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200７= /10/２0,Tue.−
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------=_NextPart_01C81275.5C9DACD0 Content-Location: file:///C:/74785C14/07dmt_4.files/slide0008.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
多目的計画とは？
<= span style=3D'color:#006666;font-weight:normal;mso-fareast-hint:yes'>n= 瘻：ダイエット問= n <= /span>『なめがやわーる= ど』では，「神秘ケーキ」「魅惑菓子」「苦渋野菜」「過酸果物」の4つの食べ物と，「= だんはっく」「ガルジウム」「ヒタビン」という3つの栄養素と2つの食= 品含有物「糖分」「ガロリー」が存在する．4つの食べ物は3つの栄養素と2つの食= 品含有物を，そ= れぞれ右下表に示す量だけ含む．
　『なめがやわーるど』人は，3栄養素を一日に各々最低50, 40, 45は摂取しないと死ん= でしまう！　同様に，ガロリーは一日最大8000を超えても死= でしまう！！
　さて，『なめがやわーるど』人の文教花子さんはダイエットをしたい．糖分を最小にする<= span style=3D'position:absolute;top:64.75%;left:6.17%;width:108.42%;height:3.5%= '>食べ物の量と，同時にガロリーも最小にする食べ物の量を<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック"'>知りたい．しかし甘党の花子さんは神秘ケーキと魅惑菓子が大好き= ﾅ苦渋野菜と過酸果物が嫌いだった．好きなものはたくさん，嫌いなものはなるべく食べたくない．各食べ物の文教さんの好き嫌い= xは一単位あたり右下表のようになるそうである
（<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック"'>数字が大きいほど好きらしい）．
<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";mso-fareast-hint: yes'>　さあ，花子さんの3つの目的（糖分最小，ガロリー最小，好物たくさん= 食べたい）を達成するためには，各食品をどれくらいずつ食べたらよいだろうか？
制約は全て線形で書けそうだね．
目的は３つあるよ．
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多目的計画とは？
n解説：ダイエット問題
どうやって解くの？<= /span>
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
多目的計画とは？
n多目的線形計画= @(Multi-objective LP)
–線形の制約条件のもと，多数の目的・= ﾚ標が設定され，それらを<= /span>なるべく= 満たすように= 解きたい．即ち= C線形制約条件下で複数の線形目的関数を最大・最小化す= 驩を見つけるという決定問題のモデル．
どうやって解くの？<= /span>
最適解って何？
注：簡単のため，目的関数は = ;
最大化に揃えてある．このようにしても一般性は失わない．
=
k本の目的関数
m本の線形制約
n個の非負制約
変数の数は n個
一般的な表記
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2ZZ92Zid2Zmd2PL2AlLw2aAd2qI92qRd2qZ92qid2qq92qzN2pwdby8wBbI927Rd27Z927id27q9 27zd277927/92vD2AjVQ3MZ93Mid3Mq93Mzd3M793NAd3dIt3cL9bi9gA9id3dq93dzd3d793eAd 3uI93uRd3uRd3cN9A+q93uzd3u793vAd3/I93/Rd3/Z93/WN3tb9AjHQ3/793wAe4AI+4ARe4AZ+ 4Aie4Apu4PoN22L84BAe4RI+4RGeEYEAADs= ------=_NextPart_01C81275.5C9DACD0 Content-Location: file:///C:/74785C14/07dmt_4.files/slide0002.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
多目的計画とは？
n線形計画法(LP)
–線形の制約条件・目的関数による，量的データに対= する決定問題のモデル．目的関数の= 狽ﾍ1つ．
3D"ホームベース:
1本の目的関数
3D"ホームベース:
m本の線形制約
n個の非負制約
単体法や内点法で効率的に解ける！
=
変数の数は n個
一般的な表記
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多目的計画とは？
n解説：ダイエッ= g問題（続き）
–<= span style=3D'mso-ascii-font-family:Arial;mso-hansi-font-family:Arial;mso-farea= st-hint: yes'>目的関数を別々に考えてみたら？
nf1(x)のみを目的とするＬＰ （Ｐ1） ： =
n
nf2(x)のみを目的とするＬＰ （Ｐ2） ： =
n
nf3(x)のみを目的とするＬＰ （Ｐ3） ：
３つのＬＰを別々に= き，各々最適解を出す！
全ての最適解が一致= @＝　完全最適解！
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多目的計画とは？
<= span style=3D'font-weight:normal;mso-fareast-hint:yes'>n多目的線形計画= 竭閨iMLP）の最適解を考= ｦよう
