緒論.................................................................................... 1
1.1綫性 劃問題及其標準型..................................................... 81.1.2圖 法及基本概念........................................................141.2單純形法....................................................................231.2.2單純形法的 算步驟......................................................251.2.4利 MATLAB實現單純形法.............................................311.3.1大M法.................................................................351.3.3進一步討論MATLAB實現...............................................41習題1............................................................................54
2.1綫性 劃的對偶理論........................................................582.1.2綫性 劃的對偶理論......................................................642.2對偶單純形法...............................................................712.2.2MATLAB實現..........................................................732.3綫性 劃的靈敏度分析......................................................76
2.3.1 源 數變化的分析......................................................77
2.3.2價值 數變化的分析......................................................79
2.3.3技* 數變化的分析......................................................81
2.4靈敏度分析的MATLAB實現...............................................83
2.5應 舉例....................................................................94
2.6綫性 劃的原始對偶內點算法...............................................95
2.6.1原理與算法..............................................................96
2.6.2MATLAB實現.........................................................100 3章運輸問題...................................................................108
3.1運輸問題的數學模型.......................................................108
3.2錶上作 法.................................................................110
3.2.1求初始基可行 的方法..................................................111
3.2.2判斷優 的方法......................................................116
3.2.3 整的閉迴路法....................................................119
3.2.4産銷不 衡的運輸問題..................................................121
3.3運輸問題的MATLAB實現................................................123
3.4應 舉例...................................................................135習題3...........................................................................141 4章目標 劃...................................................................145
4.1目標 劃問題及其數學模型................................................145
4.1.1目標 劃問題的提齣....................................................145
4.1.2基本概念及一般模型....................................................147
4.1.3目標 劃問題的圖 法..................................................149
4.2單純形法及靈敏度分析.....................................................150
4.2.1求 目標 劃的單純形法................................................150
4.2.2目標 劃的靈敏度分析..................................................154
4.3MATLAB實現.............................................................157
4.4應 舉例...................................................................159 5章整數 劃...................................................................168
5.1整數 劃及其數學模型.....................................................168
5.2分支定界法及割 法.....................................................170
5.2.1分支定界法.............................................................170
目錄
5.2.2割 法...............................................................176
5.30-1 劃....................................................................181
5.3.10-1 劃問題的 點.....................................................181
5.3.2隱枚舉法...............................................................184
5.4應 舉例及MATLAB實現................................................185
5.4.1整數 劃的MATLAB實現..............................................185
5.4.2應 舉例...............................................................194 6章圖與網絡優化..............................................................201
6.1圖的基本概念..............................................................201
6.2小支撐樹問題............................................................205
6.2.1樹.....................................................................205
6.2.2小支撐樹.............................................................208
6.3短路問題.................................................................210
6.3.1數學模型...............................................................210
6.3.2帶有負權的Dijkstra算法..............................................213
6.3.3Floyd算法.............................................................218
6.3.4短路問題應 舉例....................................................219
6.4大流問題.................................................................222
6.4.1基本概念...............................................................223
6.4.2有關結論...............................................................225
6.4.3Ford-Fulkerson標號算法................................................226
6.4.4大流問題應 舉例....................................................229
6.5小費 大流問題.......................................................232
6.5.1標號算法...............................................................233
6.5.2應 舉例...............................................................236
6.6MATLAB實現網絡優化....................................................238 7章無 束綫性 劃.........................................................255
7.1無 束綫性 劃的基本概念..............................................255
7.1.1數學模型...............................................................256
7.1.2優性條件.............................................................257
7.1.3優化算法的一般結構..................................................259
7.2一維綫搜 .................................................................261
7.2.1綫搜 方法.........................................................261
運籌學基礎及其MATLAB應
7.2.2不綫搜 方法......................................................266
7.2.3一維綫搜 的MATLAB實現............................................270
7.3幾個算法及其MATLAB實現..............................................279
7.3.1速下降法.............................................................279
7.3.2 軛梯度法.............................................................283
7.3.3牛頓法及擬牛頓法......................................................288
7.4應 舉例...................................................................296 8章 束綫性 劃...........................................................304
8.1數學模型及基本概念.......................................................304
8.1.1數學模型...............................................................304
8.1.2基本概念...............................................................305
8.1.3優性條件.............................................................307
8.2幾個算法及其MATLAB實現..............................................311
8.2.1罰函數法...............................................................312
8.2.2可行方嚮法.............................................................326
8.3應 舉例...................................................................335 9章排隊論基礎................................................................346
9.1排隊論的基本概念..........................................................346
9.1.1問題的 入及基本概念..................................................346
9.1.2排隊論的常 分布......................................................349
9.2單服 及多服 模型..................................................353
9.2.1單服 模型...........................................................353
9.2.2多服 模型...........................................................363
9.3排隊 統優化及MATLAB實現............................................370
9.3.1優服 率.............................................................370
9.3.2優服 數目.........................................................377 錄MATLAB簡介..............................................................381
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