Adapted from:
Daskin, M. S. 1995. Network and Discrete Location: Models, Algorithms, and Applications. Hoboken, NJ, USA: John Wiley & Sons, Inc.
0. Imports and Data Creation
In [4]:
# Imports
import numpy as np
import gurobipy as gbp
import datetime as dt
# Constants
Aij = np.random.randint(5, 50, 250000)
Aij = Aij.reshape(500,500)
AijSum = np.sum(Aij)
Cj = np.random.randint(10, 20, 500)
CjSum = np.sum(Cj)
Bi = np.random.randint(10, 20, 500)
BiSum = np.sum(Bi)
# Matrix Shape
rows = range(len(Aij))
cols = range(len(Aij[0]))
1. Primal
In [5]:
# Instantiate Model
mPrimal_Standard_GUROBI = gbp.Model(' -- Standard Primal Linear Programming Problem -- ')
# Set Focus to Optimality
gbp.setParam('MIPFocus', 2)
# Decision Variables
desc_var = []
for dest in cols:
desc_var.append([])
desc_var[dest].append(mPrimal_Standard_GUROBI.addVar(vtype=gbp.GRB.CONTINUOUS,
name='y'+str(dest+1)))
# Surplus Variables
surp_var = []
for orig in rows:
surp_var.append([])
surp_var[orig].append(mPrimal_Standard_GUROBI.addVar(vtype=gbp.GRB.CONTINUOUS,
name='s'+str(orig+1)))
# Update Model
mPrimal_Standard_GUROBI.update()
#Objective Function
mPrimal_Standard_GUROBI.setObjective(gbp.quicksum(Cj[dest]*desc_var[dest][0]
for dest in cols),
gbp.GRB.MINIMIZE)
# Constraints
for orig in rows:
mPrimal_Standard_GUROBI.addConstr(gbp.quicksum(Aij[orig][dest]*desc_var[dest][0]
for dest in cols)
- surp_var[orig][0]
- Bi[orig] == 0)
# Optimize
mPrimal_Standard_GUROBI.optimize()
# Write LP file
mPrimal_Standard_GUROBI.write('LP.lp')
print '\n*************************************************************************'
print ' | Decision Variables'
for v in mPrimal_Standard_GUROBI.getVars():
print ' | ', v.VarName, '=', v.x
print '*************************************************************************'
val = mPrimal_Standard_GUROBI.objVal
print ' | Objective Value ------------------ ', val
print ' | Aij Sum -------------------------- ', AijSum
print ' | Cj Sum --------------------------- ', CjSum
print ' | Bi Sum --------------------------- ', BiSum
print ' | Matrix Dimensions ---------------- ', Aij.shape
print ' | Date/Time ------------------------ ', dt.datetime.now()
print '*************************************************************************'
print '-- Gurobi Standard Primal Linear Programming Problem --'
print '\nJames Gaboardi, 2015'
Parameter MIPFocus unchanged
Value: 2 Min: 0 Max: 3 Default: 0
Optimize a model with 500 rows, 1000 columns and 250500 nonzeros
Coefficient statistics:
Matrix range [1e+00, 5e+01]
Objective range [1e+01, 2e+01]
Bounds range [0e+00, 0e+00]
RHS range [1e+01, 2e+01]
Concurrent LP optimizer: dual simplex and barrier
Showing barrier log only...
Presolve removed 0 rows and 500 columns
Presolve time: 0.15s
Presolved: 500 rows, 500 columns, 250000 nonzeros
Ordering time: 0.00s
Barrier statistics:
AA' NZ : 1.248e+05
Factor NZ : 1.252e+05 (roughly 1 MByte of memory)
Factor Ops : 4.179e+07 (less than 1 second per iteration)
Threads : 1
Barrier performed 0 iterations in 0.23 seconds
Barrier solve interrupted - model solved by another algorithm
Solved with dual simplex
Solved in 137 iterations and 0.25 seconds
Optimal objective 7.066624192e+00
*************************************************************************
| Decision Variables
| y1 = 0.0
| y2 = 0.0
| y3 = 0.0
| y4 = 0.0
| y5 = 0.0
| y6 = 0.0
| y7 = 0.0
| y8 = 0.0297450043044
| y9 = 0.0
| y10 = 0.0
| y11 = 0.0
| y12 = 0.0
| y13 = 0.0
| y14 = 0.0
| y15 = 0.0
| y16 = 0.0
| y17 = 0.0
| y18 = 0.0
| y19 = 0.0
| y20 = 0.0
| y21 = 0.0
| y22 = 0.0
| y23 = 0.0
| y24 = 0.0
| y25 = 0.0
| y26 = 0.0
| y27 = 0.0
| y28 = 0.0
| y29 = 0.0
| y30 = 0.0
| y31 = 0.0
| y32 = 0.0
| y33 = 0.0
| y34 = 0.0
| y35 = 0.0
| y36 = 0.00309800638742
| y37 = 0.0
| y38 = 0.0
| y39 = 0.0
| y40 = 0.0
| y41 = 0.0
| y42 = 0.0323769910168
| y43 = 0.0
| y44 = 0.0
| y45 = 0.0
| y46 = 0.0
| y47 = 0.00363618800667
| y48 = 0.0
| y49 = 0.0
| y50 = 0.0
| y51 = 0.00733088026363
| y52 = 0.0
| y53 = 0.0
| y54 = 0.0
| y55 = 0.0
| y56 = 0.0
| y57 = 0.0
| y58 = 0.0413457660598
| y59 = 0.0
| y60 = 0.0
| y61 = 0.0
| y62 = 0.0
| y63 = 0.0
| y64 = 0.0
| y65 = 0.0
| y66 = 0.0
| y67 = 0.0
| y68 = 0.0
| y69 = 0.0
| y70 = 0.0
| y71 = 0.0
| y72 = 0.0
| y73 = 0.0
| y74 = 0.0
| y75 = 0.0
| y76 = 0.0012775913953
| y77 = 0.0
| y78 = 0.0193342731175
| y79 = 0.0
| y80 = 0.0
| y81 = 0.0
| y82 = 0.0
| y83 = 0.0312992343975
| y84 = 0.0
| y85 = 0.0
| y86 = 0.0
| y87 = 0.0
| y88 = 0.0
| y89 = 0.0
| y90 = 0.0
| y91 = 0.0
| y92 = 0.0
| y93 = 0.0
| y94 = 0.0
| y95 = 0.0
| y96 = 0.0
| y97 = 0.0
| y98 = 0.0
| y99 = 0.0
| y100 = 0.0
| y101 = 0.0
| y102 = 0.0
| y103 = 0.0
| y104 = 0.0
| y105 = 0.0
| y106 = 0.0
| y107 = 0.0
| y108 = 0.0
| y109 = 0.0
| y110 = 0.0
| y111 = 0.0
| y112 = 0.0
| y113 = 0.0
| y114 = 0.0
| y115 = 0.0
| y116 = 0.0081321789105
| y117 = 0.0
| y118 = 0.0
| y119 = 0.0
| y120 = 0.0
| y121 = 0.0
| y122 = 0.0
| y123 = 0.0
| y124 = 0.0
| y125 = 0.0
| y126 = 0.0
| y127 = 0.0
| y128 = 0.0
| y129 = 0.0
| y130 = 0.0
| y131 = 0.0
| y132 = 0.0
| y133 = 0.0
| y134 = 0.0
| y135 = 0.0
| y136 = 0.0
| y137 = 0.0
| y138 = 0.0
| y139 = 0.0
| y140 = 0.0
| y141 = 0.0
| y142 = 0.0
| y143 = 0.0
| y144 = 0.0
| y145 = 0.0
| y146 = 0.0
| y147 = 0.010541772305
| y148 = 0.0
| y149 = 0.0
| y150 = 0.0
| y151 = 0.0
| y152 = 0.0
| y153 = 0.0
| y154 = 0.0
| y155 = 0.0
| y156 = 0.0
| y157 = 0.0
| y158 = 0.0
