最適化手法 第1回 [3mm] 整数計画法 (1) [3mm]
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- てるえ うるしはた
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1 1 (1) & ( ) (1) / 39
2 2013 ( ) (1) / 39
3 OR 1 OR 2 OR Excel ( ) (1) / 39
4 1 (4 9 ) 2 (4 16 ) 3 (4 23 ) 4 (4 30 ) 5 (5 7 ) 6 (5 14 ) 7 1 (5 21 ) ( ) (1) / 39
5 8 ( ) (5 28 ) 9 ( ) (6 4 ) 10 ( ) (6 11 ) 11 2 (6 18 ) 12 ( ) (6 25 ) 13 ( ) (7 2 ) 14 ( ) (7 9 ) 15 ( ) (7 16 ) ( ) ( ) (1) / 39
6 ( ) : 14:50 16:20 jgoto@indsys.chuo-u.ac.jp Web jgoto/ Web jgoto/opt.html 20 ( ) (1) / 39
7 :50 16:20 ( ) (1) / 39
8 20 ( ) (1) / 39
9 ( ) (1) / 39
10 OK ( ) (1) / 39
11 ( ) (1) / 39
12 1 2 3 ( ) (1) / 39
13 (linear program) x 1,x 2 2x 1 + x 2 2x 1 3x 2 6, x 1 2x 2 2, x 1 0, x 2 0, x 1, x 2 R ( ) (linear programming) ( ) (1) / 39
14 (linear programming) JISZ8121 D5 1 1 LP 4 ( ) (1) / 39
15 x 1,x 2 2x 1 + x 2 2x 1 3x 2 6, x 1 2x 2 2, x 1 0, x 2 0, x 1, x 2 R x 1 = 3, x 2 = 0 6 ( ) x 2 x 1 2x 2 = 2 2x 1 3x 2 = 6 O 3 ( ) (1) / 39 x 1
16 x 1,x 2 x 1 x 2 x 1 x 2 1, x 1 + x 2 1, x 1 0, x 2 0, x 1, x 2 R x 2 x 1 +x 2 = 1 ( ) O 1 x 1 x 2 = 1 x 1 ( ) (1) / 39
17 x 1,x 2 2x 1 3x 2 2x 1 3x 2 6, x 1 2x 2 2, x 1 0, x 2 0, x 1, x 2 R ( ) x 2 x 1 2x 2 = 2 1 2x 1 3x 2 = 6 O 3 x 1 ( ) (1) / 39
18 1 1 ) ( ) O x2 x1 2x2 = 2 2x1 3x2 = 6 x1 3 ( ) O x 2 1 x 1 +x 2 = 1 x 1 x 2 = 1 x 1 ( ) O x 2 1 x 1 +x 2 = 1 x 1 x 2 = 1 x 1 ( ) (1) / 39
19 2 2 ( ) x 2 x 1 2x 2 = 2 1 2x 1 3x 2 = 6 O 3 x 1 ( ) (1) / 39
20 (simplex methods) Dantzig ( ) (interior-point methods) Karmarkar ( ) ( ) (1) / 39
21 1 2 3 ( ) (1) / 39
22 (integer program) x 1,x 2 2x 1 + x 2 2x 1 3x 2 6, x 1 2x 2 2, x 1 0, x 2 0, x 1, x 2 Z ( ) (integer programming) ( ) (1) / 39
23 (mixed integer program) x 1,x 2 2x 1 + x 2 2x 1 3x 2 6, x 1 2x 2 2, x 1 0, x 2 0, x 1 Z, x 2 R ( ) (mixed integer programming) ( ) (1) / 39
24 (linear programming) JISZ8121 D10 4 R n S f : S R ( ) A R m n b R m c R n x = (x 1, x 2,..., x n ) R n P 0 : {c x Ax = b, x j 0 (j = 1,..., n), x j (j = 1,..., n 1 )} n 1 n ( ) (1) / 39
25 x 1,x 2 2x 1 + x 2 2x 1 3x 2 6, x 1 2x 2 2, x 1 0, x 2 0, x 1, x 2 Z x 1 = 3, x 2 = 0 6 ( ) x 2 x 1 2x 2 = 2 2x 1 3x 2 = 6 O 3 ( ) (1) / 39 x 1
26 x 1,x 2 2x 1 + x 2 2x 1 3x 2 6, x 1 2x 2 2, x 1 0, x 2 0, x 1 Z, x 2 R x 1 = 3, x 2 = 0 6 ( ) x 2 x 1 2x 2 = 2 2x 1 3x 2 = 6 O 3 ( ) (1) / 39 x 1
27 (0-1 integer program) x 1,x 2 2x 1 + x 2 2x 1 3x 2 6, x 1 2x 2 2, x 1 0, x 2 0, x 1, x 2 {0, 1} 0 1 ( ) 0-1 (integer programming) ( ) (1) / 39
28 x 1,x 2 2x 1 + x 2 2x 1 3x 2 6, x 1 2x 2 2, x 1 0, x 2 0, x 1, x 2 {0, 1} x 1 = 1, x 2 = 0 2 ( ) x 2 x 1 2x 2 = 2 2x 1 3x 2 = 6 O 3 ( ) (1) / 39 x 1