–完全最適解　absolutely optimal solution
n実行可能解　　= @　　　 　　が
n
n
nを満たすとき，= iＭＰ）の完全最適解であるという．
–
<= span style=3D'mso-fareast-hint:yes'>–ダイエット問題では，目的関数が
n
n
n
–なので，以下を= 桙ｽす解 x* = が完全最適解！<= /span>
= なるほど，完全最適解を求め= ればいいんだね？
注：不等号の向きに注意．
目的関数 f<= i>1(x) と f<= i>2(x) は最小化， <= /span>
目的関数 f<= i>3(x) は最大化
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多目的計画とは？
n解説：ダイエッ= g問題（続き）
–LP（Ｐ<= b>1）, （Ｐ2）, = （Ｐ3）の最適解は…
= 完全最適解があるならば，それが多目的線形計画問= 閧ﾌ最適解となる．
しかし，この例題のように，一般に完全最適解が存= ﾝすることは稀である．
別の，何らかの意味= ﾅの解を求めないと…
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多目的計画とは？
n多目的線形計画法(MLP)　表記の簡略化
(MP)
3D"ホームベ=
k本の目的関数
3D"ホームベース:
m本の線形制約
n個の非負制約
変数の数は n個
「x <= /span>は実行可能領域 X <= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:89%;mso-fareast-hint:yes'>に入ってるよ」ということ
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演習１：
n以下の問題を多目的線形計画問題として定式化= ｵ，各目的関数ごとのＬＰと見たときの最適解をそれぞれ求め= ﾈさい．最適解の求解はLINDOやExcelのソルバーなどを用いて良い．
R= 11;株式会社文教商事の湘南支店では，湘南及び県北の2箇所にそれぞれ営業所を新設する計画がある．
–施設新設に必要な初期投資額はほぼ建坪に比例し，= t帯設備込みで，1坪あたり湘南営業所で400万円，県北営業所で200万円である．
&= #8211;投資予算額は，両営業所合わせて4億円である．
–支店長は，傘下の既存営業所及び各地域の需要動向など= 勘案した結果，次のような3種の目標を満足させたいと望んでいる．
n目標1：投資= 総額を投資予算額にできるだけ近づけたい．
n目標2：湘南営業所の建坪をできるだけ大きくしたい．
n目標3：県北営業所の建坪をできるだけ大きくしたい．
= n（出展：伏見多美雄他「経営の多目標計画」森= k出版(1987)） =
------=_NextPart_01C81275.5C9DACD0 Content-Location: file:///C:/74785C14/07dmt_4.files/slide0004.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
X
多目的線形計画問題の解
n簡単な例題= ﾅ考えてみよう！
x1
x2
0
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0
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多目的線形計画問題の解
n簡単な例題= ﾅ考えてみよう！
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多目的線形計画問題の解
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UXNMApPDJbP2JDqjqSmVZL1+stoOt4v5Nn9aIZZqBnvSZyYbJYZLj29yM76V4vO6fanm11YVKFhC WLh2KGeodlgXFfiIFqboEyfZxWWjdnOzyelpUolRAAA7 ------=_NextPart_01C81275.5C9DACD0 Content-Location: file:///C:/74785C14/07dmt_4.files/slide0014.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
多目的線形計画問題の解
nパレート最適解(Pareto optimal sol.)
–x*<= /span>∈<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>X<= /span>がパレート最適であるとは，&#= 13;
–
= 211;で，かつ少なくとも一つは厳密な不等号（＞）を満たすx∈<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>X<= /span>が存在しないこと．
x1
x2
0
X
0
f1(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>x<= /span>)<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-language:JA;mso-special-format:lastCR;display:none'>
f2(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>x<= /span>)<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-language:JA;mso-special-format:lastCR;display:none'>
パレート最適解
パレート最適値
l個の目的のい= ずれか1つを犠牲にせずに，他= を改善できない状態
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多目的線形計画問題の解
n弱パレート最適解(weakly Pareto optimal sol.)