| y159 = 0.0
| y160 = 0.0
| y161 = 0.0
| y162 = 0.0
| y163 = 0.0
| y164 = 0.0
| y165 = 0.0
| y166 = 0.0
| y167 = 0.0203635806378
| y168 = 0.0
| y169 = 0.0
| y170 = 0.0
| y171 = 0.0
| y172 = 0.0
| y173 = 0.0
| y174 = 0.0
| y175 = 0.0
| y176 = 0.0
| y177 = 0.0
| y178 = 0.0101300194963
| y179 = 0.0
| y180 = 0.0
| y181 = 0.0
| y182 = 0.0
| y183 = 0.0
| y184 = 0.0
| y185 = 0.0
| y186 = 0.0162390452175
| y187 = 0.0
| y188 = 0.0
| y189 = 0.0
| y190 = 0.0
| y191 = 0.0
| y192 = 0.0
| y193 = 0.0
| y194 = 0.0
| y195 = 0.0
| y196 = 0.0
| y197 = 0.0164811872445
| y198 = 0.0420364330557
| y199 = 0.0
| y200 = 0.0
| y201 = 0.0
| y202 = 0.0
| y203 = 0.0
| y204 = 0.0
| y205 = 0.0
| y206 = 0.0
| y207 = 0.0
| y208 = 0.0
| y209 = 0.0
| y210 = 0.0
| y211 = 0.0
| y212 = 0.0
| y213 = 0.0
| y214 = 0.0
| y215 = 0.0
| y216 = 0.0
| y217 = 0.0
| y218 = 0.0
| y219 = 0.0
| y220 = 0.0
| y221 = 0.0
| y222 = 0.0
| y223 = 0.0
| y224 = 0.0
| y225 = 0.0
| y226 = 0.0
| y227 = 0.0
| y228 = 0.0
| y229 = 0.0
| y230 = 0.0
| y231 = 0.00347616598865
| y232 = 0.0
| y233 = 0.0
| y234 = 0.0
| y235 = 0.0
| y236 = 0.0
| y237 = 0.0
| y238 = 0.0
| y239 = 0.0
| y240 = 0.0
| y241 = 0.0
| y242 = 0.0
| y243 = 0.0
| y244 = 0.0
| y245 = 0.0
| y246 = 0.0
| y247 = 0.0
| y248 = 0.0
| y249 = 0.0
| y250 = 0.0
| y251 = 0.0
| y252 = 0.0
| y253 = 0.0
| y254 = 0.0
| y255 = 0.0
| y256 = 0.0
| y257 = 0.0
| y258 = 0.0
| y259 = 0.0
| y260 = 0.0
| y261 = 0.0
| y262 = 0.0
| y263 = 0.0
| y264 = 0.0
| y265 = 0.0
| y266 = 0.0
| y267 = 0.0
| y268 = 0.0
| y269 = 0.0
| y270 = 0.0
| y271 = 0.0
| y272 = 0.0
| y273 = 0.0
| y274 = 0.0
| y275 = 0.0
| y276 = 0.0185508525488
| y277 = 0.0
| y278 = 0.0
| y279 = 0.0
| y280 = 0.0
| y281 = 0.0
| y282 = 0.00143623868282
| y283 = 0.0
| y284 = 0.0
| y285 = 0.0
| y286 = 0.0
| y287 = 0.0
| y288 = 0.0
| y289 = 0.0
| y290 = 0.0
| y291 = 0.0
| y292 = 0.0
| y293 = 0.0
| y294 = 0.0
| y295 = 0.0
| y296 = 0.0
| y297 = 0.0
| y298 = 0.0
| y299 = 0.0
| y300 = 0.0
| y301 = 0.0
| y302 = 0.0113611561678
| y303 = 0.0
| y304 = 0.0
| y305 = 0.0
| y306 = 0.00933459969759
| y307 = 0.0
| y308 = 0.0
| y309 = 0.0
| y310 = 0.0
| y311 = 0.0
| y312 = 0.0
| y313 = 0.0
| y314 = 0.0
| y315 = 0.0
| y316 = 0.0
| y317 = 0.0
| y318 = 0.0
| y319 = 0.0446832004251
| y320 = 0.0
| y321 = 0.0
| y322 = 0.0
| y323 = 0.0
| y324 = 0.0
| y325 = 0.0
| y326 = 0.0
| y327 = 0.0
| y328 = 0.0
| y329 = 0.0171422095858
| y330 = 0.0
| y331 = 0.0
| y332 = 0.0
| y333 = 0.0
| y334 = 0.0
| y335 = 0.0349569727637
| y336 = 0.0
| y337 = 0.0
| y338 = 0.0
| y339 = 0.0
| y340 = 0.0
| y341 = 0.0
| y342 = 0.0
| y343 = 0.0
| y344 = 0.0
| y345 = 0.0
| y346 = 0.0
| y347 = 0.0
| y348 = 0.0
| y349 = 0.0
| y350 = 0.0
| y351 = 0.0137774824154
| y352 = 0.0
| y353 = 0.0
| y354 = 0.0
| y355 = 0.0429525667159
| y356 = 0.0
| y357 = 0.0
| y358 = 0.0043929152691
| y359 = 0.0
| y360 = 0.0
| y361 = 0.0
| y362 = 0.033670762128
| y363 = 0.0
| y364 = 0.0
| y365 = 0.0
| y366 = 0.0
| y367 = 0.0
| y368 = 0.0
| y369 = 0.0
| y370 = 0.0
| y371 = 0.0
| y372 = 0.0
| y373 = 0.0
| y374 = 0.0
| y375 = 0.0
| y376 = 0.0
| y377 = 0.0
| y378 = 0.0
| y379 = 0.0
| y380 = 0.0
| y381 = 0.0
| y382 = 0.0
| y383 = 0.0
| y384 = 0.0
| y385 = 0.0
| y386 = 0.0
| y387 = 0.0
| y388 = 0.0
| y389 = 0.0
| y390 = 0.0
| y391 = 0.0
| y392 = 0.0
| y393 = 0.0
| y394 = 0.0
| y395 = 0.0
| y396 = 0.0280221742432
| y397 = 0.0
| y398 = 0.0
| y399 = 0.0
| y400 = 0.0
| y401 = 0.0
| y402 = 0.0
| y403 = 0.0207117832696
| y404 = 0.0
| y405 = 0.0188410351676
| y406 = 0.00809370127025
| y407 = 0.0
| y408 = 0.0
| y409 = 0.0
| y410 = 0.0
| y411 = 0.0
| y412 = 0.0
| y413 = 0.0
| y414 = 0.0
| y415 = 0.0
| y416 = 0.00824441816134
| y417 = 0.0
| y418 = 0.0
| y419 = 0.0
| y420 = 0.0
| y421 = 0.0
| y422 = 0.00832520809828
| y423 = 0.0
| y424 = 0.0
| y425 = 0.0
| y426 = 0.0
| y427 = 0.0
| y428 = 0.0
| y429 = 0.0
| y430 = 0.0132992012412
| y431 = 0.0
| y432 = 0.0
| y433 = 0.0
| y434 = 0.0
| y435 = 0.0
| y436 = 0.0
| y437 = 0.0
| y438 = 0.0
| y439 = 0.0
| y440 = 0.0
| y441 = 0.0
| y442 = 0.0
| y443 = 0.0
| y444 = 0.0
| y445 = 0.000249671739067
| y446 = 0.0
| y447 = 0.0
| y448 = 0.0
| y449 = 0.0
| y450 = 0.0
| y451 = 0.0
| y452 = 0.0
| y453 = 0.0
| y454 = 0.0
| y455 = 0.0
| y456 = 0.0
| y457 = 0.0281740516236
| y458 = 0.0
| y459 = 0.0
| y460 = 0.0
| y461 = 0.0
| y462 = 0.0
| y463 = 0.0
| y464 = 0.0
| y465 = 0.0
| y466 = 0.0
| y467 = 0.0
| y468 = 0.0
| y469 = 0.0
| y470 = 0.0
| y471 = 0.0
| y472 = 0.0
| y473 = 0.0
| y474 = 0.0
| y475 = 0.0
| y476 = 0.0
| y477 = 0.0
| y478 = 0.0
| y479 = 0.0
| y480 = 0.0
| y481 = 0.0
| y482 = 0.0
| y483 = 0.0
| y484 = 0.0
| y485 = 0.0
| y486 = 0.00488388161999
| y487 = 0.0
| y488 = 0.024836095265
| y489 = 0.0
| y490 = 0.0
| y491 = 0.0
| y492 = 0.0
| y493 = 0.0
| y494 = 0.0
| y495 = 0.0
| y496 = 0.0
| y497 = 0.0
| y498 = 0.0
| y499 = 0.0
| y500 = 0.0
| s1 = 4.93364765819
| s2 = 0.26256158562
| s3 = 7.65238398937
| s4 = 6.07751504516
| s5 = 1.79181841376
| s6 = 1.49473638722
| s7 = 2.36842385865
| s8 = 0.134665368795
| s9 = 4.3521964619
| s10 = 2.91977360533
| s11 = 2.42064619955
| s12 = 0.353319679909
| s13 = 4.35152959355
| s14 = 0.914916326533
| s15 = 2.59613572673
| s16 = 6.51499624128
| s17 = 5.23019975598
| s18 = 1.79603349732
| s19 = 3.46758468734
| s20 = 2.32071344305
| s21 = 6.31575816654
| s22 = 7.69298488462
| s23 = 4.92171753149
| s24 = 5.87838803896
| s25 = 0.431090631679
| s26 = 6.48239068291