29 x 1,x 2 2x 1 + x 2 2x 1 3x 2 6, x 1 2x 2 2, x 1, x 2 {0, 1} x 1,x 2 2x 1 + x 2 2x 1 3x 2 6, x 1 2x 2 2, x 1 0, x 2 0, x 1 1, x 2 1, x 1, x 2 Z 0-1 ( ) (1) / 39
30 LP IP MIP ( ) (1) / 39
31 ( ) ( ) (1) / 39
32 R. Bixby (2012) ,000 2,000 id=62130 ( ) (1) / 39
33 1 2 3 ( ) (1) / 39
34 3 ( ) ( ) (1) / 39
35 ( ) (1) / 39
36 ( ) ( ) ( ) ( ) ( ) ( ) (1) / 39
37 ( ) OK ( ) (1) / 39
38 1 2 3 ( ) (1) / 39
株主通信：第16期 中間報告書
9 1 20,000 15,000 10,000 5,000 2007/4 2008/4 2009/4 2010/4 2011/4 2012/4 2013/4 01 02 2 3 03 04 4 05 06 5 133,362 206,945 344,360 363,936 67,583 128,114 819 18,583 412,477 846,445 164,935 422,265 1,433,645
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株主通信：第18期 中間
19 01 02 03 04 290,826 342,459 1,250,678 276,387 601,695 2,128,760 31,096 114,946 193,064 45,455 18,478 10,590 199,810 22,785 2,494 3,400,763 284,979 319,372 1,197,774 422,502 513,081 2,133,357 25,023
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1 2 3 4 5 6 7 Point 60,000 50,000 40,000 30,000 20,000 10,000 0 29,979 41,972 31,726 45,468 35,837 37,251 24,000 20,000 16,000 12,000 8,000 4,000 0 16,795 22,071 20,378 14 13 12 11 10 0 12.19 12.43 12.40
株主通信 第16 期 報告書
10 15 01 02 1 2 3 03 04 4 05 06 5 153,476 232,822 6,962 19,799 133,362 276,221 344,360 440,112 412,477 846,445 164,935 422,265 1,433,645 26,694 336,206 935,497 352,675 451,321 1,739,493 30,593 48,894 153,612
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総セク報告書（印刷発出版_.PDF
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例題で学ぶオペレーションズ リサーチ入門 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
例題で学ぶオペレーションズ リサーチ入門 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009641 このサンプルページの内容は, 初版 1 刷発行時のものです. i OR OR OR OR OR OR OR OR OR 2015 5 ii 1 OR 1 1.1 OR... 1 1.2 OR...
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1 2 3 4 POINT! 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 POINT! 32 POINT! 33 34 35 給与 36 37 POINT! 38 POINT! 39 POINT! 40 41 42 43 44 45 46 POINT! 47 48 49 50 51 52 53
CONTENTS 5 6 8 7 11 12 14 13 16 15 18 17 18 19 20 21 22 23 24 25 26 28 27 29 31 30 32 1 33 35 34 2 POINT POINT POINT 37 36 3 POINT POINT 39 38 4 POINT POINT 41 40 5 POINT POINT 43 42 6 POINT POINT 45
1 Point 2 Point 3 Point 5 490,000 10 20 25 35 1,059,000 2,235,500 2,890,500 4,449,500 777,000 1,554,000 3,108,000 3,885,000 3,885,000 4,132,000106.3 6
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卓球の試合への興味度に関する確率論的分析
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