–x*<= /span>∈<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>X<= /span>が弱パレート最適であるとは，&#= 13;
–
= 211;を満たすx∈X<= /span>が存在しないこと．
x1
x2
0
X
パレート最= 適解
x1
x2
0
X<= /span>
=
パレート最適解
f1(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>x<= /span>)<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-language:JA;mso-special-format:lastCR;display:none'>
f2(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>x<= /span>)<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-language:JA;mso-special-format:lastCR;display:none'>
f<= /span>2(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>x<= /span>)<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-language:JA;mso-special-format:lastCR;display:none'>
f<= /span>1(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>x<= /span>)<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-language:JA;mso-special-format:lastCR;display:none'>
弱パレート最適解
弱パレート最適解
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n以下のＭＬＰについて，解空間を図示し，パレ= [ト最適解，及び弱パレート最適解を求めよう．
R= 11;（１）
= 211;
R= 11;（２）
= 211;
R= 11;（３）
演習２：
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目的関数の増加方向
演習２：
o<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:89%;position:relative;top:.37em;mso-text-raise:-25%;mso-fareast-= language: JA;mso-special-format:lastCR;display:none'>
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x2
f1(x) : (1, 1)
f2(x) : (-3,-2)
1
1
2
2
3
3
4
5
f1(x) : (2, 1)
f2(x) : (-3,-2)
f1(x) : (5, 2)
f2(x) : (-3,-2)
実行可能領= 域
(1)
(2)
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text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
多目的線形計画問題の解法
n多目的計画法と= ﾚ標計画法
–選好最適化による解法
n加重平均法 the weighting method
n制約化法 the constraint method
nマキシミン法 the maximin method
–満足化による解法
n目標計画法 the goal program
–多目的単体法 the multiobje= ctive simplex method
------=_NextPart_01C81275.5C9DACD0 Content-Location: file:///C:/74785C14/07dmt_4.files/slide0020.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
<= ![endif]>
多目的線形計画問題の解法
n加重平均法（the Weighting Method） <= /span>
–意思決定者の選好により，目的関数に重み付けを行い，その総和を1目的関数として解く．
（<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>MLP）
（P(ω<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>)）
目的関数・制約：凸性
x<= /span>*<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes;mso-fareast-language:JA'>∈X = が（MLP）の<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; display:none'>
パレート最適解
x<= /span>*<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes;mso-fareast-language:JA'>∈X = がある ω<= /span>>0 <= /i>に対し，
（P(ω)）の最適解
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多目的線形計画問題の解法
n加重平均法
–例題：&= #13;
–（１）
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–
–（２）
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A
B
C
D
E
多目的線形計画問題の解法
n加重平均法
–特徴
n重みが決まれば適用は簡単 =
–問題点
n重みωをどう決定するか？　そもそも事前に決= 閧ﾅきるか？
n意思決定者の価値基準にあ= った解を出せるとは限らない．
R= 11;（実行可能解集合が非凸のとき，線形加重和は= s適切）→乗法，maximin
n単体法では端点解しか出せない．→2目的なら連= 続変形法など
x1
x2
0
数学
英語
例：2教科の点数による5人の学生の順位
–<= /span>英語重視の評価　→　Ａくん（100,45 　　　　例）ω1=3D5,ω2=3D1 <= /span>
–<= /span>数学重視の評価　→　Ｅくん（45,100 　　　　例）ω1=3D1,ω2=3D5 <= /span>
<= span style=3D'font-family:"ＭＳ Ｐゴシック";font-size:89%;mso-fareast-hint:yes'= >–<= /span>同等の評価　　　　→　Ｃくん(70,70）が1番ではない　例）ω1=3D1,ω2=3D1 <= /span>
様々な評価法
注：Cくんはパ= 戟[ト最適ではないので，パレート最適を求める方法= ﾅはCくんを評= ｿすることは難しい．目的関数= 纏めるときに非線形化などする必要がある．<= /span>&= #13;
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ABIAgQAAAGZmmczM/wECAwJcjI+py+0Po5z0iYuz3rz7D4biSJZfYKbqyrbuhr7yTNdkbOf63uL8 DwxqfMKisUY8KpepJPMJ7Tij1Oi0ilVes9zgtgvWfcPk2biMZp3T7NK6DQdV5vS6/Y5nFAAAOw== ------=_NextPart_01C81275.5C9DACD0 Content-Location: file:///C:/74785C14/07dmt_4.files/slide0022.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