| s27 = 3.34369009145
| s28 = 0.0
| s29 = 8.80915865938
| s30 = 0.501175650913
| s31 = 1.04893338292
| s32 = 5.20262283311
| s33 = 6.30067284526
| s34 = 8.86891737438
| s35 = 5.21094049017
| s36 = 9.67184635018
| s37 = 2.63119698185
| s38 = 6.39556146163
| s39 = 9.14642172376
| s40 = 3.80775920328
| s41 = 5.93706434654
| s42 = 3.28094799761
| s43 = 3.81282391601
| s44 = 2.32613350316
| s45 = 7.37216077183
| s46 = 2.00855862417
| s47 = 0.329803351297
| s48 = 3.06398384792
| s49 = 4.67449829578
| s50 = 3.80624307006
| s51 = 0.137499453718
| s52 = 5.18727350768
| s53 = 4.27512503036
| s54 = 0.59982117088
| s55 = 4.01231391488
| s56 = 12.2055528452
| s57 = 4.14715248867
| s58 = 6.08137506285
| s59 = 3.6236501055
| s60 = 1.00727748551
| s61 = 0.0
| s62 = 0.0
| s63 = 8.62669766699
| s64 = 0.0
| s65 = 0.289448277451
| s66 = 2.45362887691
| s67 = 2.13326743373
| s68 = 3.20059669118
| s69 = 6.45467660507
| s70 = 1.01626416665
| s71 = 10.6013616844
| s72 = 3.18043744703
| s73 = 5.13833544552
| s74 = 0.0
| s75 = 1.76335050143
| s76 = 0.0
| s77 = 0.838791560302
| s78 = 1.08784499212
| s79 = 0.0
| s80 = 5.82075782373
| s81 = 4.47276119582
| s82 = 2.48408570818
| s83 = 0.0
| s84 = 9.65214380797
| s85 = 6.96343091326
| s86 = 3.45056501728
| s87 = 2.45311368426
| s88 = 1.74090873264
| s89 = 0.0
| s90 = 3.30265524334
| s91 = 0.0
| s92 = 7.79789264695
| s93 = 4.90903333209
| s94 = 10.1463214626
| s95 = 0.110205590537
| s96 = 4.99595862098
| s97 = 4.61893673934
| s98 = 6.99597346355
| s99 = 6.58315420071
| s100 = 6.44897807171
| s101 = 6.03700665948
| s102 = 0.0
| s103 = 4.78187974704
| s104 = 7.03353374114
| s105 = 9.00868689442
| s106 = 7.71426391901
| s107 = 2.14156686389
| s108 = 3.61126437
| s109 = 5.32957821484
| s110 = 1.93661968879
| s111 = 2.13325280023
| s112 = 1.20944973939
| s113 = 5.7634367531
| s114 = 7.05166420727
| s115 = 9.11923565556
| s116 = 6.0290638908
| s117 = 0.260163484952
| s118 = 7.76017738408
| s119 = 7.51424543827
| s120 = 1.6850956514
| s121 = 0.919334249922
| s122 = 6.31172648158
| s123 = 3.67909520487
| s124 = 2.10497221656
| s125 = 5.1123678946
| s126 = 0.0
| s127 = 3.93725114369
| s128 = 4.40461623198
| s129 = 7.90737975823
| s130 = 5.09912346013
| s131 = 8.74302450272
| s132 = 3.97770386309
| s133 = 2.6107419823
| s134 = 0.580027801873
| s135 = 9.37914054188
| s136 = 0.0
| s137 = 4.29128341911
| s138 = 0.425105932557
| s139 = 9.44430869113
| s140 = 5.24184314553
| s141 = 7.61615664946
| s142 = 1.51138949717
| s143 = 3.84365705378
| s144 = 2.13692465347
| s145 = 6.41513055045
| s146 = 1.96529784299
| s147 = 3.59387826988
| s148 = 0.30227248363
| s149 = 0.0
| s150 = 3.63973051502
| s151 = 7.99852816549
| s152 = 10.0398518962
| s153 = 2.21183261085
| s154 = 6.79890216701
| s155 = 4.63523751414
| s156 = 4.54038219366
| s157 = 3.37974878919
| s158 = 4.31034879952
| s159 = 7.75428774327
| s160 = 4.72948073183
| s161 = 4.60569717893
| s162 = 4.68553419454
| s163 = 8.78735668388
| s164 = 11.9485155966
| s165 = 6.50002001039
| s166 = 9.35953156628
| s167 = 9.8765458541
| s168 = 4.81731945395
| s169 = 6.4737133792
| s170 = 1.63522283906
| s171 = 6.45156373113
| s172 = 0.0
| s173 = 4.9555469349
| s174 = 3.45741408996
| s175 = 4.42884981017
| s176 = 3.77854487312
| s177 = 6.09706327469
| s178 = 3.4276116021
| s179 = 1.49767629508
| s180 = 5.54573581695
| s181 = 2.96009018348
| s182 = 5.81424041279
| s183 = 1.16318750876
| s184 = 6.44176044963
| s185 = 2.5230918946
| s186 = 5.31811306183
| s187 = 7.26777265348
| s188 = 3.06952786283
| s189 = 0.0
| s190 = 0.493536995106
| s191 = 1.11192670981
| s192 = 0.0
| s193 = 3.17521634902
| s194 = 4.45332829144
| s195 = 3.98344588944
| s196 = 1.98602569967
| s197 = 6.20224583842
| s198 = 4.91148436633
| s199 = 0.722885595685
| s200 = 4.80421137137
| s201 = 6.32671919214
| s202 = 0.735629427889
| s203 = 0.0
| s204 = 7.31888430604
| s205 = 2.11883214696
| s206 = 8.74847456057
| s207 = 2.38076797105
| s208 = 5.37394959045
| s209 = 1.05956150616
| s210 = 12.1915374746
| s211 = 6.82289354981
| s212 = 5.24811740174
| s213 = 6.2047660282
| s214 = 1.20829838879
| s215 = 11.0868555902
| s216 = 4.69529172331
| s217 = 2.79942312506
| s218 = 7.13229488459
| s219 = 8.07460831221
| s220 = 0.0
| s221 = 4.86463796014
| s222 = 3.57239852797
| s223 = 5.92499778602
| s224 = 11.8743020834
| s225 = 3.50613816227
| s226 = 1.91136823927
| s227 = 2.42727977179
| s228 = 0.0
| s229 = 5.31090882782
| s230 = 0.907021707874
| s231 = 4.15477641894
| s232 = 5.36864300007
| s233 = 6.63602103667
| s234 = 3.2280770528
| s235 = 4.51837931956
| s236 = 2.30969844368
| s237 = 4.37165095323
| s238 = 7.19748852131
| s239 = 7.77752301687
| s240 = 0.889186976791
| s241 = 3.19480969168
| s242 = 4.73251923407
| s243 = 3.71815487917
| s244 = 4.88223748526
| s245 = 4.94671512856
| s246 = 8.73819337732
| s247 = 2.87407919297
| s248 = 3.53850107033
| s249 = 4.32918428171
| s250 = 7.82254495876
| s251 = 2.78382852269
| s252 = 4.58850920397
| s253 = 4.15955315274
| s254 = 7.74665233606
| s255 = 6.2876313435
| s256 = 10.2481068115
| s257 = 5.47513337389
| s258 = 6.49968392686
| s259 = 3.23254295878
| s260 = 1.6902785191
| s261 = 1.20196963869
| s262 = 5.10672785017
| s263 = 3.205961324
| s264 = 7.57144583125
| s265 = 4.02701090592
| s266 = 4.55901700229
| s267 = 0.0
| s268 = 2.96058030091
| s269 = 3.20066899321
| s270 = 4.38901855565
| s271 = 10.4127365207
| s272 = 7.02198059079
