Phd Thesis Nts 104 s

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Linear programming is considered to be, beyond any doubt, one of the most popular tools of operational research and management science in general. In many decision problems, which are modeled by using lineal systems, there is a necessity of finding new solutions (post-optimal), not so far from the optimal one. The subject of the present thesis is the study of several post-optimal analysis methods (robustness analysis) in linear programming problems and the proposition of a new approach. In order to compare and evaluate the post-optimal analysis methods with each other and with the new approach, these methods were implemented in software (using C# as the programming language). Following, these software modules were intergraded in a decision support system which also includes the MUSA (Mulitctiteria Satisfaction Analysis) method, developed by Grigoroudis and Siskos for measuring customers satisfaction. For the implementation of the relevant evaluation experiments regarding these methods, data from real-world surveys were used as well as synthetic data sets which were produced by a data set generator, also developed under this thesis and intergraded in the aforementioned decision support system. This DSS supports the analysts, who use MUSA method, in selecting the most appropriate post-optimal analysis method in each case and also in selecting the levels of the two basic method parameters.

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....................................................................................................................... 20 1: - ....................................... 24 1.1 ............................................... 25 1.1.1 ....................... 27 1.1.2 ............................................................ 33 1.1.3 ............... 39 1.2 ............................................... 42 1.2.1 .............................................................................. 48 1.2.2 ............................................................ 50 1.2.3 ................................................... 52 1.3 - ....................................................... 55 1.3.1 ....................................................................................... 55 1.3.2 - .............................................. 57 1.3.3 ..................................................... 61 1.4 ..................................................................................... 64 2: ................................................................................................... 68 2.1 ......................................................... 69 2.1.1 ....................................................................................... 71 2.1.2 ................................................................................. 71 2.1.3 ............................................................................................. 72 2.2 .................................................... 73 2.3 ......................................................................... 79 2.3.1 Tarry ..................................................................................... 81 2.3.2 Manas - Nedoma ................................................................. 85 2.3.3 Simplex ................................................................ 98 2.3.4 ............................................................................ 114 3: ................................................................. 122 3.1 ..................................................................................... 123 3.2 ................................................................................... 132 3.3 ........................................................................................... 144 4: ............................ 146 4.1 ...................................................................................... 147 4.1.1 ................................................................................... 147

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4.1.2 ............................................................................... 151 4.1.3 ..................................................... 152 4.1.4 ........................................................... 154 4.2 ............................. 157 4.3 M UTA .................................................................. 159 4.3.1 .......................................................................................... 159 4.3.2 UTA ............................................................................................... 161 4.3.3 UTASTAR ................................................................................. 165 4.3.4 UTA ................................................ 168 4.4 M MUSA ................................................................................................... 171 4.4.1 .......................................................................................... 171 4.4.2 .................................................................................................. 173 4.4.3 ................................................................ 176 4.4.4 MUSA ................................................................ 179 4.4.5 MUSA......................................................... 182 5: .............. 186 5.1 H UTA .............................................. 187 5.1.1 ................................................... 187 5.1.2 ............................................... 189 5.1.3 ........................................................ 191 5.2 H MUSA ........................................... 195 5.2.1 ....................................... 195 5.2.2 ........................................................ 197 5.2.3 ........................................................................................ 200 5.2.4 MUSA ..................................................................... 209 5.2.5 MUSA ............................ 210 6: MUSA ............................. 212 6.1 ...................................... 213 6.2 .................................................................................... 214 6.3 ......................................................... 217 6.4 ................................................................................................ 221 6.5 ......................................................................................................... 229 6.6 .......................................................................................... 230 7: ............ 238 7.1 ................................................................................................................ 239 7.2 ............................................................................. 241 7.3 ........................................................................... 242 7.4 .................................................................... 244