多目的線形計画問題の解法
n制約化法（the Constraint Method）
–目的関数を一つを除き，境界値を設定して制約条件にして解く．
（<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>MLP）
（P(ε<= /span>)<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";mso-fareast-hint: yes'>）
x<= /span>*<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes;mso-fareast-language:JA'>∈X = が（ＭＰ）の
パレート最適解
x<= /span>*<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes;mso-fareast-language:JA'>∈X = がある ε<= /span>p に対し，
（Ｐ（ε））の一= 意最適解
x<= /span>*<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes;mso-fareast-language:JA'>∈X = が（ＭＰ）の
パレート最適解
x<= /span>*<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes;mso-fareast-language:JA'>∈X = がある ε<= /span>p に対し，
（Ｐ（ε））の最適解
一意でない= 場合= 弱パレート最適解
<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>q<= /span>番目の目的関数だけを目的として残し，
残りは境界条件εk を設定して= 制約に入れる．
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MkMWyHZ2sJ/NrGhHS9rSmva0qC2tEDLA2ta69rWwja1sZ0vb2tr2trjNrW53y9vexlYIGgiucIdL 3OIa97jITa5yl8vc5jr3udCNrnSN+wdJWPe62M2udrfLXUOooQ/gDa94x0ve8po3DkLYKYB618ve 9rr3vfCNr3znS9/62ve++M2vfvf7Xir4978ADrCAB0xgJgQBADs= ------=_NextPart_01C81275.5C9DACD0 Content-Location: file:///C:/74785C14/07dmt_4.files/slide0042.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
多目的線形計画問題の解法
n制約化法　（εの取り方について，ある一つの= 法）
–ペイオフ表（pay-off t= able）を利用する．
（LP<= i>p）
（<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>MLP）
k<= /span>個の最適解
min.
max.
=
全てのtについて（P(ε<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>)<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes'>）を解く
より
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多目的線形計画問題の解法
n制約化法
–例題：&= #13;
x1
x2
0
X
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the Constrained Method
pay-off table
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多目的線形計画問題の解法
n制約化法
–例題：&= #13;
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多目的線形計画問題の解法
nマキシミン法 （the maximin method）
–目的関数をmaximinにして解く．
（<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>MLP）
（Pm）
x<= /span>*<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes;mso-fareast-language:JA'>∈X = が（MLP）の<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; display:none'>
パレート最適解
x<= /span>*<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes;mso-fareast-language:JA'>∈X = が
（Pm）の<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes;color:red'>一意最適解
x<= /span>*<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes;mso-fareast-language:JA'>∈X = が（MLP）の<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; display:none'>
パレート最適解
x<= /span>*<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes;mso-fareast-language:JA'>∈X = が
（Pm）の最適解
一意でない= 場合= 弱パレート最適解
注：（ＭＰ）が最小化問題ならminimax
LPだよ
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多目的線形計画問題の解法
nマキシミン法
–例題：
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多目的線形計画問題の解法
n補足：一意最適= でない場合のパレート最適性の判定
–最適解x*<= span style=3D'mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Ti= mes New Roman"; mso-fareast-hint:yes'>の一意性が保証されない場合，x*<= /span>がもとの問題（MLP）のパレート最適解であるかどうかをテストする（以下の問題を解く）
実行可能解xに対し，
fp(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>x*<= /span>)<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";mso-fareast-hint: yes'>が最大ならば，εp=3D0
そうでなければ，あるp<= /span>について
他の目的を犠牲にせずに
fp(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>x)<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes'>をもっと大きくできる！
上記テスト問題の最適解　　　　について，&#= 13;
（１）　　　　　ならば，x*<= /span>は（MLP）のパレート= 最適解
（２）　　　　　ならば，　 が（MLP）のパレート= 最適解
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
多目的線形計画問題の解法