| s273 = 0.209571375341
| s274 = 3.05174482995
| s275 = 0.93412445125
| s276 = 7.05236349045
| s277 = 1.13755561262
| s278 = 1.77142821518
| s279 = 4.96136099654
| s280 = 6.44807736995
| s281 = 9.63412518025
| s282 = 0.0
| s283 = 4.25267372775
| s284 = 8.55224719544
| s285 = 6.15890979088
| s286 = 6.05025972353
| s287 = 9.42994360697
| s288 = 1.35745805908
| s289 = 5.72165772867
| s290 = 1.6286302704
| s291 = 4.67200073798
| s292 = 8.41623491018
| s293 = 3.3853266944
| s294 = 10.3378505424
| s295 = 2.91457983902
| s296 = 1.49342450644
| s297 = 6.30356422193
| s298 = 5.32129398882
| s299 = 4.7876374118
| s300 = 3.04258620975
| s301 = 2.54128841973
| s302 = 6.22252385632
| s303 = 1.37758656736
| s304 = 0.0
| s305 = 1.25074949846
| s306 = 6.78432062123
| s307 = 7.69247888211
| s308 = 2.51408786017
| s309 = 5.80617068453
| s310 = 2.47509404201
| s311 = 8.9849368453
| s312 = 8.99617172575
| s313 = 4.3480278518
| s314 = 1.78511299284
| s315 = 6.77160426183
| s316 = 10.9690159698
| s317 = 2.23847944689
| s318 = 2.23749475141
| s319 = 6.88348108548
| s320 = 0.58138228547
| s321 = 1.56863204895
| s322 = 5.18086227801
| s323 = 0.273725750215
| s324 = 1.58639559365
| s325 = 3.74432337822
| s326 = 4.21624828575
| s327 = 9.13611396809
| s328 = 1.85175571639
| s329 = 1.31078333208
| s330 = 0.0
| s331 = 6.08534365624
| s332 = 10.00701805
| s333 = 6.62973437783
| s334 = 1.50284517894
| s335 = 6.68912957163
| s336 = 0.0
| s337 = 3.86111646677
| s338 = 3.98379017128
| s339 = 0.986587236458
| s340 = 3.32566903065
| s341 = 8.84958435571
| s342 = 0.0
| s343 = 5.79217797543
| s344 = 7.57412123682
| s345 = 7.65384794869
| s346 = 0.0
| s347 = 11.4798280991
| s348 = 7.66892988459
| s349 = 3.36792758854
| s350 = 8.20321065358
| s351 = 10.1451496046
| s352 = 3.08950209756
| s353 = 0.524585733033
| s354 = 9.63543436849
| s355 = 2.08934810448
| s356 = 6.67023630127
| s357 = 5.66429131816
| s358 = 1.12466763861
| s359 = 5.44296789607
| s360 = 2.82432633696
| s361 = 0.0
| s362 = 0.407303705438
| s363 = 10.5937281266
| s364 = 6.07567754659
| s365 = 5.9213408671
| s366 = 6.94551863107
| s367 = 1.73727133
| s368 = 8.99269236983
| s369 = 2.02201119597
| s370 = 10.2666080207
| s371 = 0.0
| s372 = 2.79448705345
| s373 = 3.13836793772
| s374 = 5.32567374484
| s375 = 9.37070264853
| s376 = 2.42395758694
| s377 = 1.83294329716
| s378 = 0.800471290736
| s379 = 5.8608448089
| s380 = 3.98178599259
| s381 = 5.42873284793
| s382 = 2.15898399601
| s383 = 2.29234085472
| s384 = 3.41193325457
| s385 = 2.11756553635
| s386 = 6.69106478494
| s387 = 4.59224672991
| s388 = 9.23314172671
| s389 = 0.347602270813
| s390 = 2.57634810783
| s391 = 3.90091131532
| s392 = 2.69980283704
| s393 = 9.90777756979
| s394 = 6.17813965441
| s395 = 0.0
| s396 = 10.1677783338
| s397 = 0.0
| s398 = 4.98399735162
| s399 = 0.985767919051
| s400 = 0.785801332359
| s401 = 0.315466673176
| s402 = 3.42276408059
| s403 = 7.20692886884
| s404 = 5.38876674344
| s405 = 5.43184844903
| s406 = 4.53031638483
| s407 = 5.05892062933
| s408 = 3.1046330123
| s409 = 0.743190723332
| s410 = 4.57407553004
| s411 = 2.46062334479
| s412 = 0.750933510505
| s413 = 1.91008685133
| s414 = 5.86696872799
| s415 = 10.5472623352
| s416 = 6.61173682671
| s417 = 2.97006546421
| s418 = 5.66724428139
| s419 = 2.39333283303
| s420 = 5.33910752854
| s421 = 6.68395271129
| s422 = 7.48492399376
| s423 = 0.411620478671
| s424 = 6.81475568128
| s425 = 0.92050519929
| s426 = 9.27997613804
| s427 = 5.48081478075
| s428 = 2.42923451988
| s429 = 2.95020479498
| s430 = 7.0866322824
| s431 = 0.0
| s432 = 0.348706163916
| s433 = 0.0
| s434 = 1.97981052564
| s435 = 8.48476295076
| s436 = 1.80612245254
| s437 = 0.0
| s438 = 0.815387649842
| s439 = 8.90473356581
| s440 = 5.22843006261
| s441 = 2.77962013941
| s442 = 6.04090058731
| s443 = 5.08121611093
| s444 = 0.468512042134
| s445 = 3.67040309572
| s446 = 0.401533220351
| s447 = 0.0
| s448 = 8.04138154425
| s449 = 6.96609247698
| s450 = 6.55448233169
| s451 = 1.23683414251
| s452 = 0.0
| s453 = 7.07792233369
| s454 = 1.91239033519
| s455 = 8.5788072212
| s456 = 2.49717882832
| s457 = 4.10382550992
| s458 = 7.11920521342
| s459 = 0.873039597571
| s460 = 6.15112831307
| s461 = 6.17313885745
| s462 = 0.0
| s463 = 5.90301486591
| s464 = 5.94687343395
| s465 = 4.12237280838
| s466 = 1.17835288075
| s467 = 6.6837126494
| s468 = 1.06197157809
| s469 = 3.15174160456
| s470 = 2.61344983821
| s471 = 6.18928109287
| s472 = 6.16011355983
| s473 = 0.280596082635
| s474 = 2.79676658975
| s475 = 8.36698858967
| s476 = 8.18159105523
| s477 = 8.66074261221
| s478 = 6.16145546645
| s479 = 7.57743692763
| s480 = 6.8554747153
| s481 = 0.0
| s482 = 4.51928690564
| s483 = 1.99369332144
| s484 = 8.90655411653
| s485 = 2.47606428499
| s486 = 7.337626669
| s487 = 2.76111792663
| s488 = 0.639672214375
| s489 = 2.57103906738
| s490 = 5.56188676747
| s491 = 1.42368042591
| s492 = 10.1428718249
| s493 = 2.47488123485
| s494 = 2.24848231888
| s495 = 7.71895122681
| s496 = 0.0
| s497 = 5.17277928674
| s498 = 3.79931084558
| s499 = 6.15334059175
| s500 = 6.3978726733
*************************************************************************
| Objective Value ------------------ 7.06662419245
| Aij Sum -------------------------- 6755703
| Cj Sum --------------------------- 7296
| Bi Sum --------------------------- 7333
| Matrix Dimensions ---------------- (500, 500)
