2014冬季学期运筹与优化2

üX/{

üX/ {

üX/ { g üX/ {Ú½üX/L ~

üX/ { g ÚÚ½

ÀJÐ©Ä 1) u ) `5 XJØ´ `§(½ Tº: ë ^¦8I¼êeü>¶÷T>£Ä(½ Tº: :#º:¶…8I¼êq`uTº

-EþãÚ½§ –é `)"

`5ub A=[B, N]§B´ m× m‘ _Ý"éA/§ x= xB xN= B 1 b B 1 N xN xN,c= cB cN .

A/§8I¼êµT f (x)= cT x= cT B xB+ cN xN 1 1 T= cT B (B b B N xN )+ cN xN 1 T T 1= cT B B b+ (cN cB B N )xN T 1 1 XJcT N cB B N≥ 0§KxB= B b§xN= 0´ `), T 1 XJ(cT N cB B N )j< 0£j∈ N§N´ ÄCþ I 8¤§KØ´ `)"

`5ub A=[B, N]§B´ m× m‘ _Ý"éA/§ x= xB xN= B 1 b B 1 N xN xN,c= cB cN .

A/§8I¼êµT f (x)= cT x= cT B xB+ cN xN 1 1 T= cT B (B b B N xN )+ cN xN 1 T T 1= cT B B b+ (cN cB B N )xN T 1 1 XJcT N cB B N≥ 0§KxB= B b§xN= 0´ `), T 1 XJ(cT N cB B N )j< 0£j∈ N§N´ ÄCþ I 8¤§KØ´ `)"

`5ub A=[B, N]§B´ m× m‘ _Ý"éA/§ x= xB xN= B 1 b B 1 N xN xN,c= cB cN .

A/§8I¼êµT f (x)= cT x= cT B xB+ cN xN 1 1 T= cT B (B b B N xN )+ cN xN 1 T T 1= cT B B b+ (cN cB B N )xN T 1 1 XJcT N cB B N≥ 0§KxB= B b§xN= 0´ `), T 1 XJ(cT N cB B N )j< 0£j∈ N§N´ ÄCþ I 8¤§KØ´ `)"

`5ub A=[B, N]§B´ m× m‘ _Ý"éA/§ x= xB xN= B 1 b B 1 N xN xN,c= cB cN .

A/§8I¼êµT f (x)= cT x= cT B xB+ cN xN 1 1 T= cT B (B b B N xN )+ cN xN 1 T T 1= cT B B b+ (cN cB B N )xN T 1 1 XJcT N cB B N≥ 0§KxB= B b§xN= 0´ `), T 1 XJ(cT N cB B N )j< 0£j∈ N§N´ ÄCþ I 8¤§KØ´ `)"

#Ä

1)

T 1 XJ(cT N cB B N )j< 0£j∈ N§N´ ÄCþ I 8¤§KØ´ `)" T 1À cT K©þ¥ §Ø” j§À N cB B N Jxj \ÄCþ" xj d0O xNÙ{©þ± 0 §xB= B 1 b B 1 aj xj .1 2

XJB 1 aj≤ 0§K¯KÃ.¶B b)i 1ÄK§-xj= min1≤i≤m{ (( aj )i> 0}, B 1 aj )i|(B q 4 I§Kxq= 0(ÑÄCþ)§ 1

xB= B 1 b B 1 aj xj .

#Ä

1)

T 1 XJ(cT N cB B N )j< 0£j∈ N§N´ ÄCþ I 8¤§KØ´ `)" T 1À cT K©þ¥ §Ø” j§À N cB B N Jxj \ÄCþ" xj d0O xNÙ{©þ± 0 §xB= B 1 b B 1 aj xj .1 2

XJB 1 aj≤ 0§K¯KÃ.¶B b)i 1ÄK§-xj= min1≤i≤m{ (( aj )i> 0}, B 1 aj )i|(B q 4 I§Kxq= 0(ÑÄCþ)§ 1

xB= B 1 b B 1 aj xj .