n目標計画法　　(goal program: goal attainment)
–各目的関数 fp(x) に目標値 gp* = を設定し，目標値との乖離を最小化．
（<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>MLP）
Charne= s-Cooper= (1961)
…　目標値 gp*より以下にしたい場合
…　目標値 gp*より以上にしたい場合
…　目標値 gp*に等しくしたい場合
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超過達成（over-attainment）
不足達成（under-attainment）
多目的線形計画問題の解法
n目標計画法
–各目的関数 fp(x) に目標値 gp* = を設定し，目標値との乖離を最小化．
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多目的線形計画問題の解法
n目標計画法
–各目的関数 fp(x) に目標値 gp* = を設定し，目標値との乖離を最小化．
（<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>MLP）
（GA）
は，満たされるので，
制約から省ける．
LPとして解ける！
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多目的線形計画問題の解法
n目標計画法
–多目標の付順と加重
（１）目標値をちょうど達成することが望ましい
（２）目標値の超過は困るが，不足は構わない
（３）目標値の不足は困るが，超過は構わない
（４）目標値に関わりなく最大・最小
目的関数への付加変数=
= =
を最小化
である限り= ，
を最小化
である限り= ，
を最小化
を最小化
を最大化
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多目的線形計画問題の解法
n目標計画法
–例題：
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多目的線形計画問題の解法
n補足：目標計画法
–目標値との乖離最小化において，目的関数のスケールが大幅に違う場合
例：
相対偏差を= 使う方がよい．例えば，目標値を最適値とすると，
例：
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目的関数の絶対優先順位係数(primitive priority factor)<= /div>
多目的線形計画問題の解法
n目標計画法（多目標付順・加重） <= /span>
–各目的関数 fk(x) に目標値 fk* = を設定し，目標値との乖離を最小化．
（<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>GA= ）
に対し，どんな自然数 n についても&#= 13;
とはならない．
補助変数個々の重み
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–例題：
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多目的線形計画問題の解法
n目標計画法（希求水準[aspiration level] 達成）<= /span>
–各目的関数 fp(x) に希求水準 α<= i>p を設定し，目標値との乖離を最小化．
（<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>MLP）
を満たすxを求めることで満足= ｵよう！
（MP<= i>p）
k個の問題&= #13;
それぞれ最適値 fp* を導出&= #13;
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多目的線形計画問題の解法
n目標計画法（希求水準[aspiration level] 達成）<= /span>
–各目的関数 fp(x) に希求水準 α<= i>p を設定し，目標値との乖離を最小化．
（<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>MP= p）
k個の最適値 fp*
なら，その希求水準の要求が強すぎるので緩和し，
全ての問題（ＭＰp ）を解き直す．
なら，全ての希求水準を満たしている
即ち
を満たすxが（1つ以上）存在し，かつ
これを満た= しながら，各目的の個々の最適値がわかっている状態 <= /div>
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多目的線形計画問題の解法
n目標計画法= i希求水準[aspiration level] 達成）<= /span> <= /div>
<= span style=3D'position:absolute;top:0%;left:4.36%;width:95.63%;height:100.0%'><= span style=3D'mso-fareast-hint:yes'>Øθ=3D1のとき，実行可能解が存在． <= /div>
<= span style=3D'font-family:"Times New Roman";mso-fareast-hint:yes'>Øθ=3D0で実行可能なら，完全最適解が存在．
なら，全て= の希求水準を満たしている
しかし
現在得られている解のどれかが「最良」とは限らない！
もっと良い解を見つけよう！<= span style=3D'font-family: "ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-special-fo= rmat:lastCR; display:none'>
…
θ∈(0,1) について以下の不等式系を考える．
x1*
x2*
xk*
あるθに対= し，実行可能かどうかは単体法のP= haseTで判定可能
実行可能な= 中で，最大のθを見つけたい！
本質的に
制約化法と同じ
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charset="shift_jis" 意思決定論：　4．多目的線形計画法
多目的線形計画問題の解法
n目標計画法= i希求水準[aspiration level] 達成）<= /span> <= /div> = = =
…
<= ![endif]>
x<= i>1*
x<= i>2*
x<= i>k*
とし，　　に= 対応する実行可能解をxq-1とする．
θ*の近似値
を解き，最適解をxqとする．
q=3Dk = なら終了（ xqが（MLP）の最適解）
そうでなければ，q:=3Dq+1として繰返= し．
は，k 個の解x1*,= …, xk*について
としてもよいし，簡単に1で始めても良い．
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多目的線形計画問題の解法
n目標計画法（希求水準[aspiration level] 達成）<= /span>
–例題：
0
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f2(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>x<= /span>)<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-language:JA;mso-special-format:lastCR;display:none'>
= <= ![endif]>
aspiration level
<= ![endif]>
