math_prog_cee3804_excel

math_prog_cee3804_excel - 1 o f 5 8 V i r g i n i a T e c h...

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Unformatted text preview: 1 o f 5 8 V i r g i n i a T e c h C E E 3 8 4- C o m p u t e r A p p l i c a t i o n s M a t h e m a t i c a l P r o g r a m m i n g ( L P ) a n d E x c e l S o l v e r D r . A n t o n i o A . T r a n i A s s o c i a t e P r o f e s s o r o f C i v i l a n d E n v i r o n m e n t a l E n g i n e e r i n g V i r g i n i a P o l y t e c h n i c I n s t i t u t e a n d S t a t e U n i v e r s i t y B l a c k s b u r g , V i r g i n i a S p r i n g 2 3 2 o f 5 8 V i r g i n i a T e c h R e c a l l- L i n e a r P r o g r a m m i n g G e n e r a l F o r m u l a t i o n M a x i m i z e s u b j e c t t o : f o r f o r c j j 1 = n ∑ x j a i j j 1 = n ∑ x j b i ≤ i 1 2 … m , , , = x j ≥ j 1 2 … n , , , = 3 o f 5 8 V i r g i n i a T e c h L i n e a r P r o g r a m m i n g O b j e c t i v e F u n c t i o n ( O F ) F u n c t i o n a l C o n s t r a i n t s ( m o f t h e m ) N o n n e g a t i v i t y C o n d i t i o n s ( n o f t h e s e ) a r e d e c i s i o n v a r i a b l e s t o b e o p t i m i z e d ( m i n o r m a x ) a r e c o s t s a s s o c i a t e d w i t h e a c h d e c i s i o n v a r i a b l e c j j 1 = n ∑ x j a i j j 1 = n ∑ x j b i ≤ x j ≥ x j c j 4 o f 5 8 V i r g i n i a T e c h L i n e a r P r o g r a m m i n g a r e t h e c o e f fi c i e n t s o f t h e f u n c t i o n a l c o n s t r a i n t s a r e t h e a m o u n t s o f t h e r e s o u r c e s a v a i l a b l e ( R H S ) a i j i 5 o f 5 8 V i r g i n i a T e c h L P E x a m p l e ( C o n s t r u c t i o n ) D u r i n g t h e c o n s t r u c t i o n o f a n o f f- s h o r e a i r p o r t i n J a p a n t h e m a i n c o n t r a c t o r u s e d t w o t y p e s o f c a r g o b a r g e s t o t r a n s p o r t m a t e r i a l s f r o m a fi l l c o l l e c t i o n s i t e t o t h e a r t i fi c i a l i s l a n d b u i l t t o a c c o m m o d a t e t h e a i r p o r t . T h e t y p e s o f c a r g o v e s s e l s h a v e d i f f e r e n t c a r g o c a p a c i t i e s a n d c r e w m e m b e r r e q u i r e m e n t s a s s h o w n i n t h e t a b l e : V e s s e l T y p e C a p a c i t y ( m- t o n ) C r e w r e q u i r e d N u m b e r a v a i l a b l e F u j i 3 3 4 H a n e d a 5 2 6 6 o f 5 8 V i r g i n i a T e c h O s a k a B a y M o d e l A c c o r d i n g t o c o m p a n y r e c o r d s t h e r e a r e 1 8 c r e w m e m b e r s i n t h e p a y r o l l a n d a l l c r e w m e m b e r s a r e t r a i n e d t o e i t h e r m a n a g e t h e “ H a n e d a ” o r “ F u j i ” v e s s e l s . O s a k a A i r p o r t K a n s a i B r i d g e 7 o f 5 8 V i r g i n i a T e c h O s a k a B a y M o d e l M a t h e m a t i c a l F o r m u l a t i o n M a x i m i z e s u b j e c t t o : a n d N o t e : l e t a n d b e t h e n o . “ F u j i ” a n d “ H a n e d a ” v e s s e l s Z 3 x 1 5 x 2 + = 3 x 1 2 x 2 + 1 8 ≤ x 1 4 ≤ x 2 6 ≤ x 1 ≥ x 2 ≥ x 1 x 2 8 o f 5 8 V i r g i n i a T e c h O s a k a B a y P r o b l e m ( G r a p h i c a l S o l u t i o n ) x 2 x 1...
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This note was uploaded on 01/01/2012 for the course CEE 3804 taught by Professor Aatrani during the Spring '07 term at Virginia Tech.

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math_prog_cee3804_excel - 1 o f 5 8 V i r g i n i a T e c h...

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