The Scheduling Zoo, preemptive problems on parallel machines
Lax434175.ZooPreemptive · concepts/Lax434175/ZooPreemptive.lean · lax-434175
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Sign in with ORCIDNatural Language Statement
Theorem
The 76 preemptive problems on parallel machines of The Scheduling Zoo, each as a specification, and the 65 relations of the zoo among them that are derived here.
A relation of the zoo states that one problem generalizes another. The 60 relations of the first list hold field by field, so that the more special problem is a special case of the more general one. The 0 relations of the second list need a threshold step, so that the decision version of the more special problem reduces to that of the more general one. The 5 relations of the third list replace completion time by flow time and likewise give a reduction of decision versions. Each pair lists the more general problem first.
Theorem. Every pair of the first list is a special case, and every pair of the other lists is a reduction of decision versions.
Concept map
Evidence
Lean source view on GitHub
| 1 | import Lax434175.OperationsFamily |
| 2 | |
| 3 | /-! |
| 4 | --- |
| 5 | title: The Scheduling Zoo, preemptive problems on parallel machines |
| 6 | type: theorem |
| 7 | --- |
| 8 | The 76 preemptive problems on parallel machines of The Scheduling Zoo, each as a |
| 9 | specification, and the 65 relations of the zoo among them that are |
| 10 | derived here. |
| 11 | |
| 12 | A relation of the zoo states that one problem generalizes another. The |
| 13 | 60 relations of the first list hold field by field, so that the more |
| 14 | special problem is a special case of the more general one. The |
| 15 | 0 relations of the second list need a threshold step, so that the |
| 16 | decision version of the more special problem reduces to that of the more |
| 17 | general one. The 5 relations of the third list replace completion |
| 18 | time by flow time and likewise give a reduction of decision versions. Each pair lists the more general problem first. |
| 19 | |
| 20 | **Theorem.** Every pair of the first list is a special case, and every pair |
| 21 | of the other lists is a reduction of decision versions. |
| 22 | -/ |
| 23 | |
| 24 | namespace Lax434175.ZooPreemptive |
| 25 | open Lax434175 Lax434175.Problems Lax434175.Assembly |
| 26 | |
| 27 | /-- The family of the problems listed here. -/ |
| 28 | abbrev F := OperationsFamily.family |
| 29 | |
| 30 | /-- `R|rj;pmtn|ΣwjCj` -/ |
| 31 | def p0 : Spec F := |
| 32 | OperationsFamily.spec (interruption := .pmtn) (environment := .unrelated) |
| 33 | (release := .releaseDates) (objective := .sumWC) |
| 34 | |
| 35 | /-- `1|prec;rj;pmtn|Lmax` -/ |
| 36 | def p1 : Spec F := |
| 37 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 38 | (precedence := ⟨.prec, .zero⟩) (machineCount := .atMost 1) (objective := .lmax) |