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Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRwAOAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAwBD AAkAgAAAAAAA/wIohI+py+0Ynpy0goCt3hRnDoaHl5HmiabqyqLia5HwPHn07Xz4nkRLAQA7 ------=_NextPart_01C81275.5C9DACD0 Content-Location: file:///C:/74785C14/07dmt_4.files/slide0041_image580.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDgBLAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAJ AEcAgAAAAP8AAAJIhBGnmBu/GDyvqmoZ0rvnDoZXZDSR6ZAipaIj6bJwS8/2WeN3ur/6zwP6gsSh USZEFpXHUm7p7DGn0WQVuro2s9yYltp9blEFADs= ------=_NextPart_01C81275.5C9DACD0 Content-Location: file:///C:/74785C14/07dmt_4.files/slide0047.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
多目的線形計画問題の解法
n多目的単体法 （the multiobjective simplex = method）
–通常の単体法を（MLP）= 用に素直に拡張
n多目的単体表 (multiobjective simplex= tableau）
M.Zele= ny(1974)
3D"テキスト
基底
3D"テキスト
目的関数
非基底
非基底 j<= /span> に対し，
目的関数値= は
最小
パレート最適
k<= /span>番目の目的
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
多目的線形計画問題の解法
n多目的単体= @ （the multiobjective simplex method） =
非基底 j<= /span> に対する ratio test
今，ある実行可能基底解=
その目的関数値
非基底 xj
を基底に
新しい実行可能基底解=
その目的関数値
実行可能基= 底解　 ，ある非基底 j に対し　　　　　であるとき
（１）　　　　　ならば，　　はパレート最適解ではない
（２）　　　　　ならば，　　はパレート最適解ではない．
実行可能基底解　 に対し，　　　　　　　　　　　　　= を満たす非基底
列 r,j<= /span> が存在するとき，列 r <= /span>の非基底変数を基底に入れて得ら
れる実行可能基底解はパレート最適解にはならない
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file:///C:/74785C14/07dmt_4.files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論：　4．多目的線形計画法
参考文献
<= span style=3D'font-size:83%;font-weight:normal;mso-fareast-hint:yes'>n坂和正敏「= 線形システムの最適化」森北出版（1984）
<= span style=3D'font-size:83%;font-weight:normal;mso-fareast-hint:yes'>n坂和正敏「= 離散システムの最適化」森北出版（2000）
<= span style=3D'font-size:83%;font-weight:normal;mso-fareast-hint:yes'>n今野浩「線形計画法」日科技連（1987）
<= span style=3D'font-size:83%;font-weight:normal;mso-fareast-hint:yes'>n中山弘隆・= 谷野哲三「多目的計画法の理論と応用」コロナ社(1994)
<= span style=3D'font-size:83%;font-weight:normal;mso-fareast-hint:yes'>n児玉正憲「= 多目的意思決定と経済分析」牧野書店(1996)
<= span style=3D'font-size:83%;font-weight:normal;visibility:hidden'>n
<= span style=3D'font-size:83%;font-weight:normal'>nM. Zeleny = ``Linear Multiobjective Programming’’ Springer-Verlag, 1974
<= span style=3D'font-size:75%;font-weight:normal'>nJared L. C= ohon ``Multiobjec= tive Programming and Planning’’ Academic Press, 1978
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CXtjb2xvcjpzaWx2ZXIgIWltcG9ydGFudDt9DQphOnZpc2l0ZWQNCgl7Y29sb3I6I0VDRUFBQyAh aW1wb3J0YW50O30NCn== ------=_NextPart_01C81275.5C9DACD0 Content-Location: file:///C:/74785C14/07dmt_4.files/script.js Content-Transfer-Encoding: quoted-printable Content-Type: application/javascript; charset="shift_jis" function LoadSld() { var sld=3DGetObj("SlideObj") if( !g_supportsPPTHTML ) { =09 sld.style.visibility=3D"visible" return } if( MakeNotesVis() ) return runAnimations =3D _InitAnimations(); =09 if( IsWin("PPTSld") ) parent.SldUpdated(GetSldId()) g_origSz=3DparseInt(SlideObj.style.fontSize) g_origH=3Dsld.style.posHeight g_origW=3Dsld.style.posWidth g_scaleHyperlinks=3D(document.all.tags("AREA").length>0) if( g_scaleHyperlinks ) InitHLinkArray() if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) ) document.body.scroll=3D"no" _RSW() if( IsWin("PPTSld") && parent.IsFullScrMode() ) FullScrInit(); =09 MakeSldVis(); ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.filter !=3D ""; } function GetSldId()=20 { var regExp =3D /file:\/\/\//i var pos =3D location.href.search(regExp) if (MHTMLPrefix !=3D "" && pos !=3D -1) sId =3D location.href.substring(pos) else { sId =3D RemoveFilePrefixFromHref(location.href); var regExp =3D /\// var fixedHref =3D sId var pos =3D -1 =09 pos =3D fixedHref.search(regExp) while (pos !