ات‬ ‫اﳌﺘﻐ‬ ‫ﺑﺄﺣﺪ‬ ‫ﻌﻮض‬
‫ﻞ‬ ‫ﻟ‬ ‫ن‬ ‫ﻧﻘﻄﺘ‬ ‫ﻟﺪﻳﻨﺎ‬ ‫ﺗﺼﺒﺢ‬ ‫ﺬﻟﻚ‬ ‫و‬
‫اﳌﻌﺎدﻟﺔ‬ ‫ﺗﻤﺜﻠﮫ‬ ‫اﻟﺬي‬ ‫اﳌﺴﺘﻘﻴﻢ‬ ‫رﺳﻢ‬ ‫ﻳﻤﻜﻦ‬ ‫ن‬ ‫اﻟﻨﻘﻄﺘ‬ ‫ن‬ ‫ﺎﺗ‬ ‫ﻮﺳﺎﻃﺔ‬ ‫و‬ (‫ﻣﻌﺎدﻟﺔ)ﻣﺴﺘﻘﻴﻢ‬
.
٣
-
‫اﳌﺤﺪﺑﺔ‬ ‫ﺑﺎﳌﻨﻄﻘﺔ‬ ‫ﺴ‬ ‫واﻟ‬ ‫اﳌﻤﻜﻦ‬ ‫ﻞ‬ ‫ا‬ ‫ﻣﻨﻄﻘﺔ‬ ‫ﺗﺤﺪﻳﺪ‬ ‫ﻳﺘﻢ‬ ‫اﻟﻘﻴﻮد‬ ‫ﺗﻤﺜﻞ‬ ‫اﻟ‬ ‫اﳌﺴﺘﻘﻴﻤﺎت‬ ‫ﺟﻤﻴﻊ‬ ‫رﺳﻢ‬ ‫ﻌﺪ‬
.
٤
-
‫ﺗﺤﻘﻖ‬ ‫اذ‬ (‫اﳌﻘﺒﻮﻟﺔ‬ ‫ل‬‫ﻠﻮ‬ ‫ا‬ ‫)ﻣﻨﻄﻘﺔ‬ ‫ل‬‫اﳌﻘﺒﻮ‬ ‫ﻲ‬ ‫ﺑﺘﺪا‬ ‫ﺳﺎ‬ ‫ﻞ‬ ‫ا‬ ‫ﻣﻨﻄﻘﺔ‬ ‫ﺗﺤﺪد‬
‫واﺣﺪ‬ ‫وﻗﺖ‬ ‫اﻟﻘﻴﻮد‬ ‫ﺟﻤﻴﻊ‬ ‫اﳌﻨﻄﻘﺔ‬ ‫ﺬﻩ‬
.

12. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
12
٥
-
‫ﻞ‬ ‫ا‬ ‫ﳌﻨﻄﻘﺔ‬ ‫اﳌﻤﺜﻠﺔ‬ ‫اﳌﺴﺘﻘﻴﻤﺎت‬ ‫ﺗﻘﺎﻃﻌﺎت‬ ‫ﻋ‬ ‫اﻟﻮاﻗﻌﺔ‬ ‫ﻗﻞ‬ ‫ﻋ‬ ‫اﻟﻨﻘﺎط‬ ‫اﺣﺪى‬ ‫ﺗﻤﺜﻞ‬ ‫اﻟ‬ ‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫ﻣﻨﻄﻘﺔ‬ ‫ﺗﺤﺪد‬
‫اﻗ‬‫او‬ ‫ﻌﻈﻴﻢ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﺎﻧﺖ‬ ‫اذا‬ ‫ﻳﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻋﻈﻢ‬ ‫ﺎح‬‫ر‬ ‫ﺗﺠﻌﻞ‬ ‫اﻟ‬ ‫اﻟﺘﻄﺮف‬ ‫ﺑﻨﻘﺎط‬ ‫ﺴ‬ ‫اﻟ‬ ‫ل‬‫اﳌﻘﺒﻮ‬ ‫ﻲ‬ ‫ﺑﺘﺪا‬ ‫ﺳﺎ‬
‫ﻞ‬
‫ﻣﺘﺪﻧﻴﺔ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﺎﻧﺖ‬ ‫اذا‬ ‫ﻳﻤﻜﻦ‬ ‫ﻣﺎ‬
.
٦
-
‫اﳌﺘﻐ‬ ‫ﻤﺎ‬ ‫اﺣﺪ‬ ‫واﻟﻌﻤﻮدي(ﻟﻴﻤﺜﻞ‬ ‫ﻓﻘﻲ‬ ) ‫ﻲ‬ ‫ﺣﺪا‬ ‫ى‬‫اﳌﺴﺘﻮ‬ ‫ﻋ‬ ‫ﻧﺮﺳﻢ‬
X1
‫ﺧﺮ‬ ‫ﻤﺜﻞ‬ ‫و‬ ‫وﻛﻤﻴﺘﮫ‬
X2
‫وﻛﻤﻴﺘﮫ‬
‫اﻟﺒﻴﺎﻧﻴﺔ‬ ‫ﻘﺔ‬‫ﺑﺎﻟﻄﺮ‬ ‫ل‬‫ﻠﻮ‬ ‫ا‬ ‫اﻧﻮاع‬
١
-
‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫ﺗﺤﺪﻳﺪ‬ ‫اﺳﻠﻮب‬
‫اﻟﻨﻘ‬ ‫)و‬ ‫اﻟﺘﻄﺮف‬ ‫ﻧﻘﺎط‬ ‫ﻧﺤﺪد‬ ‫ى‬‫اﳌﺴﺘﻮ‬ ‫ﻋ‬ ‫اﳌﺴﺘﻘﻴﻤﺎت‬ ‫ﺟﻤﻴﻊ‬ ‫رﺳﻢ‬ ‫ﻌﺪ‬
‫ﻞ‬ ‫(وﻧﺨﺘ‬ ‫اﳌﻤﻜﻨﺔ‬ ‫ل‬‫ﻠﻮ‬ ‫ا‬ ‫ﺑﻤﻨﻄﻘﺔ‬ ‫ﺗﺤﻴﻂ‬ ‫اﻟ‬ ‫ﺎط‬
‫ﺎﻧﺖ‬ ‫اذا‬ ‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫ﺗﻤﺜﻞ‬ ‫اﻟ‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬، ‫ﻳﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻛ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﺗﺠﻌﻞ‬ ‫اﻟ‬ ‫واﻟﻨﻘﻄﺔ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﺾ‬‫ﺑﺎﻟﺘﻌﻮ‬ ‫ﺎ‬ ‫ﻣ‬
‫اﻟﺘﻌﻈﻴﻢ‬ ‫ﻧﻮع‬ ‫ﻣﻦ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬
Max
‫ﺑﺎﻟﻌﻜﺲ‬ ‫واﻟﻌﻜﺲ‬
.
‫ﺣﺎ‬ ‫ﻳﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻗﻞ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﺗﺠﻌﻞ‬ ‫اﻟ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ان‬ ‫اي‬
‫داﻟﺔ‬ ‫ن‬‫ﻮ‬ ‫ﻟﺔ‬
‫ﻲ‬ ‫اﳌﺘﺪ‬ ‫اﻟﻨﻮع‬ ‫ﻣﻦ‬ ‫ﺪف‬ ‫اﻟ‬
Min
‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫ﺗﻤﺜﻞ‬ ‫اﻟ‬
.
‫ﻣﺜﺎل‬
‫ﺗﻄﺒﻴﻘﻲ‬
:
‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻟﻨﻤﻮذج‬ ‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫اوﺟﺪ‬
Max Z=4X1+3X2
S.T
٥X1+3X2 ≤30
٢X1+3X2 ≤21
X1,X2 ≥0
‫ﺑﺎﳌﺴﺎواة‬ ‫ي‬‫ﺴﺎو‬ ‫او‬ ‫ﻗﻞ‬ ‫ﻋﻼﻣﺔ‬ ‫ﺒﺪل‬ ‫ﺴ‬ ‫اي‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻋﻦ‬ ‫ﻋﺒﺎرة‬ ‫ﻧﺠﻌﻠﮫ‬ :‫ل‬‫و‬ ‫اﻟﻘﻴﺪ‬
٥X1+3X2=30
Let X1=0,X2=10 (0,10)
Let X2=0,X1=6 (٦,٠)
‫ﻲ‬ ‫اﻟﺜﺎ‬ ‫اﻟﻘﻴﺪ‬
٢X1+3X2 =21

13. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
13
Let X1=0,X2=7(٠,٧)
Let X2=0,X1=10.5(١٠.٥,٠)
‫واﺣﺪ‬ ‫وﻗﺖ‬ ‫اﻟﻘﻴﻮد‬ ‫ﺟﻤﻴﻊ‬ ‫ﺗﺤﻘﻖ‬ ‫اﻟ‬ ‫اﳌﻨﻄﻘﺔ‬ ‫و‬ ‫اﻟﻘﻴﻮد‬ ‫ﻣﻦ‬ ‫ﻣﻄﻠﻮب‬‫ﻮ‬ ‫ﻣﺎ‬ ‫وﺣﺴﺐ‬ ‫اﳌﻤﻜﻨﺔ‬ ‫ل‬‫ﻠﻮ‬ ‫ا‬ ‫ﻣﻨﻄﻘﺔ‬ ‫ﺗﺤﺪد‬ ‫ﺬا‬ ‫ﻌﺪ‬
‫ن‬ ‫ﻣﺒ‬ ‫ﻛﻤﺎ‬ ‫و‬
) ‫اﻋﻼﻩ‬ ‫ﻞ‬ ‫اﻟﺸ‬
A,B,C,D
) ‫و‬ ‫ﻣﻌﻠﻮﻣﺔ‬ ‫اﻟﻨﻘﺎط‬ ‫ﺟﻤﻴﻊ‬ ‫ﻲ‬ ‫اﺣﺪا‬ ‫ان‬ ‫ﻤﺎ‬ ‫و‬ (
A,B,C,D
) ‫اﻟﻨﻘﻄﺔ‬ ‫ﻋﺪا‬ ‫ﻣﺎ‬ (
c
‫ﺗﺤﺪﻳﺪ‬ ‫ﻓﻴﺘﻢ‬ (
: ‫ﻲ‬ ‫اﻟﻨﺤﻮ‬ ‫ﻋ‬ ‫ﺎ‬ ‫اﺣﺪاﺛﻴ‬
: ‫و‬ ‫اﻟﻮﺳﻴﻠﺔ‬
) ‫ﻣﺜﻞ‬ ‫ﺎ‬ ‫اﺣﺪاﺛﻴ‬ ‫ﻣﻌﺮﻓﺔ‬ ‫اد‬‫ﺮ‬‫اﳌ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫اﻋﻤﺪة‬ ‫ال‬‫ﺰ‬‫اﻧ‬ ‫ﺳﻠﻮب‬ ‫ﺬا‬ ‫ﻳﻘﺘ‬
C
‫ﺘﻘﺎﻃﻊ‬ ‫و‬ ‫ﻓﻘﻲ‬ ‫و‬ ‫اﻟﻌﻤﻮدي‬ ‫ن‬ ‫اﳌﺤﻮر‬ ‫ﻋ‬ (
‫ﺬﻳﻦ‬
) ‫اﻟﻨﻘﻄﺔ‬ ‫ﻲ‬ ‫اﺣﺪا‬ ‫ن‬ ‫ﻳﺘﻌ‬ ‫اﳌﺤﺎور‬ ‫ﻣﻊ‬ ‫اﻟﻌﻤﻮدﻳﻦ‬
C
‫ﻓﻘﻲ‬ ‫اﳌﺤﻮر‬ ‫وﻋ‬ ‫اﻟﻌﻤﻮدي‬ ‫اﳌﺤﻮر‬ ‫ﻋ‬ (
:‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﻮﺳﻴﻠﺔ‬
) ‫اﻟﻨﻘﻄﺔ‬ ‫ان‬ ‫ﺑﻤﺎ‬ ‫ﺎﺿﻴﺔ‬‫اﻟﺮ‬ ‫ق‬‫اﻟﻄﺮ‬ ‫اﺣﺪى‬ ‫ﻳﺘﻀﻤﻦ‬ ‫ﺳﻠﻮب‬
C
‫او‬ ‫ﺬف‬ ‫ا‬ ‫و‬ ‫ﻲ‬ ‫واﻟﺜﺎ‬ ‫ل‬‫و‬ ‫ن‬ ‫اﳌﺴﺘﻘﻴﻤ‬ ‫ﺗﻘﺎﻃﻊ‬ ‫ﻣﻦ‬ ‫ﺗﻮﻟﺪت‬ (
: ‫اﻟﺘﺎ‬‫اﻟﻨﺤﻮ‬ ‫وﻋ‬ ‫ﺾ‬ ‫اﻟﺘﻌﻮ‬
٥X1+3X2= 30
X1=33X2=±21………..(2)
±2X1
±٣X1= 9
X1=9/3=3
‫اﳌﺘﻐ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺴﺘﺨﺮج‬ ‫ذﻟﻚ‬ ‫ﻌﺪ‬
X2
‫اﳌﺘﻐ‬ ‫ﺑﻘﻴﻤﺔ‬ ‫ﺾ‬‫ﺑﺎﻟﺘﻌﻮ‬ ‫وذﻟﻚ‬
X1=3
) ‫اﻣﺎ‬ ‫ن‬ ‫اﳌﻌﺎدﻟﺘ‬ ‫ﺑﺈﺣﺪى‬
١
) ‫او‬ (
٢
‫ﺾ‬ ‫اﻟﺘﻌﻮ‬ ‫وﻟﻴﺘﻢ‬ (
‫و‬ ‫ﺑﺎﳌﻌﺎدﻟﺔ‬
٣ + (٣)٥X2= 30 3X2=15X2=5

14. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
14
‫اﳌﺤﺪ‬ ‫اﳌﻨﻄﻘﺔ‬ ‫ﺗﺤﺪﻳﺪ‬ ‫ﻳﺘﻢ‬ ‫ان‬ ‫ﻓﺒﻌﺪ‬ ‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫ﻧﻘﻄﺔ‬ ‫ﺗﺤﺪﻳﺪ‬ ‫اﻣﺎ‬
‫ﺑﺎﻟﻨﻘﺎط‬ ‫اﳌﺤﺪدة‬ ‫اﻟ‬ ‫ﺑﺔ‬
(A,B,C,D)
‫ﻣﻨﻄﻘﺔ‬ ‫ﺗﻤﺜﻞ‬ ‫اﻟ‬ ((
: ‫ﻳ‬ ‫وﻛﻤﺎ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫اﻟﻨﻘﺎط‬ ‫ﻲ‬ ‫ﺑﺈﺣﺪا‬ ‫ﺾ‬‫اﻟﺘﻌﻮ‬ ‫ﻳﺘﻢ‬ ‫اﻟﺘﻄﺮف‬ ‫ﻧﻘﺎط‬ ‫ﺟﻤﻴﻊ‬ ‫ﻲ‬ ‫اﺣﺪا‬ ‫ﻣﻌﺮﻓﺔ‬ ‫ﻳﺘﻢ‬ ‫ان‬ ‫ﻌﺪ‬‫و‬ ‫اﳌﻤﻜﻨﺔ‬ ‫ل‬‫ﻠﻮ‬ ‫ا‬
) ‫اﻟﺘﻄﺮف‬ ‫ﻧﻘﺎط‬ ‫ﻲ‬ ‫اﺣﺪا‬ ‫اﻟﺘﻄﺮف‬ ‫ﻧﻘﺎط‬
X1,X2
)‫ﺣﺪاﺛﻴﺎت‬ ‫ﻋﻨﺪ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﻗﻴﻤﺔ‬ (
X1,X2
(
A (0,0) Za=0
B (6,0) Zb=24
C (3,5) Zc=27
D (0,7)Zd=21
‫اﻟﻨﻘﻄﺔ‬ ‫ان‬ ‫ﺑﻤﺎ‬
C
‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﻋﺎﺋﺪ‬ ‫اﻋ‬ ‫ﺣﻘﻘﺖ‬
Zc=27
‫ﻧﻮع‬ ‫ﻣﻦ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ان‬ ‫ﻤﺎ‬‫و‬
Max
‫ﻧﻘﻄﺔ‬ ‫ﻓﺄن‬
C
‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫ﺗﺤﻘﻖ‬
:‫ﻣﻼﺣﻈﺔ‬
‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫ﺗﻤﺜﻞ‬ ‫اﻟﺘﻄﺮف‬ ‫ﻧﻘﺎط‬ ‫ﻣﻦ‬ ‫ﻗﻞ‬ ‫ﻋ‬ ‫واﺣﺪة‬ ‫ﻧﻘﻄﺔ‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬
.
‫ﺗ‬ ‫ﻧﻘﻄﺘﺎن‬ ‫ﻨﺎك‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬ ‫ان‬ ‫ﻣﻤﻜﻦ‬ ‫ﺬا‬ ‫ﻣﻌ‬ ‫اي‬
‫ﻞ‬ ‫ا‬ ‫ﻤﺜﻞ‬
‫ﻣﺜﻞ‬
.
"‫اﻟﺴﻤﺒﻠﻜﺲ‬ ‫ﻘﺔ‬‫ﻃﺮ‬ " ‫ﺴﻴﻄﺔ‬ ‫اﻟ‬ ‫ﻘﺔ‬‫ﻃﺮ‬
SimplexMethod
‫ﺑﺎﻟ‬ ‫اﻟﺒﻴﺎﻧﻴﺔ‬ ‫ﻘﺔ‬‫اﻟﻄﺮ‬ ‫ﺗﻤ‬
‫و‬ ‫ﻘﺪرة‬
‫اﻟ‬
‫ﻮﻟﺔ‬ ‫ﺴ‬
‫ﻣ‬ ‫ﺣﻞ‬
‫ﻞ‬ ‫ﺸﺎ‬
‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬
،
‫ن‬ ‫اﺛﻨ‬ ‫ﻳﻦ‬ ‫ﻣﺘﻐ‬ ‫وﺟﻮد‬ ‫ﺣﺎﻟﺔ‬
‫واﺳ‬
‫ﺘﺤﺎﻟﺖ‬
‫ﺎ‬ ‫ﺗﻄﺒﻴﻘ‬
‫ﺛﻼﺛﺔ‬ ‫اﻛ‬ ‫وﺟﻮد‬ ‫ﺣﺎﻟﺔ‬
‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﻣﺸﻜﻼت‬ ‫ﺣﻞ‬ ‫ﻣﺠﺪﻳﺔ‬ ‫ﻗﺘﺼﺎدﻳﺔ‬ ‫اﻟﺴﻤﺒﻠﻜﺲ‬ ‫ﻘﺔ‬‫ﻃﺮ‬ ‫ﻌﺪ‬ ،‫ات‬ ‫ﻣﺘﻐ‬
‫ﺣﻴﺚ‬ ،‫ﻳﻦ‬ ‫ﻣﺘﻐ‬ ‫ﻣﻦ‬ ‫أﻛ‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬ ‫أن‬ ‫ﺸﺮط‬ ‫اﳌﺘﻌﺪدة‬ ‫ات‬ ‫اﳌﺘﻐ‬ ‫ذات‬ ‫ﻄﻴﺔ‬ ‫ا‬
‫ﻘﺔ‬‫ﻃﺮ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﳌﻌﻴﻨﺔ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﺣﻞ‬ ‫ﻳﺘﻢ‬
‫اﳌﺮﺗﺒﺔ‬ ‫ﻄﻮات‬ ‫ا‬ ‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫اﻟﺴﻤﺒﻠﻜﺲ‬
‫اﳌﻤﻜ‬ ‫ل‬‫ﻠﻮ‬ ‫ا‬ ‫ﳌﻨﻄﻘﺔ‬ ‫اﳌﺤﺪدة‬ ‫ﺎن‬ ‫ر‬ ‫إ‬ ‫ﺎدﻓﺔ‬ ‫اﻟ‬
‫ﻟﻌﺎﺋ‬ ‫ا‬ ‫وﺗﻘﻴﻢ‬ . ‫ﻨﺔ‬
‫ﻣﻦ‬ ‫ﺪ‬
‫ﻧﺘﻘﺎل‬ ‫و‬ ، ‫رﻛﻦ‬ ‫ﻞ‬
‫اﻟﺮﻛﻦ‬ ‫إ‬ ‫اﻟﺘﻮﺻﻞ‬ ‫ﻳﺘﻢ‬ ‫ﺣ‬ ‫ﻣﻨﮫ‬ ‫اﻓﻀﻞ‬‫أﺧﺮ‬ ‫إ‬ ‫رﻛﻦ‬ ‫ﻣﻦ‬
–
‫ﻞ‬ ‫ا‬ ‫أو‬
–
‫اﻓﻀﻞ‬ ‫ﻳﺤﻘﻖ‬ ‫اﻟﺬي‬
‫ﻋﺎﺋﺪ‬
‫ﻣﻤﻜﻦ‬
.
:‫ﻞ‬ ‫ا‬ ‫ﺷﺮوط‬
١
.
‫ﻗﻞ‬ ‫ﻋ‬ ‫ﻳﻦ‬ ‫ﻣﺘﻐ‬ ‫ﻋ‬ ‫ﺎ‬ ‫ﺣﻠ‬ ‫اد‬‫ﺮ‬‫اﳌ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ي‬‫ﺗﺤﺘﻮ‬ ‫ن‬‫ﻮ‬ ‫ﻳ‬ ‫أن‬ ‫ﻳﺠﺐ‬
٢
.
‫ﻧﻮع‬ ‫ﻣﻦ‬ ‫اﻟﻘﻴﻮد‬ ‫ﺟﻤﻴﻊ‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬ ‫أن‬ ‫ﻳﺠﺐ‬
≤
٣
.
‫اﻟﻄﺮف‬ ‫ن‬‫ﻮ‬ ‫ﻳ‬ ‫أن‬ ‫ﻳﺠﺐ‬
‫ﺳﺎﻟﺐ‬ ‫ﻏ‬ ‫اﻟﻘﻴﻮد‬ ‫ﻣﺘﺒﺎﻳﻨﺎت‬ ‫ﻳﻤﻦ‬

15. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
15
:‫ﻞ‬ ‫ا‬ ‫ﺧﻄﻮات‬
١
-
‫اﻟﻘﻴﺎﺳﻴﺔ‬ ‫اﻟﺼﻴﻐﺔ‬ ‫إ‬ ‫اﻟﻘﻴﻮد‬ ‫ﻣﺘﺒﺎﻳﻨﺎت‬ ‫ﻞ‬‫ﺑﺘﺤﻮ‬ ‫ﻢ‬
ّ
‫ﻗ‬
٢
-
‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﺗﺼﻔ‬
٣
-
‫ﻲ‬ ‫ﺑﺘﺪا‬ ‫ﻞ‬ ‫ا‬ ‫ل‬‫ﺟﺪو‬ ‫ﻦ‬ ‫ﻮ‬ ‫ﺗ‬
٤
-
‫اﻟﺪاﺧﻞ‬ ‫اﳌﺘﻐ‬ ‫ﺗﺤﺪﻳﺪ‬
٥
-
‫ﺎرج‬ ‫ا‬ ‫اﳌﺘﻐ‬ ‫ﺗﺤﺪﻳﺪ‬
٦
-
(‫)اﳌﻔﺘﺎح‬‫ﺎز‬ ‫رﺗ‬ ‫ﻋﻨﺼﺮ‬ ‫ﺗﺤﺪﻳﺪ‬
:‫ﻣﺜﺎل‬
MaxZ= 1.5x1 +1.8x2
S.To
3x1 +2x2 ≤ 15000 --- ‫ﻴﻊ‬ ‫اﻟﺘﺼ‬ ‫ﻗﻴﺪ‬
x1 +2x2 ≤ 1000 --- ‫اﻟﺘﺠﻤﻴﻊ‬ ‫ﻗﻴﺪ‬
x1 ≤4000 --- ‫اﻟﻄﻠﺐ‬ ‫ﻗﻴﺪ‬
x2 ≤4500 --- ‫اﻟﻄﻠﺐ‬ ‫ﻗﻴﺪ‬
x1,x2 ≥0
:‫اﻟﺴﻤﺒﻠﻜﺲ‬ ‫ﻘﺔ‬‫ﻃﺮ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﻞ‬
‫واﻟﻘﻴﻮد‬ ‫ﺪف‬ ‫اﻟ‬ ‫وداﻟﺔ‬ ‫ة‬ ‫اﳌﺘﻐ‬ ‫ات‬‫ر‬‫اﻟﻘﺮا‬ ‫ﺑﻮﺿﻊ‬ ‫ﻠﺔ‬ ‫ﻟﻠﻤﺸ‬ ‫ﺎ‬‫اﻟﺮ‬ ‫اﻟﻨﻤﻮذج‬ ‫ﺻﻴﺎﻏﺔ‬ :
ً
‫أوﻻ‬
‫ﺻﻴﻐ‬ ‫ﻠﻴﺔ‬ ‫ﻴ‬ ‫واﻟ‬ ‫اﳌﻮﺟﺒﺔ‬
‫ﺔ‬
‫ﺎﺿﻴﺔ‬‫ر‬
Max Z= 1.5x1+1.8x2
S.To
3x1 +2x2 ≤ 15000 ‫ﻴﻊ‬ ‫اﻟﺘﺼ‬ ‫ﻗﻴﺪ‬
x1 +2x2 ≤ 1000 ‫اﻟﺘﺠﻤﻴﻊ‬ ‫ﻗﻴﺪ‬
x1 ≤4000 ‫اﻟﻄﻠﺐ‬ ‫ﻗﻴﺪ‬
x2 ≤4500 ‫اﻟﻄﺐ‬ ‫ﻗﻴﺪ‬
x1,x2 ≥0 ‫اﻟﺴﻠﺒﻴﺔ‬ ‫ﻋﺪم‬ ‫ﺷﺮط‬
‫اﻛﺪة‬‫ﺮ‬‫اﻟ‬ ‫ات‬ ‫اﳌﺘﻐ‬‫أو‬ ‫ﻤﻴﺔ‬ ‫و‬ ‫ات‬ ‫ﻣﺘﻐ‬ ‫ﻃﺮح‬‫أو‬ ‫ﺑﺈﺿﺎﻓﺔ‬ ‫وذﻟﻚ‬ ‫ﻣﻌﺎدﻻت‬ ‫إ‬ ‫ﺑﺎﻟﻘﻴﻮد‬ ‫ﺎﺻﺔ‬ ‫ا‬ ‫اﳌﺘﺒﺎﻳﻨﺎت‬ ‫ﻞ‬ ‫ﺗﺤﻮ‬ :
ً
‫ﺛﺎﻧﻴﺎ‬
Slack
Variables
–
‫اﳌﺘﺒﺎﻳﻨﺔ‬ ‫اﺷﺎرة‬ ‫ﺣﺴﺐ‬
≥
(‫ي‬‫ﺴﺎو‬ ‫أو‬ ‫ﻣﻦ‬ ‫)اﻛ‬
‫أم‬
≤
(‫ي‬‫ﺴﺎو‬ ‫أو‬ ‫)أﺻﻐﺮﻣﻦ‬
-
‫وﻏ‬ ‫ﺎﻣﻠﺔ‬ ‫ا‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻟﺘﻤﺜﻴﻞ‬ ‫وذﻟﻚ‬
‫ن‬ ‫ﺑ‬ ‫ق‬‫)اﻟﻔﺮ‬ ‫اﳌﺴﺘﻘﻠﺔ‬
(‫ﻧﺘﺎج‬ ‫واﳌﺴﺘﻘﻠﺔ‬ ‫اﳌﺘﺎﺣﺔ‬ ‫ﺎﻧﺎت‬ ‫ﻣ‬
3x1 +2x2 +S1=15000

16. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
16
x1 +2x2 +S2= 1000
x1+S3 = 4000
x2 +S4 = 4500
‫داﻟﺔ‬ ‫وﻟﺘﺼﻔ‬ ،(‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ات‬ ‫ﻣﺘﻐ‬ ‫ﺐ‬ ‫ﺗﺮﺗ‬ ‫ﺑﻨﻔﺲ‬ ‫اﻛﺪة‬‫ﺮ‬‫واﻟ‬ ‫اﻟﻔﻌﻠﻴﺔ‬ ‫ات‬ ‫اﳌﺘﻐ‬ ‫ﺎﻓﺔ‬ ‫ﺎر‬ ‫ﺑﺎﻇ‬ ‫ذﻟﻚ‬ ‫)ﻳﺘﻢ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﺗﺼﻔ‬ :
ً
‫ﺛﺎﻟﺜﺎ‬
.‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﻣﺘﻐ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻞ‬ ‫اﺷﺎرة‬ ‫ﺑﻘﻠﺐ‬ ‫ﻧﻘﻮم‬ ‫ﺪف‬ ‫اﻟ‬
Max Z= 1.5x1 +1.8x2 + 0S1 + 0S2 + 0S3 + 0S4
Max Z=-1.5x1 – 1.8x2 – 0S1 – 0S2 – 0S3 –0S4 =0
S.To:
3x1 +2x2 + S1 +0S2 + 0S3 + 0S4 = 15000
x1 +2x2 +0S1+S2 + 0S3 + 0S4 = 1000
x1 +0S1 + 0S2 + S3 + 0S4 = 4000
x2 +0S1+0S2 +0S3 + S4 = 4500
x1,x2,S1,S2,S3,S4 ≥0
‫ﻲ‬ ‫ﺑﺘﺪا‬ ‫ﻞ‬ ‫ا‬ ‫ل‬‫ﺟﺪو‬ ‫ﺸﺎء‬ ‫ا‬ :
ً
‫ﻌﺎ‬ ‫ا‬‫ر‬
InitialSolutionTable
(‫اﳌﻄﺮوﺣﺔ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﺣﻞ‬ ‫داﺧﻠﮫ‬ ‫ﺘﻢ‬ ‫ﺳ‬ ‫اﻟﺬي‬ ‫ل‬‫ﺪو‬ ‫ا‬‫ﻮ‬ ‫و‬ )
Cj Variables 1.5 1.8 0 0 0 0 R.H.S
X1 X2 S1 S2 S3 S4
0 S1 3 2 1 0 0 0 15000
0 S2 1 2 0 1 0 0 10000
0 S3 1 0 0 0 1 0 4000
0 S4 0 1 0 0 0 1 4500
Zj 0 0 0 0 0 0 0
Zj-Cj -1.5 -1.8 0 0 0 0 0
:
ً
‫ﺧﺎﻣﺴﺎ‬
‫اﳌﻔﺘﺎح‬ ‫وﺗﺤﺪﻳﺪ‬ (‫ﺎرج‬ ‫ا‬ ‫)اﳌﺘﻐ‬ ‫ﺎرج‬ ‫ا‬ ‫اﻟﺼﻒ‬ ‫وﺗﺤﺪﻳﺪ‬ (‫اﻟﺪاﺧﻞ‬ ‫)اﳌﺘﻐ‬ ‫اﻟﺪاﺧﻞ‬ ‫اﻟﻌﻤﻮد‬ ‫ﺗﺤﺪﻳﺪ‬
Cj Variables 1.5 1.8 0 0 0 0 R.H.S
X1 X2 S1 S2 S3 S4
0 S1 1 2 1 0 0 0 15000 15000/2=7500

17. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
17
0 S2 1 2 0 1 0 0 10000 10000/2=5000
0 S3 1 0 0 0 1 0 4000 4500/0=∞
0 S4 0 1 0 0 0 1 4500 4500/1=4500
Zj 0 0 0 0 0 0 0
Zj-Cj 1.5 1.8 0 0 0 0 0
‫ﻋﻨﺼﺮ‬ ‫اﻟﺪاﺧﻞ‬ ‫اﳌﺘﻐ‬ (‫ﺎرج‬ ‫ا‬ ‫ﺎرج)اﳌﺘﻐ‬ ‫ا‬ ‫اﻟﺼﻒ‬
(‫ﺎز)اﳌﻔﺘﺎح‬ ‫رﺗ‬
‫ﻹﻳﺠﺎد‬
‫ﻞ‬ ‫ا‬
‫ﻣﺜﻞ‬
‫ﺒﻊ‬ ‫ﻧ‬
‫ﻄﻮات‬ ‫ا‬
‫اﳌﺘﻜﺮرة‬
‫اﻟﺘﺎﻟﻴﺔ‬
‫اﻟ‬
‫ﺗﺒﺪا‬
‫ﺑﺈﻳﺠﺎد‬
‫ﻞ‬ ‫ا‬
‫ﻲ‬ ‫ﺑﺘﺪا‬
‫ﻟﻨﻘﻄﺔ‬‫اﳌﻨﺎﻇﺮ‬ ‫ﻞ‬ ‫ا‬‫ﻮ‬ ‫و‬ :
‫ﺻﻞ‬
‫ﻘﺔ‬‫اﻟﻄﺮ‬
-
Initial Solution
–
‫ات‬ ‫اﳌﺘﻐ‬ ‫ﻣﻦ‬ ‫ﻣﺘﻐ‬ ‫ﻞ‬ ‫ﻗﻴﻤﺔ‬ ‫أن‬ ‫ﺑﻔﺮض‬ ‫إﻟﻴﮫ‬ ‫اﻟﺘﻮﺻﻞ‬ ‫ﺘﻢ‬ ‫و‬ . ‫اﻟﺒﻴﺎﻧﻴﺔ‬ ‫ﻲ‬ ‫ﺑﺘﺪا‬ ‫ﻞ‬ ‫ا‬
‫ن‬ ‫ﻘﺘ‬‫ﻓﻴﺎﻟﻄﺮ‬ ‫وﺟﺪﻧﺎ‬ ‫وﻛﻤﺎ‬ .
ً
‫اﻗﺘﺼﺎدﻳﺎ‬ ‫وﻣﺮﻓﻮض‬ ‫ﺎﺿﻴﺎ‬‫ر‬ ‫ل‬‫ﻣﻘﺒﻮ‬ ‫ﺣﻞ‬ ‫ﻮ‬ ‫و‬ .‫ﻟﻠﺼﻔﺮ‬ ‫ﺔ‬ ‫ﻣﺴﺎو‬ ‫اﳌﺪروﺳﺔ‬ ‫ﻠﺔ‬ ‫اﳌﺸ‬ ‫ﺻﻠﻴﺔ‬
‫ﻞ‬ ‫أن‬ ‫ﻛﻤﺎ‬ ،‫ﺻﻔﺮ‬ ‫ي‬‫ﺴﺎو‬ ‫ﻞ‬ ‫ا‬ ‫ﺬا‬ ‫ﻣﻦ‬ ‫اﻟﻌﺎﺋﺪ‬ ‫ﺢ‬‫اﻟﺮ‬ ‫ﻓﺄن‬ ‫ﻳﺔ‬ ‫وا‬ ‫اﻟﺒﻴﺎﻧﻴﺔ‬
‫أﻧﮫ‬ ‫ﺑﻤﻌ‬ ‫ﻣﺴﺘﻐﻠﺔ‬ ‫ﻏ‬ ‫اﳌﺘﺎﺣﺔ‬ ‫ﺎﻧﺎت‬ ‫ﻣ‬
‫ﻋﻨﺪﻣﺎ‬
=0
2
=0 ,x
1
x
‫ﻓﺎن‬
Z=0
‫ﻣﻦ‬ ‫ﺎء‬ ‫ﻧ‬ ‫ﻌﺪ‬ ‫و‬ ،‫ات‬ ‫اﳌﺘﻐ‬ ‫ن‬ ‫ﺑ‬ ‫واﺑﺪال‬ ‫إﺣﻼل‬ ‫ﺑﺈﺣﺪاث‬ ‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫ﺑﺎﻳﺠﺎد‬ ‫ﻧﻘﻮم‬ ‫ﻟﺬﻟﻚ‬ ،
‫ﺧ‬ ‫ﻟﻠﺴﻄﺮ‬‫ﺑﺎﻟﻨﻈﺮ‬ ‫ﺗﺤﺪﻳﺪﻩ‬ ‫ﺘﻢ‬ ‫و‬ (‫اﻟﺪاﺧﻞ‬ ‫)اﻟﻌﻤﻮد‬ ‫اﻟﺪاﺧﻞ‬ ‫اﳌﺘﻐ‬ ‫ﺗﺤﺪﻳﺪ‬ ‫ﻳﺘﻢ‬ ‫أن‬ ‫ﻣﻦ‬ ‫ﺑﺪ‬ ‫ﻻ‬ ‫ﻲ‬ ‫ﺑﺘﺪا‬ ‫ﻞ‬ ‫ا‬ ‫ل‬‫ﺟﺪو‬
‫ا‬
) ‫اﳌﺘﻐ‬ ‫ﻳﻘﺎﺑﻞ‬ ‫ﻧﺠﺪ‬ ‫أﻋﻼﻩ‬ ‫اﳌﺜﺎل‬ ، ‫ﳌﺘﻐ‬ ‫ﻗﻴﻤﺔ‬ ‫أﻛ‬ ‫ﺑﺘﺤﺪﻳﺪ‬ ‫وذﻟﻚ‬ ‫أﻋﻼﻩ‬ ‫ل‬‫ﺪو‬
2
X
‫ﻣﺘﻐ‬ ‫ﺑﻘﻴﻤﺔ‬ (
1.8
-
‫ﺗﺤﺪﻳﺪ‬ ‫ﺛﻢ‬
‫اﻟﻜﻤﻴﺎت‬ ‫ﺑﻘﺴﻤﺔ‬ ‫ذﻟﻚ‬ ‫ﺘﻢ‬‫و‬ (‫ﺎرج‬ ‫ا‬ ‫)اﻟﺼﻒ‬ ‫ﺎرج‬ ‫ا‬ ‫اﳌﺘﻐ‬
RHS
‫وﺗﺤﺪﻳﺪ‬ (‫اﻟﺪاﺧﻞ‬ ‫)اﻟﻌﻤﻮد‬ ‫اﻟﺪاﺧﻞ‬ ‫اﳌﺘﻐ‬‫ﻋﻨﺎﺻﺮ‬ ‫ﻋ‬
‫ا‬ ‫اﳌﺘﻐ‬ ‫ﻮ‬ ‫ن‬‫ﻮ‬ ‫ﻟﻴ‬ ‫ﳌﺘﻐ‬ ‫ﻣﻨﺎﻇﺮة‬ ‫ﻗﻴﻤﺔ‬ ‫أﻗﻞ‬
) :‫ﻲ‬ ‫ﺎﻵ‬ ‫وذﻟﻚ‬ ‫ﺎرج‬
15000
÷
2
=
7500
،
10000
÷
2
=
5000
،
4000
÷
0
=
0
،
4500
÷
1
=
4500
‫اﳌﺘﻐ‬ ‫ﻳﻤﺜﻠﮫ‬ ‫واﻟﺬي‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺼﻒ‬ ‫أن‬ ‫ﻧﺠﺪ‬ ‫ﻟﺬﻟﻚ‬ (
4
S
(‫ﺎرج‬ ‫ا‬ ‫)اﳌﺘﻐ‬ ‫ﺎرج‬ ‫ا‬ ‫اﻟﺼﻒ‬‫ﻮ‬
‫ﻮ‬ ‫ﻗﻴﻤﺔ‬ ‫أﻗﻞ‬ ‫ﺻﺎﺣﺐ‬ ‫واﻟﻌﻨﺼﺮ‬
500
‫ﺧﺎرج‬ ‫ﻗﻴﻤﺔ‬ ‫اﻗﻞ‬ ‫ﺻﺎﺣﺐ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﻮ‬ ‫و‬ ‫اﳌﻔﺘﺎح‬ ‫أو‬ ‫ﺎز‬ ‫رﺗ‬ ‫ﻋﻨﺼﺮ‬ ‫ﻗﻴﻤﺔ‬ ‫أم‬ ‫وﻧﺠﺪ‬ .
‫ا‬ ‫ﻗﺴﻤﺔ‬
‫اﻟﺴﺎﺑﻘﺔ‬ ‫ﻄﻮة‬
1
‫اﻟﺪاﺧﻞ‬ ‫)اﻟﻌﻤﻮد‬ ‫اﻟﺪاﺧﻞ‬ ‫ﻟﻠﻤﺘﻐ‬ ‫ﻣﻘﺎﺑﻠﺔ‬
2
X
.(
‫ﻋﻨﺎﺻﺮ‬ ‫ﺑﻘﺴﻤﺔ‬ ‫ﻧﺒﺪاء‬ ‫ﺪﻳﺪ‬ ‫ا‬ ‫ﻞ‬ ‫ا‬ ‫ل‬‫ﺟﺪو‬ ‫ﻦ‬‫ﻮ‬ ‫ﻟﺘ‬
‫ﺎرج‬ ‫ا‬ ‫اﻟﺼﻒ‬
‫ﺎز‬ ‫رﺗ‬ ‫ﻋﻨﺼﺮ‬‫أو‬ ‫اﳌﻔﺘﺎح‬ ‫ﻗﻴﻤﺔ‬ ‫ﻋ‬
‫ﺑﺎ‬ ‫ﻧﻘﻮم‬ ‫ﺛﻢ‬ ،
‫ﻳﺠﺎد‬
:‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻘﺎﻋﺪة‬ ‫ﺑﺎﺗﺒﺎع‬
ً
‫ﺗﺒﺎﻋﺎ‬ ‫ات‬ ‫اﳌﺘﻐ‬ ‫ﻟﻠﺒﻘﻴﺔ‬ ‫ل‬‫ﺪو‬ ‫ا‬ ‫اﻟﻘﻴﻢ‬ ‫ﺑﻘﻴﺔ‬
‫اﻟﻘﺪﻳﻢ‬‫اﻟﻌﻨﺼﺮ‬ = ‫اﻟﺼﻒ‬ ‫ﺪﻳﺪ‬ ‫ا‬‫اﻟﻌﻨﺼﺮ‬
–
‫اﻟﺪاﺧﻞ‬ ‫اﻟﻌﻤﻮد‬ ‫ﻣﻊ‬ ‫اﻟﻘﺪﻳﻢ‬ ‫اﻟﺼﻒ‬ ‫ﺗﻘﺎﻃﻊ‬‫ﻋﻨﺼﺮ‬
×
‫اﳌﻨﺎﻇﺮ‬‫اﻟﻌﻨﺼﺮ‬
‫اﻟﺪاﺧﻞ‬ ‫اﻟﻌﻤﻮد‬
‫ﻟﻠﻤﺘﻐ‬ ‫اﻟﺼﻒ‬ ‫اﻟﻘﺪﻳﻤﺔ‬ ‫اﻟﻘﻴﻢ‬ ‫ﺑﺮﺻﺪ‬ ‫ﻗﻢ‬ :‫ل‬‫و‬ ‫اﻟﺼﻒ‬
ً
‫ﻣﺜﻼ‬
S1
‫اﻟﻌﻤﻮد‬ ‫ﺎز‬ ‫رﺗ‬ ‫ﻟﻌﻨﺼﺮ‬ ‫اﳌﻘﺎﺑﻞ‬‫اﻟﻌﻨﺼﺮ‬ ‫ﻧﺮﺻﺪ‬ ‫ﺛﻢ‬
) ‫أﻧﮫ‬ ‫ﺘ‬‫و‬ ‫اﻟﺪاﺧﻞ‬
2
‫ﻌﻜﺲ‬ ‫ﻧﻘﻮم‬ ‫ﺛﻢ‬ (
‫ﺪﻳﺪة‬ ‫ا‬ ‫اﻟﺪاﺧﻞ‬ ‫اﻟﺼﻒ‬ ‫ﻗﻴﻢ‬ ‫ﻣﻊ‬ ‫ﻣﺤﺘﻮاﻩ‬ ‫وﺿﺮب‬ ‫ﺷﺎرة‬
‫اﻟﻘﺪﻳﻤﺔ‬ ‫اﻟﻘﻴﻢ‬
‫ﻟﻠﺼﻒ‬
S1
3 2 1 0 0 0 15,000
-2
×
0=0 -2
×
1=-2 -2
×
0=0 -2
×
0=0 -2
×
1=-2 -2
×
0=0 -2
×
4500= -9,000

18. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
18
Sum 3 0 1 0 -2 0 6,000
‫ﻟﻠﻤﺘﻐ‬ ‫ﻲ‬ ‫اﻟﺜﺎ‬ ‫اﻟﺼﻒ‬ ‫ﻣﻊ‬ ‫اﻟﺴﺎﺑﻘﺔ‬ ‫ﻘﺔ‬‫اﻟﻄﺮ‬ ‫ﻧﻜﺮر‬
S2
‫اﻟﻘﺪﻳﻤﺔ‬ ‫اﻟﻘﻴﻤﺔ‬
‫ﻟﻠﺼﻒ‬
S2
1 2 0 1 0 0 10000
-2
×
0=0 -2
×
1=-2 -2
×
0=0 -2
×
0=0 -2
×
1=-2 -2
×
0=0 -2
×
4500=-9,000
Sum 1 0 0 0 -2 0 1,000
‫اﳌﺘﻐ‬ ‫ﻣﻊ‬ ‫اﻟﺴﺎﺑﻘﺔ‬ ‫ﻘﺔ‬‫اﻟﻄﺮ‬ ‫ﻧﻜﺮر‬
S3
‫اﻟﻘﺪﻳﻤﺔ‬ ‫اﻟﻘﻴﻤﺔ‬
‫ﻟﻠﺼﻒ‬
S2
1 0 0 0 1 0 4000
-0
×
0=0 -0
×
1=0 -0
×
0=0 -0
×
0=0 -0
×
1=0 -0
×
0=0 -0
×
4500= 0
Sum 1 0 0 0 1 0 4,000
:‫ﺗﻴﺔ‬ ‫ﺑﺎﻟﺼﻮرة‬ ‫ن‬‫ﻮ‬ ‫ﻟﻴ‬ ‫ل‬‫ﺪو‬ ‫ا‬ ‫ﻧﻜﻤﻞ‬ ‫ﻟﻠﻘﻴﻢ‬ ‫ﺎ‬‫اﻟﺮ‬ ‫ﺴﺎب‬ ‫وا‬ ‫اءات‬‫ﺮ‬‫ﺟ‬ ‫ﻠﻤﺔ‬ ‫ﺗ‬ ‫ﻣﻦ‬ ‫ﺎء‬ ‫ﻧ‬ ‫ﻌﺪ‬
Cj Variables 1.5 1.8 0 0 0 0 R.H.S
1
X 2
X 1
S 2
S 3
S 4
S
0 1
S 3 0 1 0 -2 0 6000
0 2
S 1 0 0 0 -2 0 1000
0 3
S 1 0 0 0 1 0 4000
1.8 2
X 0 1 0 0 0 1 4500
Zj 0 1.8 0 0 0 0 8100
Zj-Cj 1.5 0 0 0 0 0 1.8
‫اﻧﺘﺎج‬ ‫ﻣﻦ‬ ‫ﻳﺤﻘﻖ‬ ‫اﻟﺬي‬ ‫ﺢ‬‫اﻟﺮ‬ ‫أن‬ ‫ﻧﻼﺣﻆ‬ ‫ﻞ‬ ‫ا‬ ‫ن‬ ‫ﺗﺤﺴ‬ ‫ل‬‫ﺪو‬ ‫ا‬ ‫ﻣﻦ‬
٤٥٠٠
‫ﻮ‬ ‫وﺣﺪة‬
٨١٠٠
‫ﻣﺜﻠﻴﺔ‬ ‫ﺑﺎﺧﺘﺒﺎر‬ ‫ﻧﻘﻮم‬ ‫أن‬ ‫ﻌﺪ‬ ‫و‬ ، ‫ﺟﻨﻴﮫ‬
) ‫ﻣﻮﺟﺒﺔ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻨﺎك‬ ‫أن‬ ‫أﺻﻔﺎرﻧﺠﺪ‬‫أو‬ ‫ﺳﺎﻟﺒﺔ‬ ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ﻗﻴﻢ‬ ‫ﻞ‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬ ‫ﺑﺄن‬ ‫وذﻟﻚ‬ ‫ﻞ‬ ‫ا‬
1.8
‫اﳌﺘﻐ‬ ‫ﻋﻦ‬ ‫ﻧﺎﺗﺠﺔ‬ (
1
x
.
‫ان‬ ‫ﻌ‬ ‫ﻣﻤﺎ‬
‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫ﻳﻤﺜﻞ‬ ‫ﻻ‬ ‫ﻞ‬ ‫ا‬ ‫ﺬا‬ ‫أن‬ ‫ﻧﺠﺪ‬ ‫ﻟﺬﻟﻚ‬
ً
‫اﺿﺎﻓﻴﺎ‬
ً
‫رﺤﺎ‬ ‫ﻳﺤﻘﻖ‬ ‫أﻓﻀﻞ‬
ً
‫ﺣﻼ‬ ‫ﻨﺎك‬
Cj Variables 1.5 1.8 0 0 0 0 R.H.S
1
X 2
X 1
S 2
S 3
S 4
S
0 1
S 3 0 1 0 -2 0 6000/1=6000
0 2
S 1 0 0 0 -2 0 1000/1=1000
0 3
S 1 0 0 0 1 0 4000/1=4000
1.8 2
X 0 1 0 0 0 1 4500/0=0
Zj 0 1.8 0 0 0 0 8100
Zj-Cj 1.5 0 0 0 0 0 1.8

19. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
19
(‫ﺎرج‬ ‫ا‬ ‫)اﻟﺼﻒ‬ ‫ﺎرج‬ ‫ا‬ ‫اﳌﺘﻐ‬
(‫اﻟﺪاﺧﻞ‬ ‫اﻟﻌﻤﻮد‬ ) ‫اﻟﺪاﺧﻞ‬ ‫اﳌﺘﻐ‬
‫ﺎز‬ ‫رﺗ‬ ‫ﻋﻨﺼﺮ‬
(‫)اﳌﻔﺘﺎح‬
‫ن‬‫ﻮ‬ ‫ﻳ‬
ً
‫وﺗﻠﻘﺎﺋﻴﺎ‬ ‫اﻟﺪاﺧﻞ‬ ‫اﻟﻌﻤﻮد‬ ‫ﺑﺘﺤﺪﻳﺪ‬ ‫ﻧﻘﻮم‬
x1
‫ﻋﻨﺎﺻﺮﻋﻤﻮد‬ ‫ﺑﻘﺴﻤﺔ‬ ‫وذﻟﻚ‬ ‫ﺎرج‬ ‫ا‬ ‫اﻟﺼﻒ‬ ‫ﺑﺘﺤﺪﻳﺪ‬ ‫ﻧﻘﻮم‬ ‫ﺛﻢ‬
R.H.S
‫ﻋﻨﺎﺻﺮ‬ ‫ﻋ‬
‫اﻛﺪ‬‫ﺮ‬‫اﻟ‬ ‫اﳌﺘﻐ‬ ‫ﻗﺎﺑﻠﺖ‬ ‫اﻟﻘﺴﻤﺔ‬ ‫ﺎﺻﻞ‬ ‫ﻗﻴﻤﺔ‬ ‫أﻗﻞ‬ ‫أن‬ ‫وﻧﻼﺣﻆ‬ ‫اﻟﺪاﺧﻞ‬ ‫اﻟﻌﻤﻮد‬
S2
‫أو‬ ‫ﺎرج‬ ‫ا‬ ‫اﳌﺘﻐ‬ ‫ﻮ‬ ‫اﻟﺼﻒ‬ ‫ﺬا‬ ‫ن‬‫ﻮ‬ ‫ﻳ‬ ‫ﻋﻠﻴﮫ‬
‫ﺎﻟﺘﺎ‬ ‫ﺟﺪﻳﺪ‬ ‫ﺣﻞ‬ ‫ل‬‫ﺟﺪو‬ ‫ﺘﺞ‬ ‫ﻟﻴ‬ ‫ﺎرج‬ ‫ا‬ ‫اﻟﺼﻒ‬
‫ﻟﻠﻤﺘﻐ‬ ‫اﳌﻘﺎﺑﻞ‬ ‫ﻟﻠﺼﻒ‬ ‫اﻟﺴﺎﺑﻘﺔ‬ ‫اﳌﻌﺎدﻟﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫ل‬‫ﺪو‬ ‫ا‬ ‫ﺑﺘﻜﻤﻠﺔ‬ ‫ﻧﻘﻮم‬
1
S
1
S 3 0 1 0 -2 0 6000
-3
×
1=-3 -3
×
0=0 -3
×
0=0 -3
×
0=0 -3
×
-2=6 -3
×
0=0 -3
×
1000=-
3000
Sum 0 0 1 0 4 0 3000
‫ﻟﻠﻤﺘﻐ‬ ‫اﳌﻘﺎﺑﻞ‬ ‫ﻟﻠﺼﻒ‬ ‫اﻟﺴﺎﺑﻘﺔ‬ ‫اﳌﻌﺎدﻟﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫ل‬‫ﺪو‬ ‫ا‬ ‫ﺑﺘﻜﻤﻠﺔ‬ ‫ﻧﻘﻮم‬
3
S
3
S 1 0 0 0 1 0 4000
-1
×
1=-1 -1
×
0=0 -1
×
0=0 -1
×
0=0 -1
×
-2=2 -1
×
0=0 -1
×
1000=-
1000
Sum 0 0 0 0 3 0 3000
‫ﻟﻠﻤﺘﻐ‬ ‫اﳌﻘﺎﺑﻞ‬ ‫ﻟﻠﺼﻒ‬ ‫اﻟﺴﺎﺑﻘﺔ‬ ‫اﳌﻌﺎدﻟﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫ل‬‫ﺪو‬ ‫ا‬ ‫ﺑﺘﻜﻤﻠﺔ‬ ‫ﻧﻘﻮم‬
2
X
2
X 0 1 0 0 0 1 4500
-0
×
1=0 -0
×
0=0 -0
×
0=0 -0
×
0=0 -0
×
-2=0 -0
×
0=0 -0
×
1000=0
Sum 0 1 0 0 0 1 4500
: ‫ﺎﻟﺘﺎ‬ ‫ﻞ‬ ‫ا‬ ‫ن‬‫ﻮ‬ ‫ﻓﻴ‬
Cj Variables 1.5 1.8 0 0 0 0 R.H.S
1
X 2
X 1
S 2
S 3
S 4
S
0 1
S 0 0 1 0 4 0 3000
1.5 1
X 1 0 0 0 -2 0 1000
0 3
S 0 0 0 0 3 0 3000
1.8 2
X 0 1 0 0 0 1 4500
Zj 1.5 1.8 0 0 0 0
Zj-Cj 0 0 0 0 0 0
‫اﻧﺘﺎج‬ ‫ﻋﻨﺪ‬ ‫وذﻟﻚ‬ ‫اﻟﻄﻠﺒﺎت‬ ‫ﻣﻊ‬ ‫ﻴﻌﮫ‬ ‫ﺗﺼ‬ ‫ﺗﻢ‬ ‫اﻟﺬي‬ ‫ﻞ‬ ‫ﻧﻔﺎذ‬ ‫ﺗﻢ‬ ‫ﻷﻧﮫ‬ ‫أﻣﺜﻞ‬ ‫ﺣﻞ‬‫ﻮ‬ ‫ﻞ‬ ‫ا‬ ‫أن‬ ‫ﻧﻼﺣﻆ‬
1000
‫ل‬‫و‬ ‫اﻟﻨﻮع‬ ‫ﻣﻦ‬ ‫وﺣﺪة‬
1
x
‫و‬
4500
‫اﻟﻨﻮع‬ ‫ﻣﻦ‬ ‫وﺣﺪة‬
2
x
)‫ﻮ‬ ‫ﺢ‬‫اﻟﺮ‬ ‫ن‬‫ﻮ‬ ‫ﻟﻴ‬ .
1500
‫ل‬‫و‬ ‫ﻟﻠﻨﻮع‬ (
1
x
)‫و‬
8100
‫ﻲ‬ ‫اﻟﺜﺎ‬ ‫ﻟﻠﻨﻮع‬ (
2
x
.
‫ﻣﺜﺎل‬
٢
) ‫اﻟﻌﺎﻣﺔ‬ ‫ﻘﺔ‬‫اﻟﻄﺮ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﳌﺴﺄﻟﺔ‬ ‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫ا‬ ‫أوﺟﺪ‬
simplex
(

20. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
20
Max Z=3x1+2x2
S.To:
-x1+2x2≤4
3x1+2x2≤14
x1 -x2≤3
x1,x2,x3≥0
:‫ﻞ‬ ‫ا‬
Max Z=3x1+2x2 + 0S1+0S2+0S3
-x1 + 2x2 + S1=4
3x1+2x2 + S2=14
x1 -x2 + S3 =3
x1,x2,x3,S1,S2,S3≥0
‫ﻲ‬ ‫اﳌﺒﺪ‬ ‫ﻞ‬ ‫ا‬ ‫ل‬‫ﺟﺪو‬ ‫ن‬‫ﻮ‬ ‫ﻧ‬
Cj Variables 3 2 0 0 0 R.H.S
1
X 2
X 1
S 2
S 3
S
0 1
S -1 2 1 0 0 4
0 2
S 3 2 0 1 0 14
0 3
S 1 -1 0 0 1 3
Zj 3 2 0 0 0 0
Zj-Cj 3 2 0 0 0 0
‫ﻮ‬ ‫و‬ ‫ﻟﻠﺪاﻟﺔ‬ ‫ﻗﻴﻤﺔ‬ ‫اﻛ‬ ‫ﺻﺎﺣﺐ‬‫ﻮ‬ ‫اﻟﺪاﺧﻞ‬ ‫اﳌﺘﻐ‬
x1
‫ﺑﻘﺴﻤﺔ‬ ‫ﺎرج‬ ‫ا‬ ‫اﻟﺼﻒ‬ ‫وﻧﺤﺪد‬ ،
R.H.S
‫اﻟﺪاﺧﻞ‬ ‫ﻋﻨﺎﺻﺮاﳌﺘﻐ‬ ‫ﻋ‬
Cj Variables 3 2 0 0 0 R.H.S
1
X 2
X 1
S 2
S 3
S
0 1
S -1 2 1 0 0 4/-1=-4
0 2
S 3 2 0 1 0 14/3=4.6
0 3
S 1 -1 0 0 1 3/1=3
Zj 3 2 0 0 0 0
Zj-Cj -3 -2 0 0 0 0
)‫ﺎر‬ ‫ﺗ‬‫ر‬ ‫ﻋﻨﻀﺮ‬ ‫ﺑﺘﺤﺪﻳﺪ‬ ‫ﻧﻘﻮم‬ ‫ﺎ‬ ‫ﻌﺪ‬
-1
‫ﺟﺪﻳﺪ‬ ‫ل‬‫ﺟﺪو‬ ‫ﻞ‬ ‫ا‬ ‫ن‬ ‫وﺗﺤﺴ‬ ‫اﻟﻜﻤﻴﺎت‬ ‫ﺑﻘﻴﺔ‬ ‫ﺴﺎب‬ ‫ﺎﺿﻴﺔ‬‫اﻟﺮ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺑﺎﺟﺮاء‬ ‫ﻧﻘﻮم‬ (
‫اﳌﺘﻐ‬ ‫ﻣﻌﺎﻣﻼت‬ ‫ﺣﺴﺎب‬
1
S
1
S -1 2 1 0 0 4
-1
×
-1=-1 1
×
-1=-1 -1
×
0=0 -1
×
0=0 -1
×
-1= 1 -1
×
-3= 3
SUM 0 3 1 0 1 7

21. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
21
‫اﳌﺘﻐ‬ ‫ﻣﻌﺎﻣﻼت‬ ‫ﺣﺴﺎب‬
2
S
2
S 3 2 0 1 0 14
-3
×
1=-3 -3
×
-1=3 -3
×
0=0 -3
×
0=0 -3
×
1= 3 -3
×
3=-9
SUM 0 5 0 0 -3 5
‫ﻲ‬ ‫ﺎ‬ ‫اﻟ‬ ‫ﻞ‬ ‫ا‬ ‫ل‬‫ﺟﺪو‬
Cj Variables 3 2 0 0 0 R.H.S
1
X 2
X 1
S 2
S 3
S
0 1
S 0 3 1 0 1 7
0 2
S 0 5 0 0 -3 5
3 1
X 1 -1 0 0 1 3
Zj 3 0 0 0 0 9
Zj-Cj 0 3 0 0 3 0
‫اﳌﺘﻐ‬ ‫ﻋﻦ‬ ‫ﻧﺘﺠﺖ‬ ‫ﻣﻮﺟﺒﺔ‬ ‫ﻛﻤﻴﺔ‬ ‫ﻨﺎك‬ ‫أن‬ ‫ﺐ‬ ‫ﺴ‬ ‫أﻣﺜﻞ‬ ‫ﻏ‬ ‫ﻞ‬ ‫ا‬ ‫ﺬا‬ ‫أن‬ ‫ﻧﺠﺪ‬ ‫ﻞ‬ ‫ا‬ ‫اﻣﺜﻠﻴﺔ‬‫اﺧﺘﺒﺎر‬ ‫وﻋﻨﺪ‬
2
x
‫اﳌﺘﻐ‬‫ﻮ‬ ‫ن‬‫ﻮ‬ ‫ﻟﻴ‬ .
‫اﻟﺪاﺧﻞ‬
Cj Variables 3 2 0 0 0 R.H.S
1
X 2
X 1
S 2
S 3
S
0 1
S 0 3 1 0 1 7/3=2.5
0 2
S 0 5 0 0 -3 5/5=1
3 1
X 1 -1 0 0 1 3/-1=-3
Zj 3 0 0 0 0 9
Zj-Cj 0 3 0 0 3 0
‫اﳌﺘﻐ‬
S1
1
S 0 3 1 0 1 7
-3
×
0= 0 -3
×
1=-3 -3
×
0=0 -3
×
0= -3
×
-0.6=1.8 -3
×
1=-3
0 0 1 0 2.8 4
‫اﳌﺘﻐ‬
X1
1
X 1 -1 0 0 1 3
-1
×
0=0 -1
×
-1=+1 -1
×
0=0 -1
×
0=0 -1
×
-0.6=0.6 -1
×
1=-1
1 0 0 0 1.6 2

22. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
22
‫ﻞ‬ ‫ا‬ ‫ل‬‫ﺟﺪو‬
Cj Variables 3 2 0 0 0 R.H.S
1
X 2
X 1
S 2
S 3
S
0 1
S 0 0 1 0 2.8 4
2 2
X 0 1 0 0 -0.6 1
3 1
X 1 0 0 0 1.6 2
Zj 3 2 2 0 10.4 14
Zj-Cj 0 0 -2 0 -10.4 14
‫ﺣﻞ‬ ‫ﻞ‬ ‫ا‬ ‫أن‬ ‫ﻌ‬ ‫ﻣﻤﺎ‬ ‫ﺎ‬ ‫ﻃﺎﻗ‬ ‫اﺳﺘﻔﺬت‬ ‫ﻗﺪ‬ ‫ات‬ ‫اﳌﺘﻐ‬ ‫ﺟﻤﻴﻊ‬ ‫أن‬ ‫ﻧﺠﺪ‬ ، ‫ﻞ‬ ‫ا‬ ‫اﻣﺜﻠﻴﺔ‬‫اﺧﺘﺒﺎر‬ ‫اﺟﺮاء‬ ‫ﻋﻨﺪ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫ل‬‫ﺪو‬ ‫ا‬ ‫ﻣﻦ‬
‫ﻲ‬ ‫اﻟﺜﺎ‬ ‫اﻟﻨﻮع‬ ‫ﻣﻦ‬ ‫ن‬ ‫وﺣﺪﺗ‬ ‫اﻧﺘﺎج‬ ‫ﻋﻨﺪ‬ ‫وذﻟﻚ‬ ،‫أﻣﺜﻞ‬
x2
‫ل‬‫و‬ ‫اﻟﻨﻮع‬ ‫ﻣﻦ‬ ‫وﺣﺪات‬ ‫ﺛﻼﺛﺔ‬‫و‬ ،
x1
‫اﳌﺘﻮﻗﻊ‬ ‫ﺢ‬‫اﻟﺮ‬ ‫اﺟﻤﺎ‬ ‫ن‬‫ﻮ‬ ‫ﻟﻴ‬
١٤
.

23. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
23
‫اﻟﻨﻘﻞ‬ ‫ﻧﻤﻮذج‬
Transition Model
‫ﻣﻘﺪﻣﺔ‬
‫ﻣﺮﻋ‬ ‫ﺑﺎدىء‬ ‫اﻋﺘﻤﺪت‬ ‫ﺣﻴﺚ‬ ‫ات‬‫ر‬‫ا‬‫ﺮ‬‫اﻟﻘ‬ ‫اﺗﺨﺎذ‬ ‫ﻋ‬ ‫ﺳﺎﻋﺪت‬ ‫اﻟ‬ ‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫اﻟ‬ ‫ﺗﻄﺒﻴﻘﺎت‬ ‫اوﺟﮫ‬ ‫اﺣﺪ‬ ‫اﻟﻨﻘﻞ‬ ‫ﻣﺠﺎل‬ ‫ﻌﺘ‬
‫ﺎﻟﻴﻒ‬ ‫ﺗ‬ ‫ﻳﺠﻌﻞ‬ ‫ﻤﺎ‬‫و‬‫ﺻﻐﺮ‬ ‫اﻟﻮﺣﺪات‬ ‫ا‬ ‫ﺴﻴﺔ‬ ‫اﻟﺮﺋ‬ ‫ﻘﻴﺔ‬‫ﺴﻮ‬ ‫اﻟ‬‫او‬ ‫ﻧﺘﺎﺟﻴﺔ‬ ‫اﳌﻨﺎﻓﺬ‬ ‫ﻣﻦ‬ ‫اﻟﺴﻠﻊ‬ ‫ﺗﺪﻓﻖ‬ ‫ﻴﻞ‬ ‫ﺴ‬ ‫دارة‬ ‫ﻣﺴﺎﻋﺪة‬
‫ا‬ ‫اﻟﻨﻘﻞ‬
‫ن‬ ‫ﺑ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫اﺑﻂ‬‫ﺮ‬‫ﺗ‬ ‫اﻳﺠﺎد‬ ‫ﺎ‬ ‫ﻧﻔﺴ‬ ‫ﻧﺘﺎﺟﻴﺔ‬ ‫اﻟﻮﺣﺪات‬ ‫ن‬ ‫ﺑ‬ ‫اﻟﻨﻘﻞ‬ ‫ﺗﻜﻨﻴﻚ‬ ‫ﺴﺘﺨﺪم‬ ‫ان‬ ‫ﻳﻤﻜﻦ‬ ‫ﻛﻤﺎ‬. ‫ﻣﻤﻜﻦ‬ ‫ﺣﺪ‬ ‫ﻰ‬ ‫اد‬
‫ﻠﺔ‬ ‫ﻟﻠﻤﺸ‬ ‫او‬ ‫ﺣﻞ‬ ‫اﻳﺠﺎد‬ ‫ﻣﻦ‬ ‫ﺗﺒﺪأ‬ ‫اﻟﻨﻘﻞ‬ ‫ﺑﺮﻣﺠﺔ‬ ‫اﻟﻌﻤﻞ‬ ‫اﻟﻴﺔ‬ ‫ان‬ . ‫ﻣﺴﺘﻘﺒﻼ‬ ‫ﺎ‬ ‫اﻗﺎﻣ‬ ‫اﳌﺘﻮﻗﻊ‬ ‫اﳌﺸﺎرﻊ‬ ‫ن‬ ‫ﺑ‬‫او‬ ‫اﻟﻘﺎﺋﻤﺔ‬ ‫اﻟﻮﺣﺪات‬
‫ﻮ‬ ‫ﻣﻦ‬ ‫ﻟﻠﺘﺤﻘﻖ‬ ‫ﺗﺎﻟﻴﺔ‬ ‫ﻣﺮﺣﻠﺔ‬ ‫ﻧﺘﻘﺎل‬ ‫ﺛﻢ‬
.‫ﺎﻟﻴﻒ‬ ‫اﻟﺘ‬ ‫ﻣﻦ‬ ‫ى‬‫ﻣﺴﺘﻮ‬ ‫ﻰ‬ ‫اد‬ ‫ﻳﺤﻘﻖ‬ ‫اﻟﺬي‬ ‫ﻣﺜﻞ‬ ‫ﻮ‬ ‫ﻞ‬ ‫ا‬ ‫ﺬا‬ ‫ن‬
) ‫ﺪف‬ ‫اﻟ‬ ‫داﻟﺔ‬ ‫ن‬‫ﻮ‬ ‫ﺗ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﻠﻔﺔ‬ ‫اﻟ‬ ‫ﺿﻐﻂ‬ ‫ﻋ‬ ‫اﺳﺘﺨﺪاﻣﮫ‬‫ﻻﻳﻘﺘﺼﺮ‬ ‫اﻟﻨﻘﻞ‬ ‫ﻧﻤﻮذج‬ ‫ان‬
Min
‫ات‬ ‫اﻟﺘﻐ‬ ‫ﻌﺾ‬ ‫اء‬‫ﺮ‬‫اﺟ‬ ‫ﻣﻤﻜﻦ‬ ‫ﺑﻞ‬ (
) ‫ﺎ‬ ‫ﻌﻈﻴﻤ‬‫و‬ ‫ﺢ‬‫اﻟﺮ‬ ‫داﻟﺔ‬‫ار‬‫ﺮ‬‫اﻟﻘ‬ ‫ﻣﺘﺨﺬ‬ ‫ﺪف‬ ‫ﺴ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﺴﻴﻄﺔ‬ ‫اﻟ‬
Max
. (
‫ﺣﻴﺚ‬
‫ﺧﺎﺻﺔ‬ ‫ﺣﺎﻟﺔ‬ ‫ﺗﻤﺜﻞ‬ ‫اﻟﻨﻘﻞ‬ ‫ﻠﺔ‬ ‫ﻣﺸ‬ ‫إن‬
‫ا‬ ‫ﻧﻤﺎذج‬ ‫ﻣﻦ‬
‫اﻟﻄﻠﺐ‬ ‫ﻹﺷﺒﺎع‬ ‫ﻠﻔﺔ‬ ‫اﻟﺘ‬ ‫ق‬‫ﻃﺮ‬ ‫اﻗﻞ‬ ‫إﻳﺠﺎد‬ ‫اﺟﻞ‬ ‫ﻣﻦ‬ ‫وذﻟﻚ‬ ،‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫ﻟ‬
‫ﻋﺪد‬ ‫اﳌﺤﺪود‬
‫ﻊ‬ ‫اﳌﺼﺎ‬ ‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫ﻣﺤﺪود‬ ‫ﻋﺮض‬ ‫ﻣﻦ‬‫ﻳﺘﻮاﻓﺮ‬ ‫ﺑﻤﺎ‬ ،‫اﳌﻮاﻗﻊ‬ ‫ﻣﻦ‬
‫اﻟﻨﻘﻞ‬ ‫ﻧﻤﺎذج‬ ‫أن‬ ‫ﻧﺠﺪ‬ ‫ﻟﺬﻟﻚ‬ ‫ﻧﺘﺎج‬ ‫ﻣﻨﺎﻃﻖ‬ ‫أو‬
‫اﳌﻨﺘﺠﺎت‬ ‫ﻖ‬ ‫ﺴﻮ‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ة‬ ‫ﺑﻜ‬ ‫ﺴﺘﺨﺪم‬
.
.‫ﻧﺘﺎج‬ ‫ﻨﺪﺳﺔ‬ ‫اﻟﻴﻮم‬ ‫ﺴ‬ ‫ﻣﺎ‬‫او‬
: ‫ق‬‫اﻟﻄﺮ‬ ‫ﺬﻩ‬ ‫و‬ ‫اﻟﻨﻘﻞ‬ ‫ﻞ‬ ‫ﻣﺸﺎ‬ ‫ﻞ‬ ‫اﳌﺴﺘﺨﺪﻣﺔ‬ ‫اﻟﺮﺎﺿﻴﺔ‬ ‫ق‬‫اﻟﻄﺮ‬ ‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫ﻋ‬ ‫اﻟﻨﻘﻞ‬ ‫ﻧﻤﻮذج‬ ‫ي‬‫ﻳﺤﺘﻮ‬
-

‫ﻘﺔ‬‫ﻃﺮ‬
‫اﻟﺮﻛﻦ‬
‫اﻟﺸﺮﻗﻴﺔ‬ ‫اﻟﺸﻤﺎﻟﻴﺔ‬

.‫ﺎﻟﻴﻒ‬ ‫اﻟﺘ‬ ‫أﻗﻞ‬ ‫ﻘﺔ‬‫ﻃﺮ‬

.‫ﺐ‬‫اﻟﺘﻘﺮ‬ ‫ﻓﻮﺟﻞ‬ ‫ﺔ‬‫او‬‫ﺰ‬‫اﻟ‬ ‫ﻘﺔ‬‫ﻃﺮ‬

. ‫اﻟﺘﻨﻘﻞ‬‫ﺮ‬ ‫ﻘﺔ‬‫ﻃﺮ‬

. ‫اﳌﻌﺪل‬ ‫ﻊ‬ ‫اﻟﺘﻮز‬ ‫ﻘﺔ‬‫ﻃﺮ‬
‫ﺣﻴﺚ‬
‫اﻟﺜﻼﺛﺔ‬ ‫ق‬‫اﻟﻄﺮ‬ ‫ﺴﺘﺨﺪم‬
‫و‬
‫اﳌﻤﻜﻦ‬ ‫و‬ ‫ﻞ‬ ‫ا‬ ‫ﻹﻳﺠﺎد‬
،
‫ﺎﻣﺴﺔ‬ ‫وا‬ ‫ﻌﺔ‬ ‫اﻟﺮا‬ ‫ﻘﺘﺎن‬‫اﻟﻄﺮ‬ ‫أﻣﺎ‬
‫إ‬ ‫ل‬‫ﻟﻠﻮﺻﻮ‬ ‫ﻓﺴﺘﺨﺪﻣﺎن‬
‫ـﻞ‬ ‫ا‬
‫ﻓﻀﻞ‬ ‫ﻮ‬ ‫و‬ ‫ﻣﺜﻞ‬
.‫ﻠﻔﺔ‬ ‫ﺗ‬ ‫ﺑﺄﻗﻞ‬ ‫ﻳﺰودﻧﺎ‬ ‫واﻟﺬي‬ ‫اﳌﻤﻜﻦ‬ ‫ﻞ‬ ‫ا‬‫ﻮ‬ ،‫ﻣﺜﻞ‬ ‫ﻞ‬ ‫وا‬ ‫ﺪف‬ ‫اﻟ‬ ‫ﻟﺪاﻟﺔ‬ ‫ﻗﻴﻤﺔ‬
‫ﻌﺘ‬
‫ﻋﻤﻠﻴﺔ‬
‫ﻤ‬ ‫ﻣ‬ ‫اﻟﻨﻘﻞ‬
‫ﺔ‬
ً
‫ﺟﺪا‬
‫اﻟﻨﻘﻞ‬ ‫ن‬‫ﻮ‬ ‫ذﻟﻚ‬ ‫اﳌﻨﺘﺠﺎت‬ ‫ﻴﻊ‬ ‫و‬ ‫ﺴﻌ‬ ‫ﻋﻤﻠﻴﺔ‬
‫ﻣﻦ‬ ‫ﻳﻤﺜﻞ‬
٢٥
‫إ‬
٣٠
%
‫ﺑﻴﻊ‬‫ﺳﻌﺮ‬ ‫ﻣﻦ‬ ‫ﻲ‬ ‫اد‬ ‫ﻛﺤﺪ‬
‫اﳌﻨﺘﺞ‬
،
‫ﻟﺬﻟﻚ‬
‫ﺘﻤﺎم‬ ‫ﺎن‬
‫ﻷﻧﮫ‬ ‫ﺑﺎﻟﻨﻘﻞ‬
‫ﻋﻨﺼﺮ‬ ‫ﻻﻋﺘﺒﺎرﻩ‬
‫ﺎﻟﻴﻒ‬ ‫ﻟﺘ‬
ً
‫ﺟﺪا‬ ‫ﻢ‬ ‫ﻣ‬
‫ﻧﺘﺎ‬
‫ج‬
‫ﺔ‬‫ﺮ‬ ‫ﻮ‬ ‫ا‬
‫واﻟ‬
‫ﺳ‬ ‫ﻋ‬ ‫اﳌﺤﺎﻓﻈﺔ‬ ‫ﻳﺠﺐ‬
‫ﺎ‬ ‫ﺮ‬
‫و‬
‫ﻣﺴﻤﻮح‬ ‫ﻏ‬
‫ن‬ ‫اﳌﻨﺎﻓﺴ‬
‫ق‬‫اﻟﺴﻮ‬
‫ﻧﻤﻮذج‬ ‫أن‬ ‫ﻧﺠﺪ‬ ‫ﻟﺬﻟﻚ‬ ‫ﺎ‬ ‫ﻣﻌﺮﻓ‬ ‫ﻣﻦ‬
‫اﻟﺼﻨﺎﻋﺔ‬ ‫اﻟﻨﻘﻞ‬ ‫ﻞ‬ ‫ﻣﺸﺎ‬ ‫ﺟﻤﻴﻊ‬ ‫ﻌﺎ‬ ‫اﻟﻨﻘﻞ‬
‫و‬
‫ﻗﻄﻊ‬
‫اﻟﻐﻴﺎر‬
‫ﺧﻼل‬ ‫وﻣﻦ‬
‫ﻣ‬
‫ﻨﺎ‬
.‫ﻄﻴﺔ‬ ‫ا‬ ‫ﻣﺠﺔ‬ ‫ﻟﻠ‬ ‫ﺧﺎﺻﺔ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻳﻤﺜﻞ‬‫ﻮ‬ ‫ﻓ‬ ‫اﳌﻮاد‬ ‫وﻟﺔ‬
‫ﻣﺜﺎ‬ ‫ﻮﺣﻞ‬ ‫ﻞ‬ ‫ﻌﻠﻢ‬ ‫ﻻ‬ ‫اﳌﻤﻜﻦ‬ ‫و‬ ‫ﻞ‬ ‫ا‬
‫ل‬‫ﻟﻠﻮﺻﻮ‬ ‫ن‬ ‫ﻘﺘ‬‫ﻃﺮ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫ﻩ‬ ‫ﻧﺨﺘ‬ ‫أن‬ ‫ﻳﺠﺐ‬ ‫اي‬ ،، ‫ﻣﻤﻜﻦ‬ ‫ﻮﺣﻞ‬ ،، ‫ﻣﺜﺎ‬ ‫ﺲ‬ ‫أوﻟ‬
‫اﳌﺜﺎ‬ ‫ﻞ‬ ‫ا‬ ‫إ‬