| Date/Time ------------------------ 2015-08-20 16:18:25.752603
*************************************************************************
-- Gurobi Standard Primal Linear Programming Problem --
James Gaboardi, 2015
2. Dual
In [6]:
# Instantiate Model
mDual_Standard_GUROBI = gbp.Model(' -- Standard Dual Linear Programming Problem -- ')
# Set Focus to Optimality
gbp.setParam('MIPFocus', 2)
# Decision Variables
desc_var = []
for orig in rows:
desc_var.append([])
desc_var[orig].append(mDual_Standard_GUROBI.addVar(vtype=gbp.GRB.CONTINUOUS,
name='u'+str(orig+1)))
# Slack Variables
slack_var = []
for dest in cols:
slack_var.append([])
slack_var[dest].append(mDual_Standard_GUROBI.addVar(vtype=gbp.GRB.CONTINUOUS,
name='t'+str(dest+1)))
# Update Model
mDual_Standard_GUROBI.update()
#Objective Function
mDual_Standard_GUROBI.setObjective(gbp.quicksum(Bi[orig]*desc_var[orig][0]
for orig in rows),
gbp.GRB.MAXIMIZE)
# Constraints
for dest in cols:
mDual_Standard_GUROBI.addConstr(gbp.quicksum(Aij[orig][dest]*desc_var[orig][0]
for orig in rows) +
slack_var[dest][0] -
Cj[dest] == 0)
# Optimize
mDual_Standard_GUROBI.optimize()
# Write LP file
mDual_Standard_GUROBI.write('LP.lp')
print '\n*************************************************************************'
print ' | Decision Variables'
for v in mDual_Standard_GUROBI.getVars():
print ' | ', v.VarName, '=', v.x
print '*************************************************************************'
val = mDual_Standard_GUROBI.objVal
print ' | Objective Value ------------------ ', val
print ' | Aij Sum -------------------------- ', AijSum
print ' | Cj Sum --------------------------- ', CjSum
print ' | Bi Sum --------------------------- ', BiSum
print ' | Matrix Dimensions ---------------- ', Aij.shape
print ' | Date/Time ------------------------ ', dt.datetime.now()
print '*************************************************************************'
print '-- Gurobi Standard Dual Linear Programming Problem --'
print '\nJames Gaboardi, 2015'
Parameter MIPFocus unchanged
Value: 2 Min: 0 Max: 3 Default: 0
Optimize a model with 500 rows, 1000 columns and 250500 nonzeros
Coefficient statistics:
Matrix range [1e+00, 5e+01]
Objective range [1e+01, 2e+01]
Bounds range [0e+00, 0e+00]
RHS range [1e+01, 2e+01]
Concurrent LP optimizer: dual simplex and barrier
Showing barrier log only...
Presolve removed 0 rows and 500 columns
Presolve time: 0.06s
Presolved: 500 rows, 500 columns, 250000 nonzeros
Ordering time: 0.00s
Barrier statistics:
AA' NZ : 1.248e+05
Factor NZ : 1.252e+05 (roughly 1 MByte of memory)
Factor Ops : 4.179e+07 (less than 1 second per iteration)
Threads : 1
Barrier performed 0 iterations in 0.14 seconds
Barrier solve interrupted - model solved by another algorithm
Solved with dual simplex
Solved in 210 iterations and 0.16 seconds
Optimal objective 7.066624192e+00
*************************************************************************
| Decision Variables
| u1 = 0.0
| u2 = 0.0
| u3 = 0.0
| u4 = 0.0
| u5 = 0.0
| u6 = 0.0
| u7 = 0.0
| u8 = 0.0
| u9 = 0.0
| u10 = 0.0
| u11 = 0.0
| u12 = 0.0
| u13 = 0.0
| u14 = 0.0
| u15 = 0.0
| u16 = 0.0
| u17 = 0.0
| u18 = 0.0
| u19 = 0.0
| u20 = 0.0
| u21 = 0.0
| u22 = 0.0
| u23 = 0.0
| u24 = 0.0
| u25 = 0.0
| u26 = 0.0
| u27 = 0.0
| u28 = 0.0229185718377
| u29 = 0.0
| u30 = 0.0
| u31 = 0.0
| u32 = 0.0
| u33 = 0.0
| u34 = 0.0
| u35 = 0.0
| u36 = 0.0
| u37 = 0.0
| u38 = 0.0
| u39 = 0.0
| u40 = 0.0
| u41 = 0.0
| u42 = 0.0
| u43 = 0.0
| u44 = 0.0
| u45 = 0.0
| u46 = 0.0
| u47 = 0.0
| u48 = 0.0
| u49 = 0.0
| u50 = 0.0
| u51 = 0.0
| u52 = 0.0
| u53 = 0.0
| u54 = 0.0
| u55 = 0.0
| u56 = 0.0
| u57 = 0.0
| u58 = 0.0
| u59 = 0.0
| u60 = 0.0
| u61 = 0.00850197714598
| u62 = 0.00357984332056
| u63 = 0.0
| u64 = 0.0074246880496
| u65 = 0.0
| u66 = 0.0
| u67 = 0.0
| u68 = 0.0
| u69 = 0.0
| u70 = 0.0
| u71 = 0.0
| u72 = 0.0
| u73 = 0.0
| u74 = 0.02746652325
| u75 = 0.0
| u76 = 0.00607416092011
| u77 = 0.0
| u78 = 0.0
| u79 = 0.0089680459336
| u80 = 0.0
| u81 = 0.0
| u82 = 0.0
| u83 = 0.00997333973717
| u84 = 0.0
| u85 = 0.0
| u86 = 0.0
| u87 = 0.0
| u88 = 0.0
| u89 = 0.00844266364563
| u90 = 0.0
| u91 = 0.00245013257581
| u92 = 0.0
| u93 = 0.0
| u94 = 0.0
| u95 = 0.0
| u96 = 0.0
| u97 = 0.0
| u98 = 0.0
| u99 = 0.0
| u100 = 0.0
| u101 = 0.0
| u102 = 0.00418455035148
| u103 = 0.0
| u104 = 0.0
| u105 = 0.0
| u106 = 0.0
| u107 = 0.0
| u108 = 0.0
| u109 = 0.0
| u110 = 0.0
| u111 = 0.0
| u112 = 0.0
| u113 = 0.0
| u114 = 0.0
| u115 = 0.0
| u116 = 0.0
| u117 = 0.0
| u118 = 0.0
| u119 = 0.0
| u120 = 0.0
| u121 = 0.0
| u122 = 0.0
| u123 = 0.0
| u124 = 0.0
| u125 = 0.0
| u126 = 0.00663518852399
| u127 = 0.0
| u128 = 0.0
| u129 = 0.0
| u130 = 0.0
| u131 = 0.0
| u132 = 0.0
| u133 = 0.0
| u134 = 0.0
| u135 = 0.0
| u136 = 0.0147103837236
| u137 = 0.0
| u138 = 0.0
| u139 = 0.0
| u140 = 0.0
| u141 = 0.0
| u142 = 0.0
| u143 = 0.0
| u144 = 0.0
| u145 = 0.0
| u146 = 0.0
| u147 = 0.0
| u148 = 0.0
| u149 = 0.00646124859479
| u150 = 0.0
| u151 = 0.0
| u152 = 0.0
| u153 = 0.0
| u154 = 0.0
| u155 = 0.0
| u156 = 0.0
| u157 = 0.0
| u158 = 0.0
| u159 = 0.0
| u160 = 0.0
| u161 = 0.0
| u162 = 0.0
| u163 = 0.0
| u164 = 0.0
| u165 = 0.0
| u166 = 0.0
| u167 = 0.0
| u168 = 0.0
| u169 = 0.0
| u170 = 0.0
| u171 = 0.0
| u172 = 0.0132235128846
| u173 = 0.0
| u174 = 0.0
| u175 = 0.0
| u176 = 0.0
| u177 = 0.0
| u178 = 0.0
| u179 = 0.0
