ﻣﺒﺎﻧﻲ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺩﻛﺘﺮ ﻋﻠﻲ ﺍﻛﺒﺮ

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ﻣﺒﺎﻧﻲ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺩﻛﺘﺮ ﻋﻠﻲ ﺍﻛﺒﺮ ﺟﻼﻟﻲ ﺩﺍﻧﺸﻜﺪﻩ ﺑﺮﻕ ﺩﺍﻧﺸگﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ گﺮﻭﻩ ﻛﻨﺘﺮﻝ - ﺗﺮﻡ پﺎﺋﻴﺰ 8831

ﻣﺒﺎﻧﻲ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻫﻔﺘﻪ ﺍﻭﻝ پﺎﺋﻴﺰ 8831

ﻣﺒﺎﻧﻲ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ • Instructor: Dr. Ali A. Jalali • Office: Electronic Research Center • Email: ajalali@webmail. iust. ac. ir • Class hour: Saturday and Monday 8: 00 AM-9: 30 AM • Office hour: Saturday and Monday 13: 00 PM-14: 00 PM, or any other time by appointment • Website: www. drjalali. ir • Textbook: Introduction to Operations Research by: Hillier/Lieberman 7 th Edition with CD 1388 پﺎﺋﻴﺰ

ﺗﻮﺿﻴﺢ ﺩﺭﺱ • This course is an introduction to deterministic operations research models. • Topics include linear programming, network flow problems, transportation and dynamic programming. • We will learn how to model real-world decision-making problems by using operations research methods, how to solve the problems, and how to analyze and interpret the results. • Basic knowledge on linear algebra and calculus is assumed. Microsoft Excel will be used in the course. 1388 پﺎﺋﻴﺰ

Homework • The due date of the homework should be enforced. Late homework is only accepted for emergency or medical reasons with official proofs. • There are total 6 homework assignments and projects. All 6 of them will be counted into your final grade. • You can discuss with your classmates when doing homework and projects, but you have to write it out in your own words. If necessary, you may be asked to explain in person what you have written in your homework and projects. • Copied homework and projects will not be graded if detected. • Both exams are closed book, final exam is comprehensive. • Homework and class projects: 10% • Midterm exam: 35% • Final exam: 55% 1388 پﺎﺋﻴﺰ

ﻣﻘﺪﻣﻪ ﺍﻱ ﺑﺮ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ) (Hillier/Lieberman • • 83 ﺳﺎﻝ ﺍﺳﺖ ﺍﻳﻦ ﻛﺘﺎﺏ ﺩﺭ ﺩﻧﻴﺎ ﺗﺪﺭﻳﺲ ﻣﻲ ﺷﻮﺩ! ﻫﻔﺘﻤﻴﻦ چﺎپ آﻦ )ﺳﺎﻝ 2002( ﺩﺭ ﺩﺳﺘﺮﺱ ﻛﻼﺱ ﺍﺳﺖ. چﺎپ ﻫﺸﺘﻢ ﻛﺘﺎﺏ ﻫﻢ ﺩﺭ ﺳﺎﻝ 5002 آﻤﺎﺩﻩ ﺍﺳﺖ. ﺍﻳﻦ ﻛﺘﺎﺏ ﺩﺍﺭﺍﻱ ﺳﺎﻳﺖ ﺑﻪ آﺪﺭﺱ: www. mhhe. com/hillier ﺍﺳﺖ. پﺎﺋﻴﺰ 8831

1 Text. Book – CD آﻤ ﻮﺯ ﺵ ﻫﻤﺮﺍ ﻩ ﺑﺎ ﺗ ﺼﻮﻳ ﺮ ﻣﺘﺤﺮ ﻙ ﻞ ﻛﺘﺎﺏ ﻣﺘﻦ ﻛﺎﻣ پﺎﺋﻴﺰ 8831

Text. Book – CD 2 1388 پﺎﺋﻴﺰ

http: //mhhe. com/engcs/industrial/hillier/s plash/ 1388 پﺎﺋﻴﺰ

آﺨﺮﻳﻦ ﻧﺴﺨﻪ ﻛﺘﺎﺏ ﺳﺎﻝ 0102 پﺎﺋﻴﺰ 8831

ﻣﻄﺎﻟﺐ ﺍﻓﺰﻭﺩﻩ ﺩﺭ ﻧﺴﺨﻪ ﻛﺘﺎﺏ ﺳﺎﻝ 0102 پﺎﺋﻴﺰ 8831

آﻨچﻪ ﺩﺭ ﺍﻳﻦ ﻛﻼﺱ ﺑﻪ آﻨﻬﺎ ﺧﻮﺍﻫﻴﻢ پﺮﺩﺍﺧﺖ. پﺎﺋﻴﺰ 8831

ﻣﻘﺪﻣﻪ ﺍﻱ ﺑﺮ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ) (Hillier/Lieberman پﺎﺋﻴﺰ 8831

ﻣﺘﻦ ﺍﻟﻜﺘﺮﻭﻧﻴﻜﻲ پﺎﺋﻴﺰ 8831

چﺎپ ﻫﺸﺘﻢ ﻛﺘﺎﺏ ﺳﺎﻝ 5002 پﺎﺋﻴﺰ 8831

پﺎﺋﻴﺰ 8831

ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ چﻴﺴﺖ؟ • • • • ﺩﺭ ﺟﻨگ ﺟﻬﺎﻧﻲ ﺩﻭﻡ ﻓﺮﻣﺎﻧﺪﻫﻲ ﻧﻈﺎﻣﻲ ﺩﺭ ﺍﻧگﻠﺴﺘﺎﻥ ﺍﺯ گﺮﻭﻫﻲ ﺍﺯ ﺩﺍﻧﺸﻤﻨﺪﺍﻥ ﺩﻋﻮﺗﻲ ﺑﻌﻤﻞ آﻮﺭﺩ ﺗﺎ ﺩﺭ ﻣﺴﺎﺋﻞ ﺳﻮﻕ ﺍﻟﺠﻴﺸﻲ ﻭ ﺗﺪﺍﺑﻴﺮ ﺟﻨگﻲ ﻣﺮﺑﻮﻁ ﺑﻪ ﺩﻓﺎﻉ ﺯﻣﻴﻨﻲ ﻭ ﻫﻮﺍﻳﻲ ﺍﻳﻦ کﺸﻮﺭ ﻣﻄﺎﻟﻌﻪ ﻧﻤﺎﻳﻨﺪ. ﻫﺪﻑ آﻨﻬﺎ ﺗﻌﻴﻴﻦ ﻣﻮﺛﺮﺗﺮﻳﻦ ﺭﻭﺵ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﻨﺎﺑﻊ ﻣﺤﺪﻭﺩ ﻧﻈﺎﻣﻲ ﺑﻮﺩ. ﺍﺯ ﺟﻤﻠﻪ ﻣﺴﺎﺋﻠﻲ کﻪ ﻣﻮﺭﺩ ﺑﺮﺭﺳﻲ ﻗﺮﺍﺭ گﺮﻓﺖ ﻣﻄﺎﻟﻌﻪ کﺎﺭﺍﻳﻲ ﺑﻤﺐ ﺍﻓکﻨﻬﺎﻱ ﻧﻮﻉ ﺟﺪﻳﺪ ﻭ ﺭﻭﺵ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺭﺍﺩﺍﺭﻱ ﺑﻮﺩ کﻪ ﺑﻪ ﺗﺎﺯگﻲ ﺍﺧﺘﺮﺍﻉ ﺷﺪﻩ ﺑﻮﺩ. ﺗﺸکﻴﻞ ﺍﻳﻦ گﺮﻭﻩ ﻋﻠﻤﻲ ﺑﻪ ﻋﻨﻮﺍﻥ ﺍﻭﻟﻴﻦ ﻓﻌﺎﻟﻴﺖ ﺭﺳﻤﻲ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺑﻪ ﺷﻤﺎﺭ آﻤﺪﻩ ﺍﺳﺖ. ﻧﺎﻡ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻇﺎﻫﺮ ﺑﺪﻳﻦ ﻣﻨﺎﺳﺒﺖ ﺩﺍﺩﻩ ﺷﺪﻩ ﺑﻮﺩ کﻪ ﺍﻳﻦ گﺮﻭﻩ ﺑﻪ پژﻮﻫﺶ ﺩﺭ ﻋﻤﻠﻴﺎﺕ )ﻧﻈﺎﻣﻲ( پﺮﺩﺍﺧﺘﻪ ﺑﻮﺩ. ﺍﻳﻦ ﺭﺷﺘﻪ ﺟﺪﻳﺪ ﺗﺼﻤﻴﻢ گﻴﺮﻱ ﺍﺯ آﻐﺎﺯ ﺑﻪ ﻋﻨﻮﺍﻥ ﺭﺷﺘﻪ ﺍﻱ ﺷﻨﺎﺧﺘﻪ ﺷﺪﻩ ﺍﺳﺖ کﻪ ﺍﻃﻼﻋﺎﺕ ﻋﻠﻤﻲ ﺭﺍ ﺍﺯ ﻃﺮﻳﻖ ﺗﻼﺵ گﺮﻭﻫﻲ ﻣﺘﺨﺼﺺ ﺩﺭ ﻧﻈﺎﻣﻬﺎﻱ ﻣﺨﺘﻠﻒ ﺑﻪ ﻣﻨﻈﻮﺭ ﺗﻌﻴﻴﻦ ﺑﻬﺘﺮﻳﻦ ﻧﺤﻮﻩ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﻨﺎﺑﻊ ﻣﺤﺪﻭﺩ ﺑﻪ کﺎﺭ ﻣﻲ گﻴﺮﺩ. ﻧﺘﺎﻳﺞ ﺍﻣﻴﺪﺑﺨﺸﻲ کﻪ ﺗﻮﺳﻂ گﺮﻭﻫﻬﺎﻱ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺩﺭ ﺑﺮﻳﺘﺎﻧﻴﺎ ﺑﻪ ﺩﺳﺖ آﻤﺪﻩ ﺑﻮﺩ ﻓﺮﻣﺎﻧﺪﻫﻲ ﻧﻈﺎﻣﻲ ﺍﻳﺎﻻﺕ ﻣﺘﺤﺪﻩ ﺭﺍ ﺑﺮ آﻦ ﺩﺍﺷﺖ ﺗﺎ ﻓﻌﺎﻟﻴﺘﻬﺎﻱ ﻣﺸﺎﺑﻬﻲ ﺭﺍ ﺷﺮﻭﻉ ﻧﻤﺎﻳﺪ. ﺍﺯ ﻓﻌﺎﻟﻴﺘﻬﺎﻱ ﻣﻮﻓﻘﻴﺖ آﻤﻴﺰ گﺮﻭﻫﻬﺎﻱ آﻤﺮﻳکﺎﻳﻲ ﻣﻲ ﺗﻮﺍﻥ ﻣﻄﺎﻟﻌﻪ ﻣﺴﺎﺋﻞ پﻴچﻴﺪﻩ ﺗﺪﺍﺭکﺎﺕ ﻧﻈﺎﻣﻲ، ﺍﺑﺪﺍﻉ ﺍﻟگﻮﻫﺎﻱ ﺟﺪﻳﺪ پﺮﻭﺍﺯ، ﻃﺮﺡ ﻣﻴﻦ گﺬﺍﺭﻱ ﺩﺭﻳﺎ ﻭ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻮﺛﺮ ﺍﺯ ﻭﺳﺎﺋﻞ ﺍﻟکﺘﺮﻭﻧﻴکﻲ ﺭﺍ ﻧﺎﻡ ﺑﺮﺩ. پﺎﺋﻴﺰ 8831

ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ چﻴﺴﺖ؟ • • • • پﺲ ﺍﺯ ﺟﻨگ ﻣﻮﻓﻘﻴﺖ گﺮﻭﻫﻬﺎﻱ ﻧﻈﺎﻣﻲ ﺗﻮﺟﻪ ﻣﺪﻳﺮﺍﻥ ﺻﻨﻌﺘﻲ ﺭﺍ ﺑﻪ ﺧﻮﺩ ﺟﻠﺐ کﺮﺩ. ﺍﻳﻨﺎﻥ ﺩﺭ ﺟﺴﺘﺠﻮﻱ ﺭﺍﻩ ﺣﻠﻬﺎﻳﻲ ﺑﺮﺍﻱ ﻣﺴﺎﺋﻞ ﺧﻮﺩ ﺑﻮﺩﻧﺪ کﻪ ﺑﺮ ﺍﺛﺮ ﻭﺍﺭﺩ ﺷﺪﻥ ﺗﺨﺼﺺ ﺷﻐﻠﻲ ﺩﺭ ﺗﺸکﻴﻼﺕ ﺗﺠﺎﺭﻱ ﺭﻭﺯ ﺑﻪ ﺭﻭﺯ ﺣﺎﺩﺗﺮ ﻣﻲ ﺷﺪﻧﺪ. ﺯﻳﺮﺍ ﺑﺎ ﻭﺟﻮﺩ ﺍﻳﻦ ﻭﺍﻗﻌﻴﺖ کﻪ ﺍﺻﻮﻻ ﻣﺸﺎﻏﻞ ﺗﺨﺼﺼﻲ ﺑﺮﺍﻱ ﺧﺪﻣﺖ ﺑﻪ ﻫﺪﻑ کﻠﻲ ﻳک ﺳﺎﺯﻣﺎﻥ ﺑﻪ ﻭﺟﻮﺩ ﻣﻲ آﻴﻨﺪ، ﺍﻫﺪﺍﻑ ﻓﺮﺩﻱ ﺍﻳﻦ ﻣﺸﺎﻏﻞ ﻣﻤکﻦ ﺍﺳﺖ ﻫﻤﻮﺍﺭﻩ ﺑﺎ ﻣﻘﺎﺻﺪ آﻦ ﺳﺎﺯﻣﺎﻥ ﺳﺎﺯگﺎﺭ ﻧﺒﺎﺷﻨﺪ. ﺍﻳﻦ ﻭﺿﻊ ﻣﻨﺠﺮ ﺑﻪ ﻣﺴﺎﺋﻞ ﺗﺼﻤﻴﻢ گﻴﺮﻱ پﻴچﻴﺪﻩ ﺍﻱ ﺷﺪﻩ ﺍﺳﺖ کﻪ ﻧﻬﺎﻳﺘﺎ ﺳﺎﺯﻣﺎﻥ ﺗﺠﺎﺭﻱ ﺭﺍ ﻣﺠﺒﻮﺭ ﻧﻤﻮﺩﻩ ﺗﺎ ﺩﺭﺻﺪﺩ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﻮﺛﺮﺗﺮﻳﻦ ﺭﻭﺷﻬﺎﻱ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺑﺮآﻴﻨﺪ. ﺍگﺮچﻪ پﻴﺸگﺎﻣﻲ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺑﻪ ﻋﻨﻮﺍﻥ ﻳک ﻧﻈﺎﻡ ﺟﺪﻳﺪ ﺑﺎ ﺑﺮﻳﺘﺎﻧﻴﺎﻱ کﺒﻴﺮ ﺑﻮﺩ چﻴﺰﻱ ﻧگﺬﺷﺖ کﻪ ﺭﻫﺒﺮﻱ ﺍﻳﻦ ﺭﺷﺘﻪ ﺑﻪ ﺳﺮﻋﺖ ﺩﺭ ﺣﺎﻝ ﺭﺷﺪ ﺭﺍ ﺍﻳﺎﻻﺕ ﻣﺘﺤﺪﻩ ﺑﻪ ﺩﺳﺖ گﺮﻓﺖ. ﺍﻭﻟﻴﻦ ﺗکﻨﻴک ﺭﻳﺎﺿﻲ ﺩﺭ ﺍﻳﻦ ﺭﺷﺘﻪ کﻪ ﻣﻮﺭﺩ ﻗﺒﻮﻝ ﻫﻤﻪ ﻗﺮﺍﺭ گﺮﻓﺖ ﻭ ﺭﻭﺵ ﺳﻴﻤپﻠکﺲ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﻧﺎﻣﻴﺪﻩ ﺷﺪ ﺩﺭ ﺳﺎﻝ ۷۴۹۱ ﺗﻮﺳﻂ ﺭﻳﺎﺿﻴﺪﺍﻥ آﻤﺮﻳکﺎﻳﻲ ﺟﻮﺭﺝ. ﺏ. ﺩﺍﻧﺘﺴﻴک ﺑﻪ ﻭﺟﻮﺩ آﻤﺪ. ﺍﺯ آﻦ ﺑﻪ ﺑﻌﺪ ﺑﺎ ﺗﻼﺷﻬﺎ ﻭ ﻫﻤکﺎﺭﻳﻬﺎﻱ ﻋﻼﻗﻪ ﻣﻨﺪﺍﻥ ﺩﺭ ﻣﻮﺳﺴﺎﺕ ﻋﻠﻤﻲ ﻭ ﺻﻨﻌﺘﻲ ﺗکﻨﻴکﻬﺎ ﻭ کﺎﺭﺑﺮﺩﻫﺎﻱ ﺟﺪﻳﺪﻱ پﺪﻳﺪ آﻤﺪﻩ ﺍﻧﺪ. پﺎﺋﻴﺰ 8831

ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻳﺎ پژﻮﻫﺶ ﻋﻤﻠﻴﺎﺗﻲ • • • ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻳﺎ پژﻮﻫﺶ ﻋﻤﻠﻴﺎﺗﻲ ) (Operations Research, Operational Research ﻛﻪ ﺑﻪ ﻃﻮﺭ ﻣﺨﻔﻒ OR ﻧﺎﻣﻴﺪﻩ ﻣﻲﺷﻮﺩ ﺷﺎﺧﻪﺍﻱ ﺑﻴﻦﺭﺷﺘﻪﺍﻱ ﺍﺯ ﺭﻳﺎﺿﻴﺎﺕ ﺍﺳﺖ ﻛﻪ ﺍﺯ گﺮﺍﻳﺶﻫﺎﻳﻲ ﻣﺎﻧﻨﺪ ﺑﺮﻧﺎﻣﻪﺭﻳﺰﻱ ﺭﻳﺎﺿﻲ، آﻤﺎﺭ ﻭ ﻃﺮﺍﺣﻲ ﺍﻟگﻮﺭﻳﺘﻢﻫﺎ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲﻛﻨﺪ ﺗﺎ ﺩﺭ ﻣﺴﺎﺋﻞ ﺑﻬﻴﻨﻪ ﺳﺎﺯﻱ ﻧﻘﻄﻪ ﺑﻬﻴﻨﻪ ﺭﺍ پﻴﺪﺍ ﻛﻨﺪ. ﻳﺎﻓﺘﻦ ﻧﻘﻄﻪ ﺑﻬﻴﻨﻪ ﺑﺮ ﺍﺳﺎﺱ ﻧﻮﻉ ﻣﺴﻠﻪ ﻣﻔﺎﻫﻴﻢ ﻣﺨﺘﻠﻒ ﺩﺍﺭﺩ ﻭ ﺩﺭ ﺗﺼﻤﻴﻢ ﺳﺎﺯﻳﻬﺎ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲﺷﻮﺩ. ﻣﺴﺎﺋﻞ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺑﺮ ﺑﻴﺸﻴﻨﻪ ﺳﺎﺯﻱ )ﻣﺎﻛﺰﻳﻤﻢ ﺳﺎﺯﻱ( - ﻣﺎﻧﻨﺪ ﺳﻮﺩ، ﺳﺮﻋﺖ ﺧﻂ ﺗﻮﻟﻴﺪ، ﺗﻮﻟﻴﺪ ﺯﺭﺍﻋﻲ ﺑﻴﺸﺘﺮ، پﻬﻨﺎﻱ ﺑﺎﻧﺪ ﺑﻴﺸﺘﺮ ﻭ ﻏﻴﺮﻩ- ﻳﺎ ﻛﻤﻴﻨﻪ ﺳﺎﺯﻱ )ﻣﻲﻧﻴﻤﻢﺳﺎﺯﻱ( -ﻣﺎﻧﻨﺪ ﻫﺰﻳﻨﻪ ﻛﻤﺘﺮ ﻭ ﻛﺎﻫﺶ ﺭﻳﺴﻚ ﻭ ﻏﻴﺮﻩ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻳﻚ ﻳﺎ چﻨﺪ ﻗﻴﺪ ﺗﻤﺮﻛﺰ ﺩﺍﺭﻧﺪ. ﺍﻳﺪﻩ ﺍﺻﻠﻲ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻳﺎﻓﺘﻦ ﺑﻬﺘﺮﻳﻦ پﺎﺳﺦ ﺑﺮﺍﻱ ﻣﺴﺎﺋﻞ پﻴچﻴﺪﻩﺍﻱ ﺍﺳﺖ ﻛﻪ ﺑﺎ ﺯﺑﺎﻥ ﺭﻳﺎﺿﻲ ﻣﺪﻝﺳﺎﺯﻱ ﺷﺪﻩﺍﻧﺪ ﻛﻪ ﺑﺎﻋﺚ ﺑﻬﺒﻮﺩ ﻳﺎ ﺑﻬﻴﻨﻪﺳﺎﺯﻱ ﻋﻤﻠﻜﺮﺩ ﻳﻚ ﺳﻴﺴﺘﻢ ﻣﻲﺷﻮﻧﺪ. ﻋﺒﺎﺭﺕ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ گﺎﻫﻲ ﻋﻠﻢ ﻣﺪﻳﺮﻳﺖ ﻳﺎ management science ﻧﻴﺰ ﻧﺎﻣﻴﺪﻩ ﻣﻲﺷﻮﺩ ﻭ ﻣﻌﻤﻮﻻ ﻋﻠﻢ ﻣﺪﻳﺮﻳﺖ ﺍﺭﺗﺒﺎﻁ ﻧﺰﺩﻳﻜﻲ ﺑﻪ ﻣﺴﺎﺋﻞ ﻣﺪﻳﺮﻳﺖ ﺗﺠﺎﺭﺕ ﺩﺍﺭﺩ. پﺎﺋﻴﺰ 8831

ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻳﺎ پژﻮﻫﺶ ﻋﻤﻠﻴﺎﺗﻲ • • • • ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻳﻜﻲ ﺍﺯ ﺯﻳﺮﺷﺎﺧﻪﻫﺎﻱ ﺭﻳﺎﺿﻴﺎﺕ ﻛﺎﺭﺑﺮﺩﻱ ﺍﺳﺖ ﻭ ﺟﻨﺒﻪﻫﺎﻱ ﻛﺎﺭﺑﺮﺩﻱ آﻦ ﺩﺭ ﻣﻬﻨﺪﺳﻲ ﺻﻨﺎﻳﻊ ﻧﻴﺰ ﻣﻮﺭﺩ ﺗﻮﺟﻪ ﻗﺮﺍﺭ ﻣﻲگﻴﺮﺩ. ﺭﻳﺎﺿﻴﺎﺕ ﻛﺎﺭﺑﺮﺩﻱ ﺑﻪ ﻣﺘﺨﺼﺼﺎﻥ ﺍﻣﻜﺎﻥ ﻣﻲﺩﻫﺪ ﺗﺎ ﺟﻨﺒﻪﻫﺎﻱ ﻧﻈﺮﻱ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺭﺍ ﺑﺮﺭﺳﻲ ﻛﺮﺩﻩ ﻭ آﻦﺭﺍ گﺴﺘﺮﺵ ﺩﻫﻨﺪ ﻭ ﺗﻮﺍﻧﺎﻳﻲ ﺍﻳﺠﺎﺩ ﻭ ﺗﻮﺳﻌﻪ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺭﺍ ﻓﺮﺍﻫﻢ ﻛﻨﻨﺪ. ﻣﻬﻨﺪﺳﻲ ﺻﻨﺎﻳﻊ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺟﻨﺒﻪﻫﺎﻱ ﻛﺎﺭﺑﺮﺩﻱ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺳﻌﻲ ﻣﻲﻛﻨﺪ ﺗﺎ آﻦﺭﺍ ﺩﺭ ﺻﻨﻌﺖ ﻭ ﺗﺠﺎﺭﺕ ﺑﻪ ﻛﺎﺭ گﻴﺮﺩ. ﺍﺑﺰﺍﺭﻫﺎﻱ ﺍﺻﻠﻲ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺗﻮﺳﻂ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻣﺪﻝﺳﺎﺯﻱ ﺭﻳﺎﺿﻲ، ﺑﻬﻴﻨﻪﺳﺎﺯﻱ، آﻤﺎﺭ، ﻧﻈﺮﻳﻪ گﺮﺍﻑ، ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱﻫﺎ، ﻧﻈﺮﻳﻪ ﺻﻒ، آﻨﺎﻟﻴﺰ ﺗﺼﻤﻴﻢگﻴﺮﻱ ﻭ ﺷﺒﻴﻪﺳﺎﺯﻱ ﺍﺳﺖ. ﺑﻪ ﺩﻟﻴﻞ ﻣﺎﻫﻴﺖ ﻣﺤﺎﺳﺒﺎﺗﻲ ﺍﻳﻦ ﺷﺎﺧﻪ، OR ﺑﺎ ﻋﻠﻮﻡ ﻛﺎﻣپﻴﻮﺗﺮ پﻴﻮﻧﺪ ﺩﺍﺭﺩ ﻭ ﺗﺤﻠﻴﻞگﺮ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻣﻌﻤﻮﻻ ﺍﺯ ﻧﺮﻡﺍﻓﺰﺍﺭﻫﺎ ﻳﺎ ﻛﺪﻫﺎﻱ ﺍﺧﺘﺼﺎﺻﻲ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲﻛﻨﻨﺪ ﻛﻪ ﺗﻮﺳﻂ ﺧﻮﺩﺷﺎﻥ ﻳﺎ ﻫﻤﻜﺎﺭﺍﻧﺸﺎﻥ ﺍﻳﺠﺎﺩ ﺷﺪﻩﺍﻧﺪ. ﻧﺮﻡﺍﻓﺰﺍﺭﻫﺎﻱ ﺗﺠﺎﺭﻱ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻣﻌﻤﻮﻻ ﺑﺎ ﻋﻨﻮﺍﻥ ﺍﺑﺰﺍﺭﻫﺎﻱ ﺣﻞ ﻣﺴﺎﻟﻪ ﺷﻨﺎﺧﺘﻪ ﻣﻲﺷﻮﻧﺪ ﻭ ﻗﺎﺑﻠﻴﺖ ﺍﺳﺘﻔﺎﺩﻩ ﺩﺭ ﻧﺮﻡﺍﻓﺰﺍﺭﻫﺎ ﻭ ﻛﺪﻫﺎﻱ ﺧﻮﺩﻧﻮﺷﺘﻪ ﺭﺍ ﺩﺍﺭﺍ ﻫﺴﺘﻨﺪ. ﻭﻳژگﻲ ﺑﺎﺭﺯ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻧگﺎﻩ ﻛﻠﻲ آﻦ ﺑﻪ ﺳﻴﺴﺘﻤﻬﺎ ﻭ ﺑﻬﺒﻮﺩ آﻦ ﺍﺳﺖ ﻭ ﺑﻪ ﺟﺎﻱ آﻨﻜﻪ ﺑﺮ ﻳﻚ ﻳﺎ چﻨﺪ ﺟﺰﺀ ﺳﻴﺴﺘﻢ ﺗﻤﺮﻛﺰ ﻛﻨﺪ ﺗﻤﺎﻡ ﺳﻴﺴﺘﻢ ﺭﺍ ﻣﺪ ﻧﻈﺮ ﻗﺮﺍﺭ ﻣﻲﺩﻫﺪ. ﺗﺤﻠﻴﻞگﺮﺍﻥ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻣﻌﻤﻮﻻ ﺑﺎ ﻣﺴﺎﺋﻞ ﺟﺪﻳﺪﻱ ﻣﻮﺍﺟﻪ ﻣﻲﺷﻮﻧﺪ ﻭ ﺑﺎﻳﺪ ﺗﺸﺨﻴﺺ ﺩﻫﻨﺪ ﻛﻪ ﻛﺪﺍﻡﻳﻚ ﺍﺯ ﺭﻭﺵﻫﺎ ﺑﻴﺸﺘﺮ ﺑﺎ ﺳﺎﺧﺘﺎﺭ ﺳﻴﺴﺘﻢ، ﺍﻫﺪﺍﻑ ﺑﻬﺒﻮﺩ ﻭ ﻗﻴﺪﻫﺎﻱ ﺯﻣﺎﻧﻲ ﻭ ﺗﻮﺍﻥ ﻣﺤﺎﺳﺒﺎﺗﻲ ﻣﻨﻄﺒﻖ ﺍﺳﺖ. ﺑﻪ ﻫﻤﻴﻦ ﺩﻟﻴﻞ )ﻭ ﺩﻻﻳﻞ ﺩﻳگﺮ( ﻧﻘﺶ ﻧﻴﺮﻭﻱ ﺍﻧﺴﺎﻧﻲ ﺩﺭ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺣﻴﺎﺗﻲ ﺍﺳﺖ. ﻫﻤﺎﻧﻨﺪ ﺍﺑﺰﺍﺭﻫﺎﻱ ﺩﻳگﺮ، ﺗﻜﻨﻴﻚﻫﺎﻱ OR ﺑﻪ ﺗﻨﻬﺎﻳﻲ ﻗﺎﺩﺭ ﺑﻪ ﺣﻞ ﻣﺴﺎﺋﻞ ﻧﻴﺴﺘﻨﺪ. پﺎﺋﻴﺰ 8831