| 39 | |
| 40 | /-- `P|pj=p;pmtn|ΣwjUj` -/ |
| 41 | def p2 : Spec F := |
| 42 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) (objective := .sumWU) |
| 43 | |
| 44 | /-- `P|pj=1;pmtn;rj|ΣwjTj` -/ |
| 45 | def p3 : Spec F := |
| 46 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .unit) |
| 47 | (release := .releaseDates) (objective := .sumWT) |
| 48 | |
| 49 | /-- `1|rj;pmtn|ΣCj` -/ |
| 50 | def p4 : Spec F := |
| 51 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 52 | (machineCount := .atMost 1) (objective := .sumC) |
| 53 | |
| 54 | /-- `1|pmtn;pj=p;rj|ΣwjUj` -/ |
| 55 | def p5 : Spec F := |
| 56 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) |
| 57 | (release := .releaseDates) (machineCount := .atMost 1) (objective := .sumWU) |
| 58 | |
| 59 | /-- `1|prec;rj;pj=p;pmtn|ΣCj` -/ |
| 60 | def p6 : Spec F := |
| 61 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) |
| 62 | (release := .releaseDates) (precedence := ⟨.prec, .zero⟩) (machineCount := .atMost 1) |
| 63 | (objective := .sumC) |
| 64 | |
| 65 | /-- `P|pj=p;pmtn|ΣCj` -/ |
| 66 | def p7 : Spec F := |
| 67 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) (objective := .sumC) |
| 68 | |
| 69 | /-- `Q|pj=p;pmtn|ΣUj` -/ |
| 70 | def p8 : Spec F := |
| 71 | OperationsFamily.spec (interruption := .pmtn) (environment := .uniform) |
| 72 | (processingTimes := .equal) (objective := .sumU) |
| 73 | |
| 74 | /-- `P2|pj=1;chains;pmtn|ΣUj` -/ |
| 75 | def p9 : Spec F := |
| 76 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .unit) |
| 77 | (precedence := ⟨.chains, .zero⟩) (machineCount := .atMost 2) (objective := .sumU) |
| 78 | |
| 79 | /-- `P|fixj;rj;pmtn|Lmax` -/ |
| 80 | def p10 : Spec F := |
| 81 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 82 | (machineSets := .par .fix) (objective := .lmax) |
| 83 | |
| 84 | /-- `P2|pmtn|ΣwjCj` -/ |
| 85 | def p11 : Spec F := |
| 86 | OperationsFamily.spec (interruption := .pmtn) (machineCount := .atMost 2) (objective := .sumWC) |
| 87 | |
| 88 | /-- `P|pmtn;rj;sizej|Lmax` -/ |
| 89 | def p12 : Spec F := |
| 90 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 91 | (machineSets := .par .size) (objective := .lmax) |
| 92 | |
| 93 | /-- `P|pj=1;pmtn;rj|ΣwjUj` -/ |
| 94 | def p13 : Spec F := |
| 95 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .unit) |
| 96 | (release := .releaseDates) (objective := .sumWU) |
| 97 | |
| 98 | /-- `P2|pj=1;pmtn;rj|ΣwjTj` -/ |
| 99 | def p14 : Spec F := |
| 100 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .unit) |
| 101 | (release := .releaseDates) (machineCount := .atMost 2) (objective := .sumWT) |
| 102 | |
| 103 | /-- `P|pj=1;outtree;rj;pmtn|ΣCj` -/ |
| 104 | def p15 : Spec F := |
| 105 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .unit) |
| 106 | (release := .releaseDates) (precedence := ⟨.outtree, .zero⟩) (objective := .sumC) |