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7.5 ............................................................................ 249 7.6 ........................................................................................................ 252 8: .......................................................... 254 8.1 E ................................................................................................................ 255 8.2 .......................................................................................................... 255 9: 18 .................................................................... 260 9.1 ................................................................................................................ 261 9.2 ................................ 262 9.2.1 - ...................................................... 262 9.2.2 - ............................................................ 263 9.3 .................................................................................................... 264 9.3.1 - ...................................................... 264 9.3.2 - ............................................................ 265 9.4 ............................. 266 9.4.1 - ...................................................... 266 9.4.2 - ............................................................ 267 9.5 ................................................................................................................. 268 9.5.1 - ...................................................... 268 9.5.2 - ............................................................ 269 9.6 ........................................................................................................... 270 9.6.1 - ...................................................... 270 9.6.2 - ............................................................ 270 9.7 ........................................................................................................... 271 9.7.1 - ...................................................... 271 9.7.2 - ............................................................ 272 9.8 ........ 273 9.8.1 - ...................................................... 273 9.8.2 - ............................................................ 273 9.9 Super Market...................... 274 9.9.1 - ...................................................... 274 9.9.2 - ............................................................ 275 9.10 Super Market .............. 276 9.10.1 - .................................................... 276 9.10.2 - .......................................................... 277 9.11 ................................................................................................................ 278 9.11.1 - .................................................... 278

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9.11.2 - .......................................................... 279 9.12 ............................... 280 9.12.1 - .................................................... 280 9.12.2 - .......................................................... 281 9.13 ................................................... 281 9.13.1 - .................................................... 281 9.13.2 - .......................................................... 282 9.14 ................................................ 283 9.14.1 - .................................................... 283 9.14.2 - .......................................................... 284 9.15 ................................................................... 284 9.15.1 - .................................................... 284 9.15.2 - .......................................................... 285 9.16 ......................................................................................................... 286 9.16.1 - .................................................... 286 9.16.2 - .......................................................... 287 9.17 Logistics.............................. 288 9.17.1 - .................................................... 288 9.17.2 - .......................................................... 288 9.18 .............................................................................................................. 289 9.18.1 - .................................................... 289 9.18.2 - .......................................................... 290 9.19 RAM................................ 291 9.19.1 - .................................................... 291 9.19.2 - .......................................................... 292 ...................................................................................................................... 294 ............................................................................................................... 298 I: Simplex ............................................................................. 318 II: ......................... 324 III: Tarry.................................................. 326 IV: ............................................................. 330 V: .............................................................. 366

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2-1: Manas-Nedoma, Simplex s=0 .......................................... 91 2-2: Manas-Nedoma, Simplex s=1 .......................................... 91 2-3: Manas-Nedoma, Simplex s=2 .......................................... 92 2-4: Manas-Nedoma, Simplex s=3 .......................................... 92 2-5: Manas-Nedoma, Simplex s=5 .......................................... 93 2-6: Manas-Nedoma, Simplex s=6 .......................................... 93 2-7: Manas-Nedoma, Simplex s=6 .......................................... 94 2-8: Manas-Nedoma, Simplex s=7 .......................................... 94 2-9: Manas-Nedoma, Simplex s=8 .......................................... 95 2-10: Manas-Nedoma, Simplex s=9 ........................................ 95 2-11: Manas-Nedoma, Simplex s=10 ...................................... 96 2-12: Manas-Nedoma, Simplex s=11 ...................................... 96 2-13: Manas-Nedoma, Simplex s=12 ...................................... 97 2-14: Simplex p .................................... 99 2-15: Simplex p+1 .............................. 100 2-16: (s=0) Simplex ................... 102 2-17: s Simplex ................... 102 2-18: Simplex ............... 112 2-19: Simplex............................................................................................................ 113 2-20: Simplex........................................................ 118 2-21: ............................................. 121 3-1: Simplex 1.1 .......................... 126 3-2: Simplex s = 0 ............................................................... 127 3-3: s ........ 129 3-4: Simplex ........................... 132 3-5: ........................................... 143 4-1: ...................................................................... 169 4-2: MUSA ....................................................... 174 5-1: UTA ........................................................................................................... 194 5-2: MUSA .............................................................................................................. 199 6-1: ........................................... 230 8-1: ......................................... 256

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8-2: .......................... 257 8-3: .......................... 258 II-1: r ............................................. 324 II-2: r ...................................... 325 V-1: ........................................ 333 V-2: , & ............................................................................................................. 349 V-3: WVi ............................................................... 364

, 1-1: 2 ...................................................................... 46 1-2: 3- simplex.............................................