ﻗﻠﻤﺮﻭ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ • • • • ﺑﺮﺧﻲ ﺍﺯ ﻧﻤﻮﻧﻪﻫﺎﻱ ﻛﺎﺭﺑﺮﺩ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺑﻪ ﺷﺮﺡ ﺯﻳﺮ ﺍﺳﺖ: ﻣﺪﻳﺮﻳﺖ ﺑﻬﻴﻨﻪ ﺣﻤﻞ ﻭ ﻧﻘﻞ ﻛﺎﻻ ﻭ ﻣﻮﺍﺩ ﺩﺭ ﺷﺒﻜﻪﻫﺎﻱ ﺍﺭﺗﺒﺎﻃﻲ ﺟﺎﺩﻩﺍﻱ، ﺩﺭﻳﺎﻳﻲ، ﻫﻮﺍﻳﻲ ﻭ ﻟﻮﻟﻪﻫﺎﻱ ﺍﻧﺘﻘﺎﻝ ﺍﺭﺯﻳﺎﺑﻲ ﺑﻬﺮﻩﻭﺭﻱ، ﻛﺎﺭﺍﻳﻲ ﻭ ﺍﺛﺮﺑﺨﺸﻲ ﺑﺮﻧﺎﻣﻪﺭﻳﺰﻱ ﺯﻣﺎﻧﻲ ﺟﻠﺴﺎﺕ ﻣﺨﺘﻠﻒ ﺩﺭ ﻣﺪﺍﺭﺱ، ﺩﺍﻧﺸگﺎﻩﻫﺎ ﻭ ﻛﻨﻔﺮﺍﻧﺲﻫﺎ ﺑﺎ ﻫﺪﻑ ﻛﺎﺳﺘﻦ ﺍﺯ ﺯﻣﺎﻥﻫﺎﻱ ﺗﻠﻒ ﺷﺪﻩ ﻭ ﺍﻓﺰﺍﻳﺶ ﺍﺛﺮﺑﺨﺸﻲ آﻤﻮﺯﺵ ﺗﺨﺼﻴﺺ ﺑﻬﻴﻨﻪ ﻧﻴﺮﻭﻫﺎﻱ ﻛﺎﺭﻱ ﺑﻪ ﻣﺸﺎﻏﻞ ﺑﻮﺩﺟﻪﺭﻳﺰﻱ ﺑﻬﻴﻨﻪ ﺑﺎ ﻫﺪﻑ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻮﺛﺮ ﺍﺯ ﻫﺰﻳﻨﻪﻫﺎ ﻃﺮﺍﺣﻲ ﺳﺎﺧﺘﺎﺭ ﻛﺎﺭﺧﺎﻧﻪ ﻫﺎ ﺑﺎ ﻫﺪﻑ ﺟﺮﻳﺎﻥ ﺑﻬﻴﻨﻪ ﻣﻮﺍﺩ ﻭ ﻛﺎﻻﻫﺎ ﺍﻳﺠﺎﺩ ﺷﺒﻜﻪﻫﺎﻱ ﺍﺭﺗﺒﺎﻃﻲ ﺑﺎ ﻛﻤﺘﺮﻳﻦ ﻫﺰﻳﻨﻪ ﻭ ﺍﻃﻤﻴﻨﺎﻥ ﺍﺯ ﻛﻴﻔﻴﺖ ﺧﺪﻣﺎﺕ ﻣﺪﻳﺮﻳﺖ ﺗﺮﺍﻓﻴﻚ ﺧﻴﺎﺑﺎﻧﻲ ﻭ ﺟﺎﺩﻩﺍﻱ ﻃﺮﺍﺣﻲ ﺳﺎﺧﺘﺎﺭ چﻴپﻫﺎﻱ ﻛﺎﻣپﻴﻮﺗﺮﻱ ﺑﺎ ﻫﺪﻑ ﻛﺎﻫﺶ ﺯﻣﺎﻥ ﺗﻮﻟﻴﺪ )ﻭ ﺑﻨﺎﺑﺮﺍﻳﻦ ﻛﺎﻫﺶ ﻫﺰﻳﻨﻪﻱ ﺗﻮﻟﻴﺪ( ﻣﺪﻳﺮﻳﺖ ﺟﺮﻳﺎﻥ ﻣﻮﺍﺩ ﻭ ﻛﺎﻻ ﺩﺭ ﺯﻧﺠﻴﺮﻩ ﺗﺎﻣﻴﻦ ﺯﻣﺎﻥﺑﻨﺪﻱ: – ﻛﺎﺭﻛﻨﺎﻥ – ﻣﺮﺍﺣﻞ ﺗﻮﻟﻴﺪ – ﻣﺪﻳﺮﻳﺖ پﺮﻭژﻪ – ﺍﻧﺘﻘﺎﻝ ﺩﺍﺩﻩﻫﺎ ﺩﺭ ﺷﺒﻜﻪﻫﺎ – ﺭﻭﻳﺪﺍﺩﻫﺎﻱ ﻭﺭﺯﺷﻲ ﻭ پﻮﺷﺶ ﺗﻠﻮﻳﺰﻳﻮﻧﻲ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﺑﻪ ﻃﻮﺭ گﺴﺘﺮﺩﻩ ﺩﺭ ﺳﺎﺯﻣﺎﻥﻫﺎ ﻭ ﻣﻮﺳﺴﺎﺕ ﺩﻭﻟﺘﻲ ﻭ ﺧﺼﻮﺻﻲ ﻣﻮﺭﺩ ﺍﺳﺘﻔﺎﺩﻩ ﻗﺮﺍﺭ ﻣﻲگﻴﺮﺩ ﻭ ﺑﻪ ﺩﻟﻴﻞ ﻣﺎﻫﻴﺖ آﻦ، ﺗﺤﻠﻴﻞگﺮﺍﻥ ﺗﺤﻘﻴﻖ ﺩﺭ ﻋﻤﻠﻴﺎﺕ ﻣﻲﺗﻮﺍﻧﻨﺪ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺩﺍﻧﺶ ﺧﻮﺩ ﺩﺭ ﺣﻮﺯﻩﻫﺎﻱ ﺗﺨﺼﺼﻲ ﺩﻳگﺮ ﻭﺍﺭﺩ ﺷﻮﻧﺪ پﺎﺋﻴﺰ 8831