| 107 | |
| 108 | /-- `P|pj=p;outtree;pmtn|ΣCj` -/ |
| 109 | def p16 : Spec F := |
| 110 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) |
| 111 | (precedence := ⟨.outtree, .zero⟩) (objective := .sumC) |
| 112 | |
| 113 | /-- `P|rj;pmtn;pj=p|ΣCj` -/ |
| 114 | def p17 : Spec F := |
| 115 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) |
| 116 | (release := .releaseDates) (objective := .sumC) |
| 117 | |
| 118 | /-- `P|rj;pmtn|ΣCj` -/ |
| 119 | def p18 : Spec F := |
| 120 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) (objective := .sumC) |
| 121 | |
| 122 | /-- `P2|pmtn;outtree;rj;pj=1|ΣCj` -/ |
| 123 | def p19 : Spec F := |
| 124 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .unit) |
| 125 | (release := .releaseDates) (precedence := ⟨.outtree, .zero⟩) (machineCount := .atMost 2) |
| 126 | (objective := .sumC) |
| 127 | |
| 128 | /-- `P2|fixj;pmtn|ΣCj` -/ |
| 129 | def p20 : Spec F := |
| 130 | OperationsFamily.spec (interruption := .pmtn) (machineSets := .par .fix) |
| 131 | (machineCount := .atMost 2) (objective := .sumC) |
| 132 | |
| 133 | /-- `P2|pj=1;pmtn;prec|ΣCj` -/ |
| 134 | def p21 : Spec F := |
| 135 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .unit) |
| 136 | (precedence := ⟨.prec, .zero⟩) (machineCount := .atMost 2) (objective := .sumC) |
| 137 | |
| 138 | /-- `P|pmtn;pj=1;sizej|Cmax` -/ |
| 139 | def p22 : Spec F := |
| 140 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .unit) |
| 141 | (machineSets := .par .size) (objective := .makespan) |
| 142 | |
| 143 | /-- `P|pmtn;sizej|ΣCj` -/ |
| 144 | def p23 : Spec F := |
| 145 | OperationsFamily.spec (interruption := .pmtn) (machineSets := .par .size) (objective := .sumC) |
| 146 | |
| 147 | /-- `R|pmtn;rj|ΣUj` -/ |
| 148 | def p24 : Spec F := |
| 149 | OperationsFamily.spec (interruption := .pmtn) (environment := .unrelated) |
| 150 | (release := .releaseDates) (objective := .sumU) |
| 151 | |
| 152 | /-- `P2|pmtn;rj|ΣUj` -/ |
| 153 | def p25 : Spec F := |
| 154 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 155 | (machineCount := .atMost 2) (objective := .sumU) |
| 156 | |
| 157 | /-- `P2|pmtn;rj|ΣCj` -/ |
| 158 | def p26 : Spec F := |
| 159 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 160 | (machineCount := .atMost 2) (objective := .sumC) |
| 161 | |
| 162 | /-- `P2|pj=p;chains;pmtn|ΣCj` -/ |
| 163 | def p27 : Spec F := |
| 164 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) |
| 165 | (precedence := ⟨.chains, .zero⟩) (machineCount := .atMost 2) (objective := .sumC) |
| 166 | |
| 167 | /-- `P2|chains;pj=1;pmtn|ΣwjCj` -/ |
| 168 | def p28 : Spec F := |
| 169 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .unit) |
| 170 | (precedence := ⟨.chains, .zero⟩) (machineCount := .atMost 2) (objective := .sumWC) |
| 171 | |
| 172 | /-- `P2|chains;pmtn|ΣCj` -/ |
| 173 | def p29 : Spec F := |