#Ä

1)

T 1 XJ(cT N cB B N )j< 0£j∈ N§N´ ÄCþ I 8¤§KØ´ `)" T 1À cT K©þ¥ §Ø” j§À N cB B N Jxj \ÄCþ" xj d0O xNÙ{©þ± 0 §xB= B 1 b B 1 aj xj .1 2

XJB 1 aj≤ 0§K¯KÃ.¶B b)i 1ÄK§-xj= min1≤i≤m{ (( aj )i> 0}, B 1 aj )i|(B q 4 I§Kxq= 0(ÑÄCþ)§ 1

xB=

B 1 b B 1 aj xj .

#Ä

1)

T 1 XJ(cT N cB B N )j< 0£j∈ N§N´ ÄCþ I 8¤§KØ´ `)" T 1À cT K©þ¥ §Ø” j§À N cB B N Jxj \ÄCþ" xj d0O xNÙ{©þ± 0 §xB= B 1 b B 1 aj xj .1 2

XJB 1 aj≤ 0§K¯KÃ.¶B b)i 1ÄK§-xj= min1≤i≤m{ (( aj )i> 0}, B 1 aj )i|(B q 4 I§Kxq= 0(ÑÄCþ)§ 1

xB= B 1 b B 1 aj xj .

üX/ {Ú½é4 z¯KµÐ©ÚµlÝ Aé Ý B (ÄÝ ),£º:¤.XJéاÒ^<óCþ.ÌÚ1

E m©:

2

T 1 x´ äkÄ Bº:. O cT N . XJù N cB B þ´¤k©þ´§Kª "(صx´ ` ). 1ÄK.À cN cT N¥©þ¥ K,Ø” 1j © BB 1þ"XJyj= B aj≤ 0, Kª ; (ص8I¼êÃ.., ¡,XJ, yj©þØ u0, K=e Ú.

3

-xj= min1≤i≤m{ (Byijb)i|yij> 0}¿O eIq§Ù¥yij´yj 1i ©þ§xq= 0§# xB= B 1 b B 1 aj xj,/¤#º:x (#Ä).=ÌÚ 1 Ú.

1

üX/LЩüX/LµÄCþ K¼ê xBÌ Ú½µ1

xT B cT B B

xT N cT N N

mà‘ 0 b

2

é1[B N b]A^pd {òB=z¤ü I§[I B 1 N B 1 b].^ þ cB Ý[I B 1 N B 1 b] z ‰Sȧ¿\– T 1[cT B cN 0]§ÄCþ xT xT mà‘ B N T 1 1 K¼ê 0 cN cT B N cT b B BB xB I B 1 N B 1 bT 1 u cT N¥ ©þ KµX K§K `¶ N cB BÄK§ K©þ Cþ \ÄCþ§¿u B 1 N¥ A aq ©þ§XJ¤k©þÑ §K `)Ã.. (½ÑÄCþµO B 1 b aq©þ ' §(½ÑÄ Cþ§l (½#̵yij§ò#\\Ù§ §#Ä 1)"

3

4

~1

Min Z= 2x1 3x2 s.t. x1+ x2≤ 3 2x1+ x2≤ 2 4x1+ x2≤ 16 x1, x2≥ 0§ IO.µ Min Z= 2x1 s.t. x1 2x1 4x1 x1≥ 0, 3x2+ 0x3+0x4+0x5+x2+ x3=3+x2+x4=2+x2+x5= 16 x2≥ 0, x3≥ 0, x4≥ 0, x5≥ 0.

~11 gS“µéuþã®IOz 55y¯K§x1= 0, x2= 0, x3= 3, x4= 2, x5= 16´ Ð©Ä 1).ÄCþ f x3 x4 x5ÄC …… 此处隐藏：1465字，全部文档内容请下载后查看。喜欢就下载吧 ……