ﻣﺮﺍﺟﻊ ﻭ ﺗﻜﻠﻴﻒ ﺩﺍﻧﺸﺠﻮﻳﺎﻥ • ﺩﺍﻧﺸﺠﻮﻳﺎﻥ ﺑﺎ ﻣﺮﺍﺟﻌﻪ ﺑﻪ آﺪﺭﺱ alihadi. blogfa. com/post-62. aspx//: http ﻣﻄﺎﻟﺐ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺭﺍ ﺧﻮﺍﻫﻨﺪ ﻳﺎﻓﺖ. • ﻟﻄﻔآ ﺩﺭ ﻣﻮﻗﻊ ﺧﻮﺍﻧﺪﻥ ﻣﺘﻦ ﻭﺍﺭﺩ ﻟﻴﻨﻜﻬﺎﻱ ﻣﺮﺑﻮﻃﻪ ﺷﻮﻳﺪ ﻭ ﺍﻃﻼﻋﺎﺕ ﺧﻮﺩ ﺭﺍ ﺩﺭ ﻣﻮﺭﺩ ﻭﺍژگﺎﻫﺎﻱ ﻣﺨﺘﻠﻒ ﻣﺜﻞ: ﺑﻬﺮﻩﻭﺭﻱ، ﻛﺎﺭﺍﻳﻲ ﻭ ﺍﺛﺮﺑﺨﺸﻲ ﺍﻓﺰﺍﻳﺶ ﺩﻫﻴﺪ. • ﺳﺎﻳﺮ ﻣﺮﺍﺟﻊ: • http: //fa. wikipedia. org • http: //kashef. ropage. com 73= • http: //isen. ir/? p • پﺎﺋﻴﺰ 8831

ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ • • ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﻣﻲ ﺗﻮﺍﻧﺪ ﺩﺭ ﺯﻣﻴﻨﻪ ﻫﺎﻱ ﻣﺨﺘﻠﻒ ﻣﻮﺭﺩ ﻣﻄﺎﻟﻌﻪ ﻭ ﺍﺳﺘﻔﺎﺩﻩ ﻗﺮﺍﺭ گﻴﺮﺩ. ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺑﻪ ﻃﻮﺭ ﻋﻤﺪﻩ ﺩﺭ ﻣﻮﻗﻌﻴﺖ ﻫﺎﻱ ﺗﺠﺎﺭﻱ ﻭ ﺍﻗﺘﺼﺎﺩﻱ ﻣﻮﺭﺩ ﺍﺳﺘﻔﺎﺩﻩ ﺑﻴﺸﺘﺮﻱ ﻗﺮﺍﺭ ﻣﻲ گﻴﺮﺩ ﺍﻣﺎ ﺑﺮﺍﻱ ﺑﻌﻀﻲ ﺍﺯ ﻣﺴﺎﺋﻞ ﻣﻬﻨﺪﺳﻲ ﻧﻴﺰ ﻣﻲ ﺗﻮﺍﻧﺪ ﺑﻪ کﺎﺭ ﺑﺮﺩﻩ ﺷﻮﺩ. ﺑﻌﻀﻲ ﺍﺯ ﺻﻨﻌﺖ ﻫﺎ کﻪ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺭﺍ ﻣﻮﺭﺩ ﺍﺳﺘﻔﺎﺩﻩ ﻗﺮﺍﺭ ﻣﻲ ﺩﻫﻨﺪ ﻋﺒﺎﺭﺗﻨﺪ ﺍﺯ ﺣﻤﻞ ﻭ ﻧﻘﻞ، ﺍﻧﺮژﻲ، ﻣﺨﺎﺑﺮﺍﺕ ﻭ کﺎﺭﺧﺎﻧﻪ ﻫﺎ ﻭ … . ﻫﻤچﻨﻴﻦ ﺩﺭ ﻣﺪﻝ کﺮﺩﻥ ﻣﺴﺎﺋﻠﻲ ﺍﺯ ﻗﺒﻴﻞ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ، ﻣﺴﻴﺮﻳﺎﺑﻲ، ﺯﻣﺎﻧﺒﻨﺪﻱ، ﺗﺨﺼﻴﺺ ﻭ ﻃﺮﺍﺣﻲ ﻣﻔﻴﺪ ﺍﺳﺖ. ﻳک ﺍﺭﺯﻳﺎﺑﻲ ﺍﻧﺠﺎﻡ ﺷﺪﻩ ﺍﺯ 005 ﺷﺮکﺖ ﺑﺰﺭگ ﺩﻧﻴﺎ، ﻧﺸﺎﻥ ﺩﺍﺩ کﻪ 58% ﺩﺭﺻﺪ آﻨﻬﺎ ﺍﺯ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺍﺳﺘﻔﺎﺩﻩ ﻧﻤﻮﺩﻩ ﺍﻧﺪ. پﺎﺋﻴﺰ 8831

ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ • • ﺩﺭ ﺭﻳﺎﺿﻴﺎﺕ، ﻣﺴﺎﺋﻞ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺷﺎﻣﻞ ﺑﻬﻴﻨﻪ ﺳﺎﺯﻱ ﺗﺎﺑﻊ ﻫﺪﻓﻲ ﺧﻄﻲ ﺍﺳﺖ کﻪ ﺑﺎﻳﺴﺘﻲ ﻳکﺴﺮﻱ ﻣﺤﺪﻭﺩﻳﺖ ﺩﺭ ﻓﺮﻡ ﻫﺎﻱ ﺗﺴﺎﻭﻱ ﻫﺎﻱ ﺧﻄﻲ ﻭ ﻧﺎﻣﺴﺎﻭﻱ ﺑﺮﻗﺮﺍﺭ ﺷﻮﻧﺪ. ﺑﻪ ﻃﻮﺭ ﺧﻴﻠﻲ ﻏﻴﺮﺭﺳﻤﻲ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺪﻝ ﺭﻳﺎﺿﻲ ﺧﻄﻲ ﺑﺮﺍﻱ ﺑﺪﺳﺖ آﻮﺭﺩﻥ ﺑﻬﺘﺮﻳﻦ ﺧﺮﻭﺟﻲ )ﺑﻪ ﻃﻮﺭ ﻣﺜﺎﻝ ﺣﺪﺍکﺜﺮ ﺳﻮﺩ، ﺣﺪﺍﻗﻞ کﺎﺭ( ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺷﺮﻁ ﻫﺎﻱ ﺩﺍﺩﻩ ﺷﺪﻩ )ﺑﺮﺍﻱ ﻣﺜﺎﻝ ﻓﻘﻂ 03 ﺳﺎﻋﺖ کﺎﺭ ﺩﺭ ﻫﻔﺘﻪ، کﺎﺭ ﻏﻴﺮ ﻗﺎﻧﻮﻧﻲ ﺍﻧﺠﺎﻡ ﻧﺪﺍﺩﻥ ﻭ ﻏﻴﺮﻩ( ﺍﺳﺖ. ﻭ ﺑﻪ ﻃﻮﺭ ﺭﺳﻤﻲ ﺗﺮ ﺩﺭ ﻳک چﻨﺪ ﺳﻘﻔﻲ )ﻣﺎﻧﻨﺪ چﻨﺪﺿﻠﻌﻲ ﻳﺎ چﻨﺪﻭﺟﻬﻲ( کﻪ ﺗﺎﺑﻌﻲ ﺑﺎ ﻣﻘﺪﺍﺭ ﺣﻘﻴﻘﻲ ﺑﺮ ﺭﻭﻱ آﻦ ﺗﻌﺮﻳﻒ ﺷﺪﻩ ﺍﺳﺖ، ﻫﺪﻑ ﻳﺎﻓﺘﻦ ﻧﻘﻄﻪ ﺍﻱ ﺩﺭ ﺍﻳﻦ چﻨﺪ ﺳﻘﻔﻲ ﺍﺳﺖ کﻪ ﺗﺎﺑﻊ ﻫﺪﻑ ﺑﻴﺸﺘﺮﻳﻦ ﻳﺎ کﻤﺘﺮﻳﻦ ﻣﻘﺪﺍﺭ ﺭﺍ ﺩﺍﺭﺍ ﺑﺎﺷﺪ. ﺍﻳﻦ ﻧﻘﺎﻁ ﻣﻤکﻦ ﺍﺳﺖ ﻣﻮﺟﻮﺩ ﻧﺒﺎﺷﺪ، ﺍﻣﺎ ﺍگﺮ ﻭﺟﻮﺩ ﺩﺍﺷﺘﻪ ﺑﺎﺷﻨﺪ ﺟﺴﺖ ﻭ ﺟﻮ ﺩﺭ ﻣﻴﺎﻥ ﺭﺋﻮﺱ چﻨﺪ ﺿﻠﻌﻲ ﻳﺎﻓﺘﻦ ﺣﺪﺍﻗﻞ ﻳکﻲ ﺍﺯ آﻦ ﻫﺎ ﺭﺍ ﺗﻀﻤﻴﻦ ﻣﻲ کﻨﺪ. پﺎﺋﻴﺰ 8831