| 174 | OperationsFamily.spec (interruption := .pmtn) (precedence := ⟨.chains, .zero⟩) |
| 175 | (machineCount := .atMost 2) (objective := .sumC) |
| 176 | |
| 177 | /-- `P|tree;pmtn|Cmax` -/ |
| 178 | def p30 : Spec F := |
| 179 | OperationsFamily.spec (interruption := .pmtn) (precedence := ⟨.tree, .zero⟩) |
| 180 | (objective := .makespan) |
| 181 | |
| 182 | /-- `P2|pj=p;pmtn;rj|ΣCj` -/ |
| 183 | def p31 : Spec F := |
| 184 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) |
| 185 | (release := .releaseDates) (machineCount := .atMost 2) (objective := .sumC) |
| 186 | |
| 187 | /-- `Q|chains;pmtn|Cmax` -/ |
| 188 | def p32 : Spec F := |
| 189 | OperationsFamily.spec (interruption := .pmtn) (environment := .uniform) |
| 190 | (precedence := ⟨.chains, .zero⟩) (objective := .makespan) |
| 191 | |
| 192 | /-- `P|fixj;pmtn|Cmax` -/ |
| 193 | def p33 : Spec F := |
| 194 | OperationsFamily.spec (interruption := .pmtn) (machineSets := .par .fix) |
| 195 | (objective := .makespan) |
| 196 | |
| 197 | /-- `Q|pj=p;rj;pmtn|ΣCj` -/ |
| 198 | def p34 : Spec F := |
| 199 | OperationsFamily.spec (interruption := .pmtn) (environment := .uniform) |
| 200 | (processingTimes := .equal) (release := .releaseDates) (objective := .sumC) |
| 201 | |
| 202 | /-- `1|chains;rj;pmtn|ΣCj` -/ |
| 203 | def p35 : Spec F := |
| 204 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 205 | (precedence := ⟨.chains, .zero⟩) (machineCount := .atMost 1) (objective := .sumC) |
| 206 | |
| 207 | /-- `P|intree;pmtn;rj|Cmax` -/ |
| 208 | def p36 : Spec F := |
| 209 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 210 | (precedence := ⟨.intree, .zero⟩) (objective := .makespan) |
| 211 | |
| 212 | /-- `R2|chains;pmtn|Cmax` -/ |
| 213 | def p37 : Spec F := |
| 214 | OperationsFamily.spec (interruption := .pmtn) (environment := .unrelated) |
| 215 | (precedence := ⟨.chains, .zero⟩) (machineCount := .atMost 2) (objective := .makespan) |
| 216 | |
| 217 | /-- `P|outtree;pmtn|Lmax` -/ |
| 218 | def p38 : Spec F := |
| 219 | OperationsFamily.spec (interruption := .pmtn) (precedence := ⟨.outtree, .zero⟩) |
| 220 | (objective := .lmax) |
| 221 | |
| 222 | /-- `P|pmtn|ΣwjCj` -/ |
| 223 | def p39 : Spec F := |
| 224 | OperationsFamily.spec (interruption := .pmtn) (objective := .sumWC) |
| 225 | |
| 226 | /-- `Q|pmtn|ΣUj` -/ |
| 227 | def p40 : Spec F := |
| 228 | OperationsFamily.spec (interruption := .pmtn) (environment := .uniform) (objective := .sumU) |
| 229 | |
| 230 | /-- `Q|pmtn|ΣwjUj` -/ |
| 231 | def p41 : Spec F := |
| 232 | OperationsFamily.spec (interruption := .pmtn) (environment := .uniform) (objective := .sumWU) |
| 233 | |
| 234 | /-- `P|outtree;pmtn;rj|Cmax` -/ |
| 235 | def p42 : Spec F := |
| 236 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 237 | (precedence := ⟨.outtree, .zero⟩) (objective := .makespan) |
| 238 | |
| 239 | /-- `P|intree;pmtn|Lmax` -/ |
| 240 | def p43 : Spec F := |