| u180 = 0.0
| u181 = 0.0
| u182 = 0.0
| u183 = 0.0
| u184 = 0.0
| u185 = 0.0
| u186 = 0.0
| u187 = 0.0
| u188 = 0.0
| u189 = 0.0146118803445
| u190 = 0.0
| u191 = 0.0
| u192 = 0.00959469214851
| u193 = 0.0
| u194 = 0.0
| u195 = 0.0
| u196 = 0.0
| u197 = 0.0
| u198 = 0.0
| u199 = 0.0
| u200 = 0.0
| u201 = 0.0
| u202 = 0.0
| u203 = 0.010935757271
| u204 = 0.0
| u205 = 0.0
| u206 = 0.0
| u207 = 0.0
| u208 = 0.0
| u209 = 0.0
| u210 = 0.0
| u211 = 0.0
| u212 = 0.0
| u213 = 0.0
| u214 = 0.0
| u215 = 0.0
| u216 = 0.0
| u217 = 0.0
| u218 = 0.0
| u219 = 0.0
| u220 = 0.0219061722475
| u221 = 0.0
| u222 = 0.0
| u223 = 0.0
| u224 = 0.0
| u225 = 0.0
| u226 = 0.0
| u227 = 0.0
| u228 = 0.00559355817929
| u229 = 0.0
| u230 = 0.0
| u231 = 0.0
| u232 = 0.0
| u233 = 0.0
| u234 = 0.0
| u235 = 0.0
| u236 = 0.0
| u237 = 0.0
| u238 = 0.0
| u239 = 0.0
| u240 = 0.0
| u241 = 0.0
| u242 = 0.0
| u243 = 0.0
| u244 = 0.0
| u245 = 0.0
| u246 = 0.0
| u247 = 0.0
| u248 = 0.0
| u249 = 0.0
| u250 = 0.0
| u251 = 0.0
| u252 = 0.0
| u253 = 0.0
| u254 = 0.0
| u255 = 0.0
| u256 = 0.0
| u257 = 0.0
| u258 = 0.0
| u259 = 0.0
| u260 = 0.0
| u261 = 0.0
| u262 = 0.0
| u263 = 0.0
| u264 = 0.0
| u265 = 0.0
| u266 = 0.0
| u267 = 0.00537641181055
| u268 = 0.0
| u269 = 0.0
| u270 = 0.0
| u271 = 0.0
| u272 = 0.0
| u273 = 0.0
| u274 = 0.0
| u275 = 0.0
| u276 = 0.0
| u277 = 0.0
| u278 = 0.0
| u279 = 0.0
| u280 = 0.0
| u281 = 0.0
| u282 = 0.00751886733222
| u283 = 0.0
| u284 = 0.0
| u285 = 0.0
| u286 = 0.0
| u287 = 0.0
| u288 = 0.0
| u289 = 0.0
| u290 = 0.0
| u291 = 0.0
| u292 = 0.0
| u293 = 0.0
| u294 = 0.0
| u295 = 0.0
| u296 = 0.0
| u297 = 0.0
| u298 = 0.0
| u299 = 0.0
| u300 = 0.0
| u301 = 0.0
| u302 = 0.0
| u303 = 0.0
| u304 = 0.00153773047514
| u305 = 0.0
| u306 = 0.0
| u307 = 0.0
| u308 = 0.0
| u309 = 0.0
| u310 = 0.0
| u311 = 0.0
| u312 = 0.0
| u313 = 0.0
| u314 = 0.0
| u315 = 0.0
| u316 = 0.0
| u317 = 0.0
| u318 = 0.0
| u319 = 0.0
| u320 = 0.0
| u321 = 0.0
| u322 = 0.0
| u323 = 0.0
| u324 = 0.0
| u325 = 0.0
| u326 = 0.0
| u327 = 0.0
| u328 = 0.0
| u329 = 0.0
| u330 = 0.00246837747021
| u331 = 0.0
| u332 = 0.0
| u333 = 0.0
| u334 = 0.0
| u335 = 0.0
| u336 = 0.00901675099015
| u337 = 0.0
| u338 = 0.0
| u339 = 0.0
| u340 = 0.0
| u341 = 0.0
| u342 = 0.00189088513833
| u343 = 0.0
| u344 = 0.0
| u345 = 0.0
| u346 = 0.0205920711009
| u347 = 0.0
| u348 = 0.0
| u349 = 0.0
| u350 = 0.0
| u351 = 0.0
| u352 = 0.0
| u353 = 0.0
| u354 = 0.0
| u355 = 0.0
| u356 = 0.0
| u357 = 0.0
| u358 = 0.0
| u359 = 0.0
| u360 = 0.0
| u361 = 0.0162605433437
| u362 = 0.0
| u363 = 0.0
| u364 = 0.0
| u365 = 0.0
| u366 = 0.0
| u367 = 0.0
| u368 = 0.0
| u369 = 0.0
| u370 = 0.0
| u371 = 0.00842909011315
| u372 = 0.0
| u373 = 0.0
| u374 = 0.0
| u375 = 0.0
| u376 = 0.0
| u377 = 0.0
| u378 = 0.0
| u379 = 0.0
| u380 = 0.0
| u381 = 0.0
| u382 = 0.0
| u383 = 0.0
| u384 = 0.0
| u385 = 0.0
| u386 = 0.0
| u387 = 0.0
| u388 = 0.0
| u389 = 0.0
| u390 = 0.0
| u391 = 0.0
| u392 = 0.0
| u393 = 0.0
| u394 = 0.0
| u395 = 0.00561491245148
| u396 = 0.0
| u397 = 0.0258384924498
| u398 = 0.0
| u399 = 0.0
| u400 = 0.0
| u401 = 0.0
| u402 = 0.0
| u403 = 0.0
| u404 = 0.0
| u405 = 0.0
| u406 = 0.0
| u407 = 0.0
| u408 = 0.0
| u409 = 0.0
| u410 = 0.0
| u411 = 0.0
| u412 = 0.0
| u413 = 0.0
| u414 = 0.0
| u415 = 0.0
| u416 = 0.0
| u417 = 0.0
| u418 = 0.0
| u419 = 0.0
| u420 = 0.0
| u421 = 0.0
| u422 = 0.0
| u423 = 0.0
| u424 = 0.0
| u425 = 0.0
| u426 = 0.0
| u427 = 0.0
| u428 = 0.0
| u429 = 0.0
| u430 = 0.0
| u431 = 0.00725135193757
| u432 = 0.0
| u433 = 0.016058155025
| u434 = 0.0
| u435 = 0.0
| u436 = 0.0
| u437 = 0.0114122480056
| u438 = 0.0
| u439 = 0.0
| u440 = 0.0
| u441 = 0.0
| u442 = 0.0
| u443 = 0.0
| u444 = 0.0
| u445 = 0.0
| u446 = 0.0
| u447 = 0.00257741818014
| u448 = 0.0
| u449 = 0.0
| u450 = 0.0
| u451 = 0.0
| u452 = 0.011682242706
| u453 = 0.0
| u454 = 0.0
| u455 = 0.0
| u456 = 0.0
| u457 = 0.0
| u458 = 0.0
| u459 = 0.0
| u460 = 0.0
| u461 = 0.0
| u462 = 0.00791411183726
| u463 = 0.0
| u464 = 0.0
| u465 = 0.0
| u466 = 0.0
| u467 = 0.0
| u468 = 0.0
| u469 = 0.0
| u470 = 0.0
| u471 = 0.0
| u472 = 0.0
| u473 = 0.0
| u474 = 0.0
| u475 = 0.0
| u476 = 0.0
| u477 = 0.0
| u478 = 0.0
| u479 = 0.0
| u480 = 0.0
| u481 = 0.00837537129609
| u482 = 0.0
| u483 = 0.0
| u484 = 0.0
| u485 = 0.0
| u486 = 0.0
| u487 = 0.0
| u488 = 0.0
| u489 = 0.0
| u490 = 0.0
| u491 = 0.0
| u492 = 0.0
| u493 = 0.0
| u494 = 0.0
| u495 = 0.0
| u496 = 0.00113596480809
| u497 = 0.0
| u498 = 0.0
| u499 = 0.0
| u500 = 0.0
| t1 = 8.80556747804
| t2 = 0.949213204007
| t3 = 4.65108411999
| t4 = 9.4194672071
| t5 = 2.41075983806
| t6 = 7.82146469361
| t7 = 5.35652763048
| t8 = 0.0
| t9 = 1.84491790395
| t10 = 9.10270634483
| t11 = 9.02714358057
| t12 = 3.05317896081
| t13 = 6.93297559643
| t14 = 7.54023837311
| t15 = 3.94258106148
| t16 = 1.37932975789
| t17 = 1.92249650307
| t18 = 5.02775896155
| t19 = 7.98759514075
| t20 = 7.1303037823
| t21 = 3.04132244912
| t22 = 0.712844298318
| t23 = 9.299595461
| t24 = 2.82580625885
| t25 = 6.78122622968
| t26 = 4.72679199041
| t27 = 4.6973706033
| t28 = 0.308572029814
| t29 = 2.42428743204
| t30 = 6.70421246508
| t31 = 7.06630005666
| t32 = 3.77126477792
| t33 = 1.53283365011
| t34 = 2.67282659414
| t35 = 0.30205578706
| t36 = 0.0
| t37 = 8.66530861185
| t38 = 5.02003758346
| t39 = 2.01313716216
| t40 = 7.99155962099
| t41 = 6.08750582826
| t42 = 0.0