ﺗﺎﺭﻳﺨچﻪ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ • • • • ﻣﺴﺌﻠﻪ ﺣﻞ ﻳک ﺳﻴﺴﺘﻢ ﻧﺎﻣﺴﺎﻭﻱ ﺧﻄﻲ ﺑﻪ ﺯﻣﺎﻥ ﻓﻮﺭﻳﻪ ﺑﺮ ﻣﻲ گﺮﺩﺩ. ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺑﻪ ﻋﻨﻮﺍﻥ ﻳک ﻣﺪﻝ ﺭﻳﺎﺿﻲ ﺑﻪ ﻭﺟﻮﺩ آﻤﺪ ﻭ ﺩﺭ ﺯﻣﺎﻥ ﺟﻨگ ﺟﻬﺎﻧﻲ ﺩﻭﻡ ﻭ پﺲ ﺍﺯ آﻦ ﻣﻌﻠﻮﻡ ﺷﺪ کﻪ ﻃﺮﺡ ﺭﻳﺰﻱ ﻭ ﻫﻢ آﻬﻨگﻲ پﺮﻭژﻪ ﻫﺎﻱ ﻣﺨﺘﻠﻒ ﻭ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻮﺛﺮ ﺍﺯ ﻣﻨﺎﺑﻊ کﻤﻴﺎﺏ ﻳک ﺿﺮﻭﺭﺕ ﺍﺳﺖ. ﺗﻴﻢ ) SCOOP ﻣﺤﺎﺳﺒﺎﺕ ﻋﻠﻤﻲ ﺑﺮﻧﺎﻣﻪ ﻫﺎﻱ ﺑﻬﻴﻨﻪ( ﻧﻴﺮﻭﻱ ﻫﻮﺍﻳﻲ ﺍﻳﺎﻻﺕ ﻣﺘﺤﺪﻩ کﺎﺭ ﺟﺪﻱ ﺧﻮﺩ ﺭﺍ ﺩﺭ ژﻮﺋﻦ 7491 ﺷﺮﻭﻉ کﺮﺩ. ﻣﺎﺣﺼﻞ آﻦ، ﺍﺑﺪﺍﻉ ﺭﻭﺵ ﺳﻴﻤپﻠکﺲ ﺗﻮﺳﻂ ﺟﻮﺭﺝ. ﺑﻲ. ﺩﺍﻧﺘﺰﻳک ﺩﺭ پﺎﻳﺎﻥ ﺗﺎﺑﺴﺘﺎﻥ 7491 ﺑﻮﺩ. ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺑﻪ ﺳﺮﻋﺖ ﻣﻮﺭﺩ ﺗﻮﺟﻪ ﺍﻗﺘﺼﺎﺩ ﺩﺍﻧﺎﻥ، ﺭﻳﺎﺿﻲ ﺩﺍﻧﺎﻥ، آﻤﺎﺭﺩﺍﻧﺎﻥ، ﻭ ﻣﻮﺳﺴﺎﺕ ﺩﻭﻟﺘﻲ ﻗﺮﺍﺭ گﺮﻓﺖ. ﺩﺭ ﺗﺎﺑﺴﺘﺎﻥ 9491 کﻨﻔﺮﺍﻧﺴﻲ ﺩﺭ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﻭ ﺑﺮﺍﻱ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﻣﺨﺎﺭﺝ ﻭ ﺑﺮگﺸﺖ ﻫﺎ ﺗﻮﺳﻌﻪ ﺩﺍﺩﻩ ﺷﺪ ﺑﻪ ﻃﻮﺭﻱ کﻪ ﺑﺎ ﻣﺴﺌﻮﻟﻴﺖ کﻤﻴﺘﻪ Cowles ﺑﺮﺍﻱ ﺗﺤﻘﻴﻖ ﺩﺭ ﺍﻗﺘﺼﺎﺩ ﺑﺮگﺰﺍﺭ ﺷﺪ. ﻣﻘﺎﻻﺕ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺩﺭ ﺍﻳﻦ کﻨﻔﺮﺍﻧﺲ ﺍﻧﺪکﻲ ﺑﻌﺪ ﺩﺭ ﺳﺎﻝ 1591 ﺑﻪ ﻫﻤﺖ T. C. Koopmans ﺩﺭ کﺘﺎﺑﻲ ﺗﺤﺖ ﻋﻨﻮﺍﻥ ﺗﺤﻠﻴﻞ ﻓﻌﺎﻟﻴﺖ ﺗﻮﻟﻴﺪ ﻭ ﺗﺨﺼﻴﺺ ﺟﻤﻊ آﻮﺭﻱ ﺷﺪ. ﺟﺎﻥ ﻭﺍﻥ ﻧﻴﻮﻣﻦ ﺩﺭ ﻫﻤﺎﻥ ﺳﺎﻝ ﺗﺌﻮﺭﻱ ﺩﻭ گﺎﻧگﻲ ﺭﺍ ﺗﻮﺳﻌﻪ ﺩﺍﺩ ﻭ ﻟﺌﻮﻧﻴﺪ ﺧﺎﺷﻴﺎﻥ ﺭﻳﺎﺿﻲ ﺩﺍﻥ ﺭﻭﺳﻲ ﺍﺭ ﺗکﻨﻴک ﻫﺎﻱ ﺳﺎﺩﻩ ﺩﺭ ﺍﻗﺘﺼﺎﺩ ﻗﺒﻞ ﺍﺯ ﺩﺍﻧﺘﺰﻳک ﺍﺳﺘﻔﺎﺩﻩ کﺮﺩ ﻭ ﺟﺎﻳﺰﻩ ﻧﻮﺑﻞ ﺭﺍ ﺩﺭ ﺳﺎﻝ 5791 ﺩﺭ ﺍﻗﺘﺼﺎﺩ ﺑﺮﺩ. پﺎﺋﻴﺰ 8831

ﺗﺎﺭﻳﺨچﻪ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ • ﻣﺜﺎﻝ ﺍﺻﻠﻲ آﻘﺎﻱ ﺩﺍﻧﺘﺰﻳک ﻳﺎﻓﺘﻦ ﺑﻬﺘﺮﻳﻦ ﺗﺨﺼﻴﺺ 07 ﻧﻔﺮ ﺑﻪ 07 ﺷﻐﻞ ﺑﻮﺩ. • ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﺍﺣﺘﻴﺎﺝ ﺑﻪ ﻧﻤﺎﻳﺶ ﻫﻤﻪ ﻱ ﺟﺎﻳگﺸﺖ ﻫﺎ ﺑﺮﺍﻱ ﺍﻧﺘﺨﺎﺏ ﺑﻬﺘﺮﻳﻦ ﺗﺨﺼﻴﺺ ﺑﺴﻴﺎﺭ ﻭﺳﻴﻊ ﻭ ﻏﻴﺮ ﻣﻤکﻦ ﺍﺳﺖ. • ﺍﻭ ﻣﺸﺎﻫﺪﻩ کﺮﺩ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺍﻟگﻮﺭﻳﺘﻢ ﺳﻴﻤپﻠکﺲ ﻳﺎﻓﺘﻦ ﺑﻬﺘﺮﻳﻦ ﺟﻮﺍﺏ ﻓﻘﻂ چﻨﺪ ﻟﺤﻈﻪ ﻃﻮﻝ ﻣﻲ کﺸﺪ ﻭ ﻫﻤچﻨﻴﻦ ﻣﺘﻮﺟﻪ ﺷﺪ کﻪ ﺟﻮﺍﺏ ﺩﺭ گﻮﺷﻪ چﻨﺪ ﺿﻠﻌﻲ کﻪ ﺑﻪ ﻭﺳﻴﻠﻪ ﻗﻴﺪ ﻫﺎﻱ ﻣﺴﺄﻠﻪ ﺗﺸکﻴﻞ ﻣﻲ ﺷﻮﺩ ﻭﺟﻮﺩ ﺩﺍﺭﺩ. ﻳﻚ ﻟﻴﻨﻚ ﺧﻮﺏ: http: //www. mang. canterbury. ac. nz/people/jfraffen/faqs/LPfaq. htm پﺎﺋﻴﺰ 8831