| 241 | OperationsFamily.spec (interruption := .pmtn) (precedence := ⟨.intree, .zero⟩) |
| 242 | (objective := .lmax) |
| 243 | |
| 244 | /-- `Q2|prec;pmtn;rj|Lmax` -/ |
| 245 | def p44 : Spec F := |
| 246 | OperationsFamily.spec (interruption := .pmtn) (environment := .uniform) |
| 247 | (release := .releaseDates) (precedence := ⟨.prec, .zero⟩) (machineCount := .atMost 2) |
| 248 | (objective := .lmax) |
| 249 | |
| 250 | /-- `P|pmtn|ΣUj` -/ |
| 251 | def p45 : Spec F := |
| 252 | OperationsFamily.spec (interruption := .pmtn) (objective := .sumU) |
| 253 | |
| 254 | /-- `1|rj;pmtn|ΣUj` -/ |
| 255 | def p46 : Spec F := |
| 256 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 257 | (machineCount := .atMost 1) (objective := .sumU) |
| 258 | |
| 259 | /-- `1|rj;pmtn|ΣwjUj` -/ |
| 260 | def p47 : Spec F := |
| 261 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 262 | (machineCount := .atMost 1) (objective := .sumWU) |
| 263 | |
| 264 | /-- `R|pmtn;rj|Lmax` -/ |
| 265 | def p48 : Spec F := |
| 266 | OperationsFamily.spec (interruption := .pmtn) (environment := .unrelated) |
| 267 | (release := .releaseDates) (objective := .lmax) |
| 268 | |
| 269 | /-- `1|rj;pmtn|ΣwjCj` -/ |
| 270 | def p49 : Spec F := |
| 271 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 272 | (machineCount := .atMost 1) (objective := .sumWC) |
| 273 | |
| 274 | /-- `Q|pmtn|ΣCj` -/ |
| 275 | def p50 : Spec F := |
| 276 | OperationsFamily.spec (interruption := .pmtn) (environment := .uniform) (objective := .sumC) |
| 277 | |
| 278 | /-- `P2|pmtn;rj|ΣwjCj` -/ |
| 279 | def p51 : Spec F := |
| 280 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 281 | (machineCount := .atMost 2) (objective := .sumWC) |
| 282 | |
| 283 | /-- `P|pj=p;pmtn;rj|ΣwjCj` -/ |
| 284 | def p52 : Spec F := |
| 285 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) |
| 286 | (release := .releaseDates) (objective := .sumWC) |
| 287 | |
| 288 | /-- `P2|pmtn;outtree;pj=p;rj|ΣCj` -/ |
| 289 | def p53 : Spec F := |
| 290 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) |
| 291 | (release := .releaseDates) (precedence := ⟨.outtree, .zero⟩) (machineCount := .atMost 2) |
| 292 | (objective := .sumC) |
| 293 | |
| 294 | /-- `P|pj=p;pmtn|ΣwjCj` -/ |
| 295 | def p54 : Spec F := |
| 296 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) (objective := .sumWC) |
| 297 | |
| 298 | /-- `P2|fixj;pmtn|ΣwjCj` -/ |
| 299 | def p55 : Spec F := |
| 300 | OperationsFamily.spec (interruption := .pmtn) (machineSets := .par .fix) |
| 301 | (machineCount := .atMost 2) (objective := .sumWC) |
| 302 | |
| 303 | /-- `R|pmtn|ΣCj` -/ |
| 304 | def p56 : Spec F := |
| 305 | OperationsFamily.spec (interruption := .pmtn) (environment := .unrelated) (objective := .sumC) |
| 306 | |
| 307 | /-- `R|pmtn|ΣUj` -/ |
| 308 | def p57 : Spec F := |
| 309 | OperationsFamily.spec (interruption := .pmtn) (environment := .unrelated) (objective := .sumU) |