| t43 = 6.51453198754
| t44 = 7.9527609905
| t45 = 5.65803360968
| t46 = 4.40250742124
| t47 = 0.0
| t48 = 8.41129911878
| t49 = 0.564728297946
| t50 = 0.642209082925
| t51 = 0.0
| t52 = 5.98152100826
| t53 = 10.4091672861
| t54 = 1.42999137865
| t55 = 8.92810096082
| t56 = 8.96132282902
| t57 = 3.57440272871
| t58 = 0.0
| t59 = 1.47362484825
| t60 = 0.702787979333
| t61 = 4.79643500859
| t62 = 3.02007823411
| t63 = 9.98125902485
| t64 = 5.7967233555
| t65 = 4.94823190766
| t66 = 3.2719806482
| t67 = 6.92912523772
| t68 = 7.64971649282
| t69 = 0.917994332512
| t70 = 6.37089409005
| t71 = 7.61757923711
| t72 = 4.22224775222
| t73 = 5.061949279
| t74 = 6.75230811103
| t75 = 2.45540094279
| t76 = 0.0
| t77 = 7.3083746122
| t78 = 0.0
| t79 = 3.23832320988
| t80 = 6.1830623293
| t81 = 6.41398462131
| t82 = 7.42247228142
| t83 = 0.0
| t84 = 1.21344352406
| t85 = 4.16009929715
| t86 = 9.98555488355
| t87 = 6.80008963832
| t88 = 4.33445588333
| t89 = 5.42930721137
| t90 = 3.94038356676
| t91 = 4.76554223039
| t92 = 4.20768913756
| t93 = 1.56564947113
| t94 = 2.31394786653
| t95 = 1.19509346073
| t96 = 6.14041746903
| t97 = 7.40509029723
| t98 = 1.05240520907
| t99 = 1.36055401624
| t100 = 4.35409853909
| t101 = 4.21900644282
| t102 = 6.08538654576
| t103 = 8.45806101578
| t104 = 5.99528785681
| t105 = 9.43339253388
| t106 = 0.578263687519
| t107 = 8.28894111732
| t108 = 0.562264852564
| t109 = 6.7196450233
| t110 = 6.89319783704
| t111 = 1.03834804005
| t112 = 4.73634456329
| t113 = 8.03455762058
| t114 = 3.02224725328
| t115 = 1.97398202048
| t116 = 0.0
| t117 = 3.57768274779
| t118 = 2.08171020817
| t119 = 8.67667013339
| t120 = 4.43058673531
| t121 = 6.75150979558
| t122 = 7.50071021167
| t123 = 2.22651393678
| t124 = 0.471070458971
| t125 = 2.74805773078
| t126 = 1.80416017705
| t127 = 3.65458364439
| t128 = 1.39190317827
| t129 = 0.270150889807
| t130 = 0.864298572791
| t131 = 1.26241193081
| t132 = 4.60243804128
| t133 = 4.11567696444
| t134 = 8.82528387595
| t135 = 1.70436480811
| t136 = 3.67836870413
| t137 = 8.60147349544
| t138 = 1.45729868674
| t139 = 6.41361569882
| t140 = 3.91810140097
| t141 = 5.35090869941
| t142 = 0.126059138418
| t143 = 2.31000077542
| t144 = 3.85752038332
| t145 = 3.51486025795
| t146 = 5.5177750081
| t147 = 0.0
| t148 = 0.943921537861
| t149 = 6.84001960239
| t150 = 8.28830373267
| t151 = 4.97466333199
| t152 = 0.29142043499
| t153 = 2.92987873956
| t154 = 5.80535807114
| t155 = 6.45131541862
| t156 = 4.87069155504
| t157 = 4.24050850573
| t158 = 4.28015731503
| t159 = 2.65618512168
| t160 = 7.33817335829
| t161 = 3.17457472268
| t162 = 1.17219564781
| t163 = 7.5167471222
| t164 = 5.21327821765
| t165 = 4.82151100244
| t166 = 2.47973390127
| t167 = 0.0
| t168 = 4.94280810999
| t169 = 6.2664179351
| t170 = 8.59605081102
| t171 = 4.83895512267
| t172 = 3.48004293086
| t173 = 4.45587761343
| t174 = 6.56963994207
| t175 = 2.10441975695
| t176 = 3.58620265722
| t177 = 9.95014539961
| t178 = 0.0
| t179 = 1.60229127027
| t180 = 3.06282725445
| t181 = 2.64972971246
| t182 = 8.90766511272
| t183 = 2.81738838353
| t184 = 1.47823339821
| t185 = 1.62230749649
| t186 = 0.0
| t187 = 8.27204883277
| t188 = 3.34438315067
| t189 = 5.47813591045
| t190 = 3.73227119884
| t191 = 2.04667718591
| t192 = 8.10330742373
| t193 = 7.84895654159
| t194 = 8.68886209099
| t195 = 0.594980682899
| t196 = 1.09338218182
| t197 = 0.0
| t198 = 0.0
| t199 = 2.07516544927
| t200 = 5.36325772249
| t201 = 10.3801320693
| t202 = 7.19706356053
| t203 = 7.38673676707
| t204 = 2.0888528871
| t205 = 4.56097940884
| t206 = 11.2397720483
| t207 = 8.7070923732
| t208 = 1.46418114587
| t209 = 8.1819213208
| t210 = 8.37421731066
| t211 = 8.20443110634
| t212 = 6.25928272579
| t213 = 5.56501289948
| t214 = 3.44261584996
| t215 = 3.03015175046
| t216 = 3.36989515556
| t217 = 1.32230452741
| t218 = 5.99253765351
| t219 = 1.20730895029
| t220 = 2.62499753367
| t221 = 2.78663795286
| t222 = 3.88578158879
| t223 = 1.82502659548
| t224 = 1.76659931366
| t225 = 0.174105005475
| t226 = 4.54296470934
| t227 = 4.29808150495
| t228 = 3.68404184865
| t229 = 1.65082094347
| t230 = 6.44501181769
| t231 = 0.0
| t232 = 3.26177634889
| t233 = 6.81476476556
| t234 = 1.20054376518
| t235 = 3.05738286302
| t236 = 3.38875978873
| t237 = 8.59409652503
| t238 = 8.03167648714
| t239 = 8.38268186139
| t240 = 5.04792089363
| t241 = 3.61412566079
| t242 = 3.18948235385
| t243 = 2.94563089667
| t244 = 6.42201927392
| t245 = 0.67029981411
| t246 = 3.76181232671
| t247 = 4.75777786184
| t248 = 1.40920006722
| t249 = 6.88878136868
| t250 = 0.261784886759
| t251 = 4.8105298737
| t252 = 4.59760038148
| t253 = 0.620390547481
| t254 = 1.20006367773
| t255 = 0.918553144789
| t256 = 5.35489215662
| t257 = 2.38027987589
| t258 = 4.841989242
| t259 = 3.13998346059
| t260 = 6.91552278678
| t261 = 6.74049941659
| t262 = 8.92426539281
| t263 = 8.34509433125
| t264 = 5.92186138715
| t265 = 0.929079736215
| t266 = 1.27000252435
| t267 = 0.542438034903
| t268 = 8.12343730529
| t269 = 7.86967196731
| t270 = 8.78424296565
| t271 = 3.4601687119
| t272 = 2.07153058451
| t273 = 2.78515745663
| t274 = 4.38999403629
| t275 = 1.14549831462
| t276 = 0.0
| t277 = 2.37828870687
| t278 = 7.38210546112
| t279 = 6.69059903673
| t280 = 8.83459265736
| t281 = 1.38298352289
| t282 = 0.0
| t283 = 7.78739898008
| t284 = 7.96530840055