کﺎﺭﺑﺮﺩﻫﺎ • • ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ کﺎﺭﺑﺮﺩ ﻫﺎﻱ ﻣﺘﻌﺪﺩﻱ ﺩﺭ ﺍﺭﺗﺶ، ﺣکﻮﻣﺖ، ﺻﻨﻌﺖ ﻭ ﻣﻬﻨﺪﺳﻲ ﺷﻬﺮ ﺳﺎﺯﻱ ﻳﺎﻓﺘﻪ ﺍﺳﺖ ﻫﻤچﻨﻴﻦ ﺍﻏﻠﺐ ﺑﻪ ﻋﻨﻮﺍﻥ ﺑﺨﺸﻲ ﺍﺯ ﻃﺮﺡ ﻫﺎﻱ ﻣﺤﺎﺳﺒﺎﺗﻲ، ﺣﻞ ﻣﺴﺎﺋﻞ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﻏﻴﺮ ﺧﻄﻲ، ﺑﺮﻧﺎﻣﻪ ﻫﺎﻱ گﺴﺴﺘﻪ، ﻣﺴﺎﺋﻞ ﺗﺮکﻴﺒﺎﺗﻲ، ﻣﺴﺎﺋﻞ کﻨﺘﺮﻝ ﺑﻬﻴﻨﻪ ﻭ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺍﺣﺘﻤﺎﻟﻲ ﺑﻪ کﺎﺭ ﻣﻲ ﺭﻭﺩ. ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺯﻣﻴﻨﻪ ﻣﻬﻤﻲ ﺩﺭ ﺑﻬﻴﻨﻪ ﺳﺎﺯﻱ ﺑﺮﺍﻱ چﻨﺪﻳﻦ ﺩﻟﻴﻞ ﺍﺳﺖ: ﺑﺴﻴﺎﺭﻱ ﺍﺯ ﻣﺴﺎﺋﻞ ﻋﻤﻠﻲ ﺩﺭ ﺗﺤﻘﻴﻖ ﻋﻤﻠﻴﺎﺕ ﺑﻪ ﻋﻨﻮﺍﻥ ﻣﺴﺌﻠﻪ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﻣﻲ ﺗﻮﺍﻧﺪ ﺑﻴﺎﻥ ﺷﻮﺩ ﻭ ﻫﻤچﻨﻴﻦ ﺗﻌﺪﺍﺩﻱ ﺍﺯ ﺍﻟگﻮﺭﻳﺘﻢ ﻫﺎﻱ ﺩﻳگﺮ ﻣﺴﺎﺋﻞ ﺑﻬﻴﻨﻪ ﺳﺎﺯﻱ ﺑﻪ ﻭﺳﻴﻠﻪ ﻱ ﺣﻞ ﻣﺴﺎﺋﻞ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ، ﺑﻪ ﻋﻨﻮﺍﻥ ﺯﻳﺮ ﻣﺴﺌﻠﻪ کﺎﺭ ﻣﻲ کﻨﻨﺪ. ﺑﻪ ﻃﻮﺭ ﺗﺎﺭﻳﺨﻲ ﺍﻳﺪﻩ ﻫﺎﻱ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺍﻟﻬﺎﻡ ﺑﺨﺶ ﺑﺴﻴﺎﺭﻱ ﺍﺯ ﻣﻔﺎﻫﻴﻢ ﺍﻭﻟﻴﻪ ﺗﺌﻮﺭﻱ ﺑﻬﻴﻨﻪ ﺳﺎﺯﻱ ﻣﺎﻧﻨﺪ ﺩﻭگﺎﻧگﻲ، ﺗﺠﺰﻳﻪ، ﺍﻫﻤﻴﺖ ﺗﺤﺪﺏ ﻭ ﺗﻌﻤﻴﻢ آﻦ ﺑﻮﺩﻩ ﺍﺳﺖ. ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺑﻪ ﻃﻮﺭ ﻋﻤﺪﻩ ﺩﺭ ﺍﻗﺘﺼﺎﺩ کﻼﻥ، ﻣﺪﻳﺮﺕ ﺗﺠﺎﺭﻱ، ﺣﺪﺍکﺜﺮ کﺮﺩﻥ ﺩﺭآﻤﺪ ﻳﺎ ﺣﺪﺍﻗﻞ کﺮﺩﻥ ﻫﺰﻳﻨﻪ ﻱ ﺗﻮﻟﻴﺪ ﺑﻪ کﺎﺭ ﻣﻲ ﺭﻭﺩ. ﺑﻪ ﻋﻨﻮﺍﻥ ﻣﺜﺎﻝ: ﻣﺪﻳﺮﺕ ﻣﻮﺟﻮﺩﻱ، ﻣﺪﻳﺮﺕ ﺩﺍﺭﺍﻳﻲ ﻭ ﺳﻬﺎﻡ، ﺗﺨﺼﻴﺺ ﻣﻨﺎﺑﻊ ﺍﻧﺴﺎﻧﻲ ﻭ ﻣﻨﺎﺑﻊ ﻏﻴﺮ ﺍﻧﺴﺎﻧﻲ، ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺳﻔﺮﻫﺎﻱ ﺗﺒﻠﻴﻐﺎﺗﻲ. پﺎﺋﻴﺰ 8831