| 310 | |
| 311 | /-- `1|pmtn;rj;pj=p|ΣTj` -/ |
| 312 | def p58 : Spec F := |
| 313 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) |
| 314 | (release := .releaseDates) (machineCount := .atMost 1) (objective := .sumT) |
| 315 | |
| 316 | /-- `P|pj=1;prec;pmtn|Cmax` -/ |
| 317 | def p59 : Spec F := |
| 318 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .unit) |
| 319 | (precedence := ⟨.prec, .zero⟩) (objective := .makespan) |
| 320 | |
| 321 | /-- `P2|pmtn|ΣwjUj` -/ |
| 322 | def p60 : Spec F := |
| 323 | OperationsFamily.spec (interruption := .pmtn) (machineCount := .atMost 2) (objective := .sumWU) |
| 324 | |
| 325 | /-- `1|online-rj;pmtn|ΣwjCj` -/ |
| 326 | def p61 : Spec F := |
| 327 | OperationsFamily.spec (interruption := .pmtn) (release := .online) (machineCount := .atMost 1) |
| 328 | (objective := .sumWC) |
| 329 | |
| 330 | /-- `1|online-rj;pmtn|ΣwjFj` -/ |
| 331 | def p62 : Spec F := |
| 332 | OperationsFamily.spec (interruption := .pmtn) (release := .online) (machineCount := .atMost 1) |
| 333 | (objective := .sumWF) |
| 334 | |
| 335 | /-- `P|pmtn;interval order|Cmax` -/ |
| 336 | def p63 : Spec F := |
| 337 | OperationsFamily.spec (interruption := .pmtn) (precedence := ⟨.intervalOrder, .zero⟩) |
| 338 | (objective := .makespan) |
| 339 | |
| 340 | /-- `P|pmtn;Am-order|Cmax` -/ |
| 341 | def p64 : Spec F := |
| 342 | OperationsFamily.spec (interruption := .pmtn) (precedence := ⟨.aOrder, .zero⟩) |
| 343 | (objective := .makespan) |
| 344 | |
| 345 | /-- `1|rj;prec;pmtn|ΣwjCj` -/ |
| 346 | def p65 : Spec F := |
| 347 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 348 | (precedence := ⟨.prec, .zero⟩) (machineCount := .atMost 1) (objective := .sumWC) |
| 349 | |
| 350 | /-- `P|rj;pmtn|ΣwjCj` -/ |
| 351 | def p66 : Spec F := |
| 352 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) (objective := .sumWC) |
| 353 | |
| 354 | /-- `P|rj;prec;pmtn|ΣwjCj` -/ |
| 355 | def p67 : Spec F := |
| 356 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 357 | (precedence := ⟨.prec, .zero⟩) (objective := .sumWC) |
| 358 | |
| 359 | /-- `1|rj;prec;pmtn|ΣFj` -/ |
| 360 | def p68 : Spec F := |
| 361 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 362 | (precedence := ⟨.prec, .zero⟩) (machineCount := .atMost 1) (objective := .sumF) |
| 363 | |
| 364 | /-- `1|rj;prec;pmtn|ΣwjFj` -/ |
| 365 | def p69 : Spec F := |
| 366 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 367 | (precedence := ⟨.prec, .zero⟩) (machineCount := .atMost 1) (objective := .sumWF) |
| 368 | |
| 369 | /-- `1|rj;pmtn|ΣwjFj` -/ |
| 370 | def p70 : Spec F := |
| 371 | OperationsFamily.spec (interruption := .pmtn) (release := .releaseDates) |
| 372 | (machineCount := .atMost 1) (objective := .sumWF) |
| 373 | |
| 374 | /-- `R|online-rj;pmtn|ΣwjFj` -/ |
| 375 | def p71 : Spec F := |