| t285 = 2.32530897422
| t286 = 7.5127999122
| t287 = 8.23205016039
| t288 = 3.0899389631
| t289 = 6.72444604677
| t290 = 3.3095529593
| t291 = 5.36363657797
| t292 = 4.02123934799
| t293 = 3.4319397897
| t294 = 6.06680067517
| t295 = 5.85793251616
| t296 = 8.44662331134
| t297 = 10.0848105427
| t298 = 0.324375905068
| t299 = 3.04210896804
| t300 = 3.93411126658
| t301 = 3.59479233327
| t302 = 0.0
| t303 = 0.21598547498
| t304 = 6.68428704244
| t305 = 1.83359650234
| t306 = 0.0
| t307 = 4.86690649253
| t308 = 2.1141196399
| t309 = 0.0857125384894
| t310 = 8.57332225865
| t311 = 7.94790745239
| t312 = 3.25596340978
| t313 = 6.59736237603
| t314 = 9.80154869706
| t315 = 4.22555253334
| t316 = 9.28090546987
| t317 = 7.26474535027
| t318 = 4.16006293428
| t319 = 0.0
| t320 = 1.5416757695
| t321 = 2.02817113857
| t322 = 3.31942729985
| t323 = 4.1275860303
| t324 = 3.3904085253
| t325 = 7.83874563833
| t326 = 4.06724764902
| t327 = 7.07416602773
| t328 = 1.05886269196
| t329 = 0.0
| t330 = 7.87203731499
| t331 = 0.0949950504521
| t332 = 1.76558687885
| t333 = 0.705182889719
| t334 = 7.46933162584
| t335 = 0.0
| t336 = 6.83697987825
| t337 = 4.47731013186
| t338 = 1.50151935762
| t339 = 6.89825235588
| t340 = 7.92797054192
| t341 = 7.9949548889
| t342 = 1.19162626253
| t343 = 10.5830879781
| t344 = 8.60585337396
| t345 = 6.81418033705
| t346 = 6.67283045844
| t347 = 1.50924332032
| t348 = 5.28999608976
| t349 = 0.170000961765
| t350 = 6.48003170544
| t351 = 0.0
| t352 = 5.69481866765
| t353 = 3.53797486695
| t354 = 0.0456336083363
| t355 = 0.0
| t356 = 5.55837003771
| t357 = 7.60829796131
| t358 = 0.0
| t359 = 4.86712712151
| t360 = 8.32684692791
| t361 = 1.69911455046
| t362 = 0.0
| t363 = 5.54197913387
| t364 = 2.10361984224
| t365 = 8.95667930323
| t366 = 0.708444668239
| t367 = 5.9822253288
| t368 = 7.24240162465
| t369 = 6.362214142
| t370 = 4.72333007771
| t371 = 7.99486704944
| t372 = 8.21879074241
| t373 = 5.34806724153
| t374 = 4.45246624663
| t375 = 10.4108990776
| t376 = 2.93495421963
| t377 = 2.48601553293
| t378 = 1.52394696843
| t379 = 4.24028980766
| t380 = 0.649395046455
| t381 = 5.06431093936
| t382 = 1.16611147095
| t383 = 4.46880584182
| t384 = 2.80341497242
| t385 = 8.80775932129
| t386 = 6.29571119056
| t387 = 0.987920106695
| t388 = 9.09500062785
| t389 = 1.69426489712
| t390 = 3.29346040417
| t391 = 8.8957143315
| t392 = 0.854844940766
| t393 = 6.69994821388
| t394 = 10.7049204318
| t395 = 3.39291875092
| t396 = 0.0
| t397 = 2.57513079693
| t398 = 0.57973356989
| t399 = 4.98102948385
| t400 = 1.44959829311
| t401 = 6.28033341727
| t402 = 1.17920889765
| t403 = 0.0
| t404 = 7.05568015162
| t405 = 0.0
| t406 = 0.0
| t407 = 6.57637070623
| t408 = 5.2937388012
| t409 = 5.4728031878
| t410 = 2.62730019711
| t411 = 8.92854347616
| t412 = 4.20714174738
| t413 = 4.47186007625
| t414 = 2.5430948433
| t415 = 5.60054775711
| t416 = 0.0
| t417 = 4.254375913
| t418 = 7.30632938892
| t419 = 7.95252692428
| t420 = 6.8392497882
| t421 = 1.75430649915
| t422 = 0.0
| t423 = 3.03021899432
| t424 = 4.7144441217
| t425 = 2.9939189522
| t426 = 0.18607136459
| t427 = 0.494120932897
| t428 = 4.67281047597
| t429 = 4.39755734624
| t430 = 0.0
| t431 = 1.81424222286
| t432 = 0.977689768571
| t433 = 2.86227294655
| t434 = 2.78817920712
| t435 = 4.98348927638
| t436 = 4.12204655374
| t437 = 7.92146011968
| t438 = 3.5104112365
| t439 = 8.26955973133
| t440 = 7.07859147438
| t441 = 3.40179306785
| t442 = 6.04278157155
| t443 = 0.246381260618
| t444 = 5.28851265137
| t445 = 0.0
| t446 = 1.63522792626
| t447 = 8.98993383984
| t448 = 1.46599387766
| t449 = 4.8484521027
| t450 = 2.15397680665
| t451 = 8.86873496019
| t452 = 3.98225654463
| t453 = 4.76742260386
| t454 = 1.74520969241
| t455 = 7.85403839559
| t456 = 1.01745597543
| t457 = 0.0
| t458 = 7.08529026042
| t459 = 0.395925458429
| t460 = 2.53448672257
| t461 = 0.991381485969
| t462 = 8.19517817632
| t463 = 7.36827015582
| t464 = 0.941551949118
| t465 = 4.22409316651
| t466 = 4.75826544482
| t467 = 9.91674418877
| t468 = 7.11401448482
| t469 = 2.37307858605
| t470 = 8.88960868273
| t471 = 8.25211713148
| t472 = 6.64144991724
| t473 = 0.983911806432
| t474 = 3.14673639877
| t475 = 7.02722343446
| t476 = 7.04718138367
| t477 = 4.77055967422
| t478 = 6.78291850447
| t479 = 9.56998983443
| t480 = 8.95467626863
| t481 = 6.34010923623
| t482 = 2.01639597761
| t483 = 9.78007213866
| t484 = 7.50587760065
| t485 = 7.87846165258
| t486 = 0.0
| t487 = 1.53143410725
| t488 = 0.0
| t489 = 2.32027356727
| t490 = 0.866920826013
| t491 = 8.83354097283
| t492 = 9.83202861151
| t493 = 5.96407103391
| t494 = 2.70875474461
| t495 = 6.66018766835
| t496 = 4.79199591082
| t497 = 6.95883752387
| t498 = 8.18787314259
| t499 = 5.79234093104
| t500 = 1.7166375613
*************************************************************************
| Objective Value ------------------ 7.06662419245
| Aij Sum -------------------------- 6755703
| Cj Sum --------------------------- 7296
| Bi Sum --------------------------- 7333
| Matrix Dimensions ---------------- (500, 500)
| Date/Time ------------------------ 2015-08-20 16:18:37.851467
*************************************************************************
-- Gurobi Standard Dual Linear Programming Problem --
James Gaboardi, 2015
Content source: jGaboardi/LP_MIP
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