ﻛﺎﺭﺑﺮﺩﻫﺎ • • • • ﺩﺭ ﺑﺴﻴﺎﺭﻱ ﺷﺮکﺖ ﻫﺎ ﻭ ﻣﻮﺳﺴﺎﺕ ﺩﻭﻟﺘﻲ ﺑﺎ ﺑﻪ کﺎﺭگﻴﺮﻱ ﻣﻮﻓﻘﻴﺖ آﻤﻴﺰ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ، ﻣﻴﻠﻴﻮﻥ ﻫﺎ ﺩﻻﺭ ﺻﺮﻓﻪ ﺟﻮﻳﻲ کﺮﺩﻩ ﺍﻧﺪ. ﺩﺭ ﺯﻳﺮ ﺑﻪ ﺑﻴﺎﻥ چﻨﺪ ﻣﻮﺭﺩ ﺍﺯ ﺍﻳﻦ ﻣﻮﻓﻘﻴﺖ ﻫﺎ ﺍﺷﺎﺭﻩ ﻣﻲ کﻨﻴﻢ: ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﻭ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﻋﺪﺩ ﺻﺤﻴﺢ، ﺭﻭﺷﻲ ﺑﺮﺍﻱ ﺯﻣﺎﻥ ﺑﻨﺪﻱ گﺸﺖ ﺍﻓﺴﺮﺍﻥ پﻠﻴﺲ ﺩﺭ ﺳﺎﻥ ﻓﺮﺍﻧﺴﻴﺴکﻮ، ﺗﻮﺳﻂ ﺗﻴﻠﻮﺭ ﻭ ﻫﺎکﺲ ﻟﻲ )9891( ﻃﺮﺍﺣﻲ گﺮﺩﻳﺪ. ﺑﺎ ﺍﻳﻦ ﺭﻭﺵ ﺳﺎﻻﻧﻪ 11 ﻣﻴﻠﻴﻮﻥ ﺩﻻﺭ ﺻﺮﻓﻪ ﺟﻮﻳﻲ ﺣﺎﺻﻞ ﺷﺪ، ﺯﻣﺎﻥ پﺎﺳﺦ گﻮﻳﻲ ﺑﻪ ﺩﺭﺧﻮﺍﺳﺖ ﻫﺎ ﻧﻴﺰ ﺣﺪﻭﺩ 3 ﻣﻴﻠﻴﻮﻥ ﺩﻻﺭ ﺩﺭ ﺳﺎﻝ ﺍﻓﺰﺍﻳﺶ ﻳﺎﻓﺖ. ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ پﻮﻳﺎ، چﺎﺋﻮ ﻭ ﺩﻳگﺮﺍﻥ )9891( ﺩﺭ ﺣﺪﻭﺩ 97پﺴﺖ ﺑﺮﻕ ﻭ ﺑﻴﺶ ﺍﺯ 521 ﻣﻴﻠﻴﻮﻥ ﺩﻻﺭ ﺩﺭ ﺧﺮﻳﺪ ﻣﻮﺟﻮﺩﻱ ﻭ ﻫﺰﻳﻨﻪ ﻫﺎﻱ کﻤﺒﻮﺩ ﺻﺮﻓﻪ ﺟﻮﻳﻲ کﺮﺩﻧﺪ. ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﻋﺪﺩ ﺻﺤﻴﺢ، ﻭﺍﺳکﻮ ﻭ ﺩﻳگﺮﺍﻥ )9891( ﺩﺭ ﻃﺮﺍﺣﻲ ﺗﺄﺴﻴﺴﺎﺕ ﻗﺎﻟﺐ ﺷﻤﺶ ﺑﻪ ﻓﻮﻻﺩ ﺑﺘﻠﻬﻢ کﻤک کﺮﺩﻧﺪ. ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﻋﺪﺩ ﺻﺤﻴﺢ ﺑﺎﻋﺚ ﺷﺪ کﻪ ﺩﺭ ﻫﺰﻳﻨﻪ ﻫﺎﻱ ﻋﻤﻠﻴﺎﺗﻲ ﺳﺎﻻﻧﻪ، 8 ﻣﻴﻠﻴﻮﻥ ﺩﻻﺭ ﺻﺮﻓﻪ ﺟﻮﻳﻲ گﺮﺩﺩ. ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺪﻝ ﻫﺎﻱ ﺷﺒکﻪ پﺎﻭﻝ ﻭ ﺩﻳگﺮﺍﻥ )8891( ﻳک ﻣﺪﻝ ﺟﻬﺖ ﺗﺨﺼﻴﺺ ﺑﺎﺭ ﺑﺮﺍﻱ ﺭﺍﻧﻨﺪگﺎﻥ کﺎﻣﻴﻮﻥ ﺩﺭ ﺷﺮکﺖ ﺧﻄﻮﻁ آﻤﺮﻳکﺎﻱ ﺷﻤﺎﻟﻲ ﺗﻮﺳﻌﻪ ﺩﺍﺩﻧﺪ. ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺍﻳﻦ ﻣﺪﻝ ﺑﺎﻋﺚ ﺍﺭﺍﺋﻪ ﺧﺪﻣﺎﺕ ﺑﻬﺘﺮ ﺑﻪ ﻣﺸﺘﺮﻳﺎﻥ ﻭ کﺎﻫﺶ ﺣﺪﻭﺩ 2/5 ﻣﻴﻠﻴﺎﺭﺩ ﺩﻻﺭ ﻫﺰﻳﻨﻪ ﺳﺎﻟﻴﺎﻧﻪ ﺷﺪﻩ ﺍﺳﺖ. ﺳﻮﻟﻴﻮﺍﻥ ﻭ ﺳکﺮﺳﺖ ﺍﺯ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺍﺳﺘﻔﺎﺩﻩ کﺮﺩﻧﺪ ﺗﺎ ﺩﺭ ﻣﻮﺭﺩ چگﻮﻧگﻲ ﻓﺮﺍﻳﻨﺪ کﺮﻩ گﻴﺮﻱ ﺍﺯ ﺩﻭﻍ، ﺷﻴﺮ ﺧﺎﻡ، کﺸک ﺷﻴﺮﻳﻦ ﻭ ﺧﺎﻣﻪ ﺑﺮﺍﻱ پﻨﻴﺮ ﺧﺎﻣﻪ ﺍﻱ، پﻨﻴﺮ ﺑﺴﺘﻪ ﺑﻨﺪﻱ، ﺧﺎﻣﻪ ﺗﺮﺵ ﻭ ﺧﺎﻣﻪ کﺸک ﺗﺼﻤﻴﻢ گﻴﺮﻱ ﺷﻮﺩ. ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺪﻝ، ﺳﻮﺩ کﺮﻩ گﻴﺮﻱ ﺭﺍ ﺳﺎﻻﻧﻪ 00084 ﺩﻻﺭ ﺍﻓﺰﺍﻳﺶ ﺩﺍﺩﻩ ﺍﺳﺖ. ﻳک ﺳﻮﺍﺭﻱ ﻳﺎ کﺎﻣﻴﻮﻥ ﻗﺒﻞ ﺍﺯ ﺟﺎﻳگﺰﻳﻨﻲ چﻨﺪ ﺳﺎﻝ ﻣﻲ ﺗﻮﺍﻧﺪ ﺩﺭ ﻳک کﺎﺭﺧﺎﻧﻪ ﻣﻮﺭﺩ ﺍﺳﺘﻔﺎﺩﻩ ﻗﺮﺍﺭ گﻴﺮﺩ؟ ﻧﻔﺖ ﻓﻴﻠﻴپﺲ ﺍﺯ ﻣﺪﻝ ﻫﺎﻱ ﺟﺎﻳگﺰﻳﻨﻲ ﺗﺠﻬﻴﺰﺍﺕ ﺑﺮﺍﻱ پﺎﺳﺦ ﺑﻪ ﺍﻳﻦ ﺳﺆﺎﻝ، ﺍﺳﺘﻔﺎﺩﻩ کﺮﺩ. ﺍﻳﻦ ﻣﺪﻝ ﻫﺎﻱ ﺟﺎﻳگﺰﻳﻨﻲ ﺗﺠﻬﻴﺰﺍﺕ، ﻃﺒﻖ ﺑﺮآﻮﺭﺩ ﺍﻧﺠﺎﻡ ﺷﺪﻩ، ﺑﺎﻋﺚ ﺻﺮﻓﻪ ﺟﻮﻳﻲ ﺳﺎﻻﻧﻪ 00009 ﺩﻻﺭ ﺑﺮﺍﻱ ﻓﻴﻠﻴپﺲ ﺷﺪﻩ ﺍﻧﺪ. پﺎﺋﻴﺰ 8831

ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ • ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﺧﻄﻲ ﺑﻪ ﺻﻮﺭﺕ ﺍﺳﺘﺎﻧﺪﺍﺭﺩ ﻣﻲ ﺗﻮﺍﻧﻨﺪ ﻧﻤﺎﻳﺶ ﺩﺍﺩﻩ ﺷﻮﻧﺪ: • Maximize c. Tx • Subject to Ax ≤ b 0 ≥ • x • X ﺑﻴﺎﻧگﺮ ﺑﺮﺩﺍﺭ ﻣﺘﻐﻴﺮ ﻫﺎ ﻣﻲ ﺑﺎﺷﺪ ﻭ ﻫﻤچﻨﻴﻦ c ﻭ b ﺑﺮﺩﺍﺭ ﺿﺮﺍﻳﺐ ﻭ A ﻣﺎﺗﺮﻳﺲ ﺿﺮﺍﻳﺐ. • ﻋﺒﺎﺭﺗﻲ کﻪ ﺑﺎﻳﺪ ﺣﺪﺍکﺜﺮ ﻳﺎ ﺣﺪﺍﻗﻞ ﺷﻮﺩ ﺗﺎﺑﻊ ﻫﺪﻑ ﻧﺎﻡ ﺩﺍﺭﺩ )ﺩﺭ ﺍﻳﻦ ﻣﻮﺭﺩ . ( c. Tx • ﻋﺒﺎﺭﺕ ≥ b Ax ﺷﺮﺍﻳﻄﻲ ﻫﺴﺘﻨﺪ کﻪ ﻳک چﻨﺪ ﻭﺟﻬﻲ ﻣﺤﺪﺏ ﺭﺍ ﻧﻤﺎﻳﺶ ﻣﻲ ﺩﻫﻨﺪ کﻪ ﺗﺎﺑﻊ ﻫﺪﻑ ﺭﻭﻱ آﻦ ﺑﺎﻳﺪ ﺑﻬﻴﻨﻪ ﺷﻮﺩ. پﺎﺋﻴﺰ 8831

6 8 40 X 1 +15 X 2 >=100 14 X 1 + 35 X 2>=140 X 1 <=5 X 2 <=5 X 1, X 2 >=0 2 4 X 2 Optimal Solution X 1 = 5 X 2 = 2 3 X 1 + 9 X 2 = ? 0 1 2 3 4 X 1 5 6

ﺭﻭﺵ ﺳﻴﻤپﻠﻜﺲ ﺍﻳﻨﺠﺎ 1388 پﺎﺋﻴﺰ http: //math. uww. edu/~mcfarlat/s-prob. htm

ﺭﻭﺵ ﺳﻴﻤپﻠﻜﺲ پﺎﺋﻴﺰ 8831

ﺭﻭﺵ ﺳﻴﻤپﻠﻜﺲ ﺍﻳﻨﺠﺎ پﺎﺋﻴﺰ 8831

ﺭﻭﺵ ﺳﻴﻤپﻠﻜﺲ پﺎﺋﻴﺰ 8831

ﺭﻭﺵ ﺳﻴﻤپﻠﻜﺲ 1388 پﺎﺋﻴﺰ http: //math. uww. edu/~mcfarlat/s-prob. htm

ﺭﻭﺵ ﺳﻴﻤپﻠﻜﺲ پﺎﺋﻴﺰ 8831

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