| 376 | OperationsFamily.spec (interruption := .pmtn) (environment := .unrelated) (release := .online) |
| 377 | (objective := .sumWF) |
| 378 | |
| 379 | /-- `1|online-rj;pmtn|ΣUj` -/ |
| 380 | def p72 : Spec F := |
| 381 | OperationsFamily.spec (interruption := .pmtn) (release := .online) (machineCount := .atMost 1) |
| 382 | (objective := .sumU) |
| 383 | |
| 384 | /-- `P|online-rj;pmtn|ΣUj` -/ |
| 385 | def p73 : Spec F := |
| 386 | OperationsFamily.spec (interruption := .pmtn) (release := .online) (objective := .sumU) |
| 387 | |
| 388 | /-- `P|pmtn|ΣTj` -/ |
| 389 | def p74 : Spec F := |
| 390 | OperationsFamily.spec (interruption := .pmtn) (objective := .sumT) |
| 391 | |
| 392 | /-- `P2|pmtn;pj=p|ΣwjUj` -/ |
| 393 | def p75 : Spec F := |
| 394 | OperationsFamily.spec (interruption := .pmtn) (processingTimes := .equal) |
| 395 | (machineCount := .atMost 2) (objective := .sumWU) |
| 396 | |
| 397 | /-- The problems with their names in three-field notation. -/ |
| 398 | def problems : List (String × Spec F) := [ |
| 399 | ("R|rj;pmtn|ΣwjCj", p0), |
| 400 | ("1|prec;rj;pmtn|Lmax", p1), |
| 401 | ("P|pj=p;pmtn|ΣwjUj", p2), |
| 402 | ("P|pj=1;pmtn;rj|ΣwjTj", p3), |
| 403 | ("1|rj;pmtn|ΣCj", p4), |
| 404 | ("1|pmtn;pj=p;rj|ΣwjUj", p5), |
| 405 | ("1|prec;rj;pj=p;pmtn|ΣCj", p6), |
| 406 | ("P|pj=p;pmtn|ΣCj", p7), |
| 407 | ("Q|pj=p;pmtn|ΣUj", p8), |
| 408 | ("P2|pj=1;chains;pmtn|ΣUj", p9), |
| 409 | ("P|fixj;rj;pmtn|Lmax", p10), |
| 410 | ("P2|pmtn|ΣwjCj", p11), |
| 411 | ("P|pmtn;rj;sizej|Lmax", p12), |
| 412 | ("P|pj=1;pmtn;rj|ΣwjUj", p13), |
| 413 | ("P2|pj=1;pmtn;rj|ΣwjTj", p14), |
| 414 | ("P|pj=1;outtree;rj;pmtn|ΣCj", p15), |
| 415 | ("P|pj=p;outtree;pmtn|ΣCj", p16), |
| 416 | ("P|rj;pmtn;pj=p|ΣCj", p17), |
| 417 | ("P|rj;pmtn|ΣCj", p18), |
| 418 | ("P2|pmtn;outtree;rj;pj=1|ΣCj", p19), |
| 419 | ("P2|fixj;pmtn|ΣCj", p20), |
| 420 | ("P2|pj=1;pmtn;prec|ΣCj", p21), |
| 421 | ("P|pmtn;pj=1;sizej|Cmax", p22), |
| 422 | ("P|pmtn;sizej|ΣCj", p23), |
| 423 | ("R|pmtn;rj|ΣUj", p24), |
| 424 | ("P2|pmtn;rj|ΣUj", p25), |
| 425 | ("P2|pmtn;rj|ΣCj", p26), |
| 426 | ("P2|pj=p;chains;pmtn|ΣCj", p27), |
| 427 | ("P2|chains;pj=1;pmtn|ΣwjCj", p28), |
| 428 | ("P2|chains;pmtn|ΣCj", p29), |
| 429 | ("P|tree;pmtn|Cmax", p30), |
| 430 | ("P2|pj=p;pmtn;rj|ΣCj", p31), |
| 431 | ("Q|chains;pmtn|Cmax", p32), |
| 432 | ("P|fixj;pmtn|Cmax", p33), |
| 433 | ("Q|pj=p;rj;pmtn|ΣCj", p34), |
| 434 | ("1|chains;rj;pmtn|ΣCj", p35), |
| 435 | ("P|intree;pmtn;rj|Cmax", p36), |
| 436 | ("R2|chains;pmtn|Cmax", p37), |
| 437 | ("P|outtree;pmtn|Lmax", p38), |
| 438 | ("P|pmtn|ΣwjCj", p39), |
| 439 | ("Q|pmtn|ΣUj", p40), |
| 440 | ("Q|pmtn|ΣwjUj", p41), |
| 441 | ("P|outtree;pmtn;rj|Cmax", p42), |
| 442 | ("P|intree;pmtn|Lmax", p43), |
| 443 | ("Q2|prec;pmtn;rj|Lmax", p44), |
| 444 | ("P|pmtn|ΣUj", p45), |
| 445 | ("1|rj;pmtn|ΣUj", p46), |
| 446 | ("1|rj;pmtn|ΣwjUj", p47), |
| 447 | ("R|pmtn;rj|Lmax", p48), |