=3D -1) { fixedHref =3D fixedHref.replace(regExp, "\\") pos =3D fixedHref.search(regExp) } =09 if (g_fBaseHyperlink =3D=3D true) sId =3D "file:///" + fixedHref; else sId =3D fixedHref.substring(fixedHref.lastIndexOf('\\') + 1) } =09 return sId } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } }function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { =09 if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"スライド ショーの最後です。 クリックすると終了します。"= , SCREEN_MODE=3D"Frames", gIsEndShow=3D0, NUM_VIS_SLDS=3D44, SCRIPT_HREF=3D= "script.js", FULLSCR_HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0008.htm",1,-1,1),new hrefList("slide0013.htm",1,-1,1),new hrefList("= slide0005.htm",1,-1,1),new hrefList("slide0002.htm",1,-1,1),new hrefList("s= lide0011.htm",1,-1,1),new hrefList("slide0007.htm",1,-1,1),new hrefList("sl= ide0010.htm",1,-1,1),new hrefList("slide0006.htm",1,-1,1),new hrefList("sli= de0003.htm",1,-1,1),new hrefList("slide0004.htm",1,-1,1),new hrefList("slid= e0016.htm",1,-1,1),new hrefList("slide0017.htm",1,-1,1),new hrefList("slide= 0014.htm",1,-1,1),new hrefList("slide0021.htm",1,-1,1),new hrefList("slide0= 018.htm",1,-1,1),new hrefList("slide0049.htm",1,-1,1),new hrefList("slide00= 19.htm",1,-1,1),new hrefList("slide0020.htm",1,-1,1),new hrefList("slide002= 4.htm",1,-1,1),new hrefList("slide0023.htm",1,-1,1),new hrefList("slide0022= .htm",1,-1,1),new hrefList("slide0042.htm",1,-1,1),new hrefList("slide0043.= htm",1,-1,1),new hrefList("slide0025.htm",1,-1,1),new hrefList("slide0026.h= tm",1,-1,1),new hrefList("slide0027.htm",1,-1,1),new hrefList("slide0044.ht= m",1,-1,1),new hrefList("slide0028.htm",1,-1,1),new hrefList("slide0045.htm= ",1,-1,1),new hrefList("slide0030.htm",1,-1,1),new hrefList("slide0034.htm"= ,1,-1,1),new hrefList("slide0031.htm",1,-1,1),new hrefList("slide0046.htm",= 1,-1,1),new hrefList("slide0032.htm",1,-1,1),new hrefList("slide0035.htm",1= ,-1,1),new hrefList("slide0033.htm",1,-1,1),new hrefList("slide0038.htm",1,= -1,1),new hrefList("slide0037.htm",1,-1,1),new hrefList("slide0039.htm",1,-= 1,1),new hrefList("slide0041.htm",1,-1,1),new hrefList("slide0047.htm",1,-1= ,1),new hrefList("slide0048.htm",1,-1,1),new hrefList("slide0015.htm",1,-1,= 1)); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('


' + ENDSHOW_MESG + '

') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice= ","nb_voiceBorder",18,parent.ToggleVNarration ) gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT= xt","nb_otlTxtBorder",23,parent.ToggleOtlText ) gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts" gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState /********************************************* Context menu implementation _CM() is the function that's hooked up to the oncontextmenu event. Once we're asked to show the menu, we first build it by creating DIVs on-the-fly. Then we position it=20 within the screen area so it doesn't get clipped. Creating the DIVs using createElement() means we don't have to write out any extra HTML into the slide HTML files. **********************************************/ var sNext=3D"次へ",sPrev=3D"前へ",sEnd=3D"スライド ショーの終了",sFont=3D"= lＳ 明朝",sArrow=3D"矢印",sFreeform=3D"フリーフォーム",sRect=3D"四角形",sOv= al=3D"楕円" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) =09 CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();= PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; 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charset="shift_jis" 意思決定論：　4．多目的線形計画法 ------=_NextPart_01C81275.5C9DACD0 Content-Location: file:///C:/74785C14/07dmt_4.files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis"
 ノ= ート
スラ= Cド ショー
アウトライン
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