24. ‫ﺷﻨﺪي‬ ‫ﺟﺎﻣﻌﺔ‬
-
‫ﻣﻘﺮر‬
:
‫اﻟﻌﻤﻠﯿﺎت‬ ‫ﺑﺤﻮث‬
–
‫أ‬
.
‫ﺣﺴﻦ‬ ‫ﺻﺪﯾﻖ‬ ‫ﻣﺤﻤﺪ‬
24
١
-
‫اﻟﺘﻨﻘﻞ‬‫ﺮ‬ ‫ﻘﺔ‬‫ﻃﺮ‬
٢
-
‫اﳌﻌﺪل‬ ‫ﻊ‬ ‫اﻟﺘﻮز‬ ‫ﻘﺔ‬‫ﻃﺮ‬
‫اﻟ‬ ‫زرق‬ ‫ﻞ‬ ‫ﺑﺎ‬ ‫اﻟ‬ ‫ن‬ ‫ﻘﺘ‬‫اﻟﻄﺮ‬ ، ‫اﻟﻔﺎرﻏﺔ‬ ‫ﻼﻳﺎ‬ ‫ا‬‫اﺧﺘﺒﺎر‬ ‫ﻣﺒﺪأ‬ ‫ﻌﺘﻤﺪ‬ ‫ن‬ ‫ﻘﺘ‬‫اﻟﻄﺮ‬ ‫ﻠﺘﺎ‬ ‫و‬
‫ﺘﺞ‬ ‫ﻳ‬ ‫ﺬي‬
‫ﺑﻴﻌﺘﻤ‬ ‫اﳌﺜﺎ‬ ‫ﻞ‬ ‫ا‬
‫ﻣﺒﺪأ‬‫اﺧﺘﺒﺎر‬ ‫ﺪ‬
. ‫اﻟﻔﺎرﻏﺔ‬ ‫ﻼﻳﺎ‬ ‫ا‬‫اﺧﺘﺒﺎر‬
‫وﺗﻢ‬ ، ‫اﳌﺼﻔﻮﻓﺔ‬ ‫اء‬‫ﺰ‬‫وأﺟ‬ ‫اﳌﺼﻔﻮﻓﺔ‬ ‫ﻮﻧﺎت‬ ‫ﻣ‬ ‫ﺴﺘﻌﺮض‬ ‫ﺳ‬ ، ‫ﻼﻳﺎ‬ ‫ا‬ ‫ﺬﻩ‬ ‫ن‬ ‫ﻣﻌ‬ ‫ﻊ‬ ‫ﺗﻮز‬ ‫وزﻋﻨﺎ‬‫ﻟﻮ‬ ) : ‫اﻟﻔﺎرﻏﺔ‬ ‫ﻼﻳﺎ‬ ‫ﺑﺎﺧﺘﺒﺎرا‬ ‫ﻌ‬ ‫و‬
‫ل‬‫وﺳﻨﺤﺎو‬ ‫ﻨﻘﺺ؟‬ ‫ﺳ‬‫أو‬ ‫ﻳﺪ‬ ‫ﺳ‬ ‫ﻞ‬ ‫؟‬ ‫ﻠﻴﺔ‬ ‫اﻟ‬ ‫ﺎﻟﻴﻒ‬ ‫ﻟﻠﺘ‬ ‫ﻳﺤﺪث‬ ‫ﺳﻮف‬ ‫اﻟﺬي‬ ‫ﻣﺎ‬ ‫ﻠﻴﺔ‬ ‫ا‬ ‫ﺬﻩ‬ ‫ﺧﻼل‬ ‫اﳌﻨﺘﺠﺎت‬ ‫ﻣﻦ‬ ‫واﺣﺪة‬ ‫وﺣﺪة‬ ‫ﻧﻘﻞ‬
‫أو‬ ‫اﳌﺜﺎ‬ ‫ﻞ‬ ‫ﻧﺨﺘﺎرا‬ ‫ﺣ‬ ‫ل‬‫وﻧﺤﺎو‬
. ‫ﻣﻤﻜﻨﺔ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬ ‫أﻗﻞ‬ ‫ﻌﻄﻴﻨﺎ‬ ‫ﺑﺤﻴﺚ‬ ‫ﺴﻠﻜﮫ‬ ‫إن‬ ‫ﻳﺠﺐ‬ ‫اﳌﻤﺮاﻟﺬي‬ ‫اﻟﻄﺮﻖ‬
‫اﻟﻨﻘﻞ‬ ‫ﻠﺔ‬ ‫ﻋﻨﺎﺻﺮﻣﺸ‬
١
.
(‫ﻣﻌﺮوﺿﺔ‬ ‫)ﻛﻤﻴﺔ‬ ‫ﻣﺤﺪدة‬ ‫ﻃﺎﻗﺔ‬ ‫ﺎ‬ ‫ﻟﺪ‬ (‫ن‬‫ﻣﺨﺎز‬ ،‫ﻣﺴﺘﻮدﻋﺎت‬ ، ‫ﻊ‬ ‫)ﻣﺼﺎ‬ ‫ﻣﻨﺘﺠﺎت‬ ‫ﻊ‬ ‫وﺗﻮز‬ ‫اﻧﺘﺎج‬ ‫ﻣﻮاﻗﻊ‬
٢
.
‫ﻣﺤﺪد‬ ‫ﻃﻠﺐ‬ ‫ﺎ‬ ‫ﻟﺪ‬ (‫ﻣﺤﺪدة‬ ‫ﻣﻮاﻗﻊ‬ ‫ﻢ‬ ‫ﻟﺪ‬ ‫ﺎﺋﻦ‬‫ز‬ ،‫ﺔ‬‫اﻛﺰﺗﺠﺎر‬‫ﺮ‬‫)ﻣ‬ ‫ﺪﻣﺎت‬ ‫وا‬ ‫اﳌﻨﺘﺠﺎت‬ ‫ﻋ‬ ‫ﻃﻠﺐ‬ ‫ﻣﻮاﻗﻊ‬
٣
.
‫ﻨﺎك‬
‫ﻼك‬ ‫ﺳ‬ ‫ﻣﻨﻄﻘﺔ‬ ‫إ‬ ‫ﻧﺘﺎج‬ ‫ﻣﻨﻄﻘﺔ‬ ‫ﻣﻦ‬ ‫وﺣﺪة‬ ‫ﻞ‬ ‫ﻟ‬ ‫ﻣﺤﺪدة‬ ‫ﻧﻘﻞ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬
٤
.
‫واﻟﻌﺮض‬ ‫اﻟﻄﻠﺐ‬ ‫ﻛﻤﻴﺔ‬ ‫ى‬‫ﺴﺎو‬ ‫ﺗ‬ ‫أن‬ ‫ﺗﺠﺐ‬ ‫اﻟﻨﻘﻞ‬ ‫ﻠﺔ‬ ‫ﻣﺸ‬ ‫ﺣﻞ‬ ‫ﺴﺘﻄﻴﻊ‬ ‫ﻲ‬ ‫ﻟ‬
‫ﻣﺜﺎل‬
‫ﺷﺮﻛﺔ‬
‫ن‬ ‫ﺳ‬
‫ﻊ‬ ‫ﻣﺼﺎ‬ ‫ﺛﻼث‬ ‫ﺎ‬ ‫ﻟﺪ‬ ‫ﻟﻠﻤﻄﺎﺣﻦ‬
‫ﺮﻃﻮم‬ ‫وا‬ ‫ﻲ‬ ‫ﻣﺪ‬‫و‬ ‫ة‬ ‫ﻌﻄ‬
‫ﺑﻤﻨﺎﻃﻖ‬ ‫ﻣﺤﺪدة‬ ‫ﻊ‬ ‫ﻟﻠﺘﻮز‬ ‫اﻗﺴﺎم‬ ‫ﺛﻼث‬ ‫ﺎ‬ ‫وﻟﺪ‬ ‫اﻟﺪﻗﻴﻖ‬ ‫ﻟﻄﺤﻦ‬
‫اﻟﺴﻮدان‬ ‫ﻣﻦ‬ ‫ﻣﺨﺘﻠﻔﺔ‬
‫اﳌﺨﺘﻠﻔﺔ‬
‫ﺴﻮدان‬ ‫ﺑﻮر‬‫و‬ ‫ﺑﻴﺾ‬ ‫ﺷﻨﺪي‬
‫ﺧﻄﺔ‬ ‫ﺗﺤﺪﻳﺪ‬ ‫ﺎ‬ ‫دﻓﺎﺗﺮ‬ ‫ﻣﻦ‬ ‫اﳌﺴﺘﺨﺮﺟﺔ‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫واﻗﻊ‬ ‫وﻣﻦ‬
‫ق‬‫اﻟﻄﺮ‬ ‫وﻓﻖ‬ ‫ﻣﻤﻜﻨﺔ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬ ‫اﻗﻞ‬ ‫ا‬ ‫اﻟﻨﻘﻞ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬ ‫ﻰ‬ ‫ﺗﺪ‬ ‫ا‬ ‫ﻳﺆدى‬ ‫اﻟﺬى‬ ‫ﻞ‬ ‫ﺑﺎﻟﺸ‬ ‫ﻊ‬ ‫اﳌﺼﺎ‬ ‫ﻣﻨﺘﺠﺎت‬ ‫وﻧﻘﻞ‬ ‫ﻊ‬ ‫ﻟﺘﻮز‬ ‫اﳌﺜ‬ ‫اﻟﻨﻘﻞ‬
.‫اﻟﻨﻘﻞ‬ ‫ﻟﻨﻤﻮذج‬ ‫اﳌﺨﺘﻠﻔﺔ‬
‫ى‬‫اﻟﻘﺼﻮ‬ ‫اﻟﻄﺎﻗﺔ‬
‫ﻊ‬ ‫ﻟﻠﻤﺼﺎ‬
‫ﺴﻮدان‬ ‫ﺑﻮر‬ ‫ﺑﻴﺾ‬ ‫ﺷﻨﺪي‬ ‫اﻗﺴﺎم‬
‫ﻊ‬ ‫ﻣﺼﺎ‬
٢٠٠٠
‫ﻃﻦ‬
‫اﻟﻄﻦ‬ ‫ﻧﻘﻞ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬
٣
‫اﻟﻄﻦ‬ ‫ﻧﻘﻞ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬
٧
‫اﻟﻄﻦ‬ ‫ﻧﻘﻞ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬
٤
‫ة‬ ‫ﻋﻄ‬
١٠٠٠
‫ﻃﻦ‬
‫اﻟﻄﻦ‬ ‫ﻧﻘﻞ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬
٨
‫اﻟﻄﻦ‬ ‫ﻧﻘﻞ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬
٧
‫اﻟﻄﻦ‬ ‫ﻧﻘﻞ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬
٣
‫ﻲ‬ ‫ﻣﺪ‬
٣٠٠٠
‫ﻃﻦ‬
‫اﻟﻄﻦ‬ ‫ﻧﻘﻞ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬
٦
‫اﻟﻄﻦ‬ ‫ﻧﻘﻞ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬
٢
‫اﻟﻄﻦ‬ ‫ﻧﻘﻞ‬ ‫ﻠﻔﺔ‬ ‫ﺗ‬
٥
‫ﺮﻃﻮم‬ ‫ا‬
٦٠٠٠
‫ﻃﻦ‬
٤٠٠٠
‫ﻃﻦ‬
٥٠٠
‫ﻃﻦ‬
١٥٠٠
‫ﻃﻦ‬
‫ﻴﻌﺎﺑﻴﺔ‬ ‫ﺳ‬ ‫اﻟﻄﺎﻗﺔ‬
‫ﻟﻼﻗﺴﺎم‬