| 448 | ("1|rj;pmtn|ΣwjCj", p49), |
| 449 | ("Q|pmtn|ΣCj", p50), |
| 450 | ("P2|pmtn;rj|ΣwjCj", p51), |
| 451 | ("P|pj=p;pmtn;rj|ΣwjCj", p52), |
| 452 | ("P2|pmtn;outtree;pj=p;rj|ΣCj", p53), |
| 453 | ("P|pj=p;pmtn|ΣwjCj", p54), |
| 454 | ("P2|fixj;pmtn|ΣwjCj", p55), |
| 455 | ("R|pmtn|ΣCj", p56), |
| 456 | ("R|pmtn|ΣUj", p57), |
| 457 | ("1|pmtn;rj;pj=p|ΣTj", p58), |
| 458 | ("P|pj=1;prec;pmtn|Cmax", p59), |
| 459 | ("P2|pmtn|ΣwjUj", p60), |
| 460 | ("1|online-rj;pmtn|ΣwjCj", p61), |
| 461 | ("1|online-rj;pmtn|ΣwjFj", p62), |
| 462 | ("P|pmtn;interval order|Cmax", p63), |
| 463 | ("P|pmtn;Am-order|Cmax", p64), |
| 464 | ("1|rj;prec;pmtn|ΣwjCj", p65), |
| 465 | ("P|rj;pmtn|ΣwjCj", p66), |
| 466 | ("P|rj;prec;pmtn|ΣwjCj", p67), |
| 467 | ("1|rj;prec;pmtn|ΣFj", p68), |
| 468 | ("1|rj;prec;pmtn|ΣwjFj", p69), |
| 469 | ("1|rj;pmtn|ΣwjFj", p70), |
| 470 | ("R|online-rj;pmtn|ΣwjFj", p71), |
| 471 | ("1|online-rj;pmtn|ΣUj", p72), |
| 472 | ("P|online-rj;pmtn|ΣUj", p73), |
| 473 | ("P|pmtn|ΣTj", p74), |
| 474 | ("P2|pmtn;pj=p|ΣwjUj", p75)] |
| 475 | |
| 476 | /-- The relations that hold field by field: general problem, special problem. -/ |
| 477 | def specialCases : List (Spec F × Spec F) := [ |
| 478 | (p41, p2), (p26, p4), (p35, p4), (p49, p4), (p47, p5), (p65, p6), (p16, p7), (p17, p7), |
| 479 | (p23, p7), (p50, p7), (p54, p7), (p74, p7), (p40, p8), (p39, p11), (p51, p11), (p3, p14), |
| 480 | (p67, p15), (p67, p16), (p18, p17), (p34, p17), (p52, p17), (p66, p18), (p15, p19), (p53, p19), |
| 481 | (p55, p20), (p12, p22), (p18, p26), (p51, p26), (p29, p27), (p53, p27), (p17, p31), (p26, p31), |
| 482 | (p53, p31), (p10, p33), (p0, p34), (p65, p35), (p66, p39), (p41, p40), (p57, p40), (p40, p45), |
| 483 | (p25, p46), (p47, p46), (p51, p49), (p65, p49), (p56, p50), (p66, p51), (p66, p52), (p39, p54), |
| 484 | (p52, p54), (p0, p56), (p24, p57), (p64, p63), (p67, p65), (p0, p66), (p67, p66), (p69, p68), |
| 485 | (p69, p70), (p73, p72), (p2, p75), (p60, p75)] |
| 486 | |
| 487 | /-- The relations that need a threshold step: general problem, special problem. -/ |
| 488 | def thresholdReductions : List (Spec F × Spec F) := [ |
| 489 | ] |
| 490 | |
| 491 | axiom specialCases_hold : ∀ e ∈ specialCases, |
| 492 | SpecialCase (problem F e.2) (problem F e.1) |
| 493 | |
| 494 | axiom thresholdReductions_hold : ∀ e ∈ thresholdReductions, |
| 495 | Reducible (problem F e.2) (problem F e.1) |
| 496 | |
| 497 | /-- The relations through flow time: general problem, special problem. -/ |
| 498 | def flowReductions : List (Spec F × Spec F) := [ |
| 499 | (p68, p6), (p68, p35), (p70, p49), (p62, p61), (p69, p65)] |
| 500 | |
| 501 | axiom flowReductions_hold : ∀ e ∈ flowReductions, |
| 502 | Reducible (problem F e.2) (problem F e.1) |
| 503 | |
| 504 | end Lax434175.ZooPreemptive |
| 505 |
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