I can’t reproduce the hang. I don’t know if this is a HiGHS bug, or just a difficult problem to solve. The hang might have been HiGHS failing to detect some degeneracy or cycling?

```
julia> using HiGHS
julia> h = Highs_create()
Ptr{Nothing} @0x00007fbe7b226200
julia> Highs_readModel(h, "fail.mps")
Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms
Number of PL entries in BOUNDS section is 77760
Number of BV entries in BOUNDS section is 38880
0
julia> Highs_run(h)
Presolving model
34557 rows, 36717 cols, 140387 nonzeros
32397 rows, 34556 cols, 130656 nonzeros
Solving MIP model with:
32397 rows
34556 cols (8639 binary, 0 integer, 0 implied int., 25917 continuous)
130656 nonzeros
Nodes | B&B Tree | Objective Bounds | Dynamic Constraints | Work
Proc. InQueue | Leaves Expl. | BestBound BestSol Gap | Cuts InLp Confl. | LpIters Time
0 0 0 0.00% -33949085.7489 inf inf 0 0 0 0 0.5s
0 0 0 0.00% -11536488.54332 inf inf 0 0 4 29671 3.4s
0 0 0 0.00% -11535621.21849 inf inf 27780 3076 13 36433 10.3s
0 0 0 0.00% -11533277.72074 inf inf 33011 4684 361 41028 17.6s
0 0 0 0.00% -11532089.46961 inf inf 39272 7064 369 46548 23.9s
0 0 0 0.00% -11530464.96164 inf inf 30013 10060 373 54197 32.1s
0 0 0 0.00% -11529769.97896 inf inf 29907 12527 381 61030 40.6s
0 0 0 0.00% -11528704.58719 inf inf 30417 14491 387 66969 48.4s
0 0 0 0.00% -11528067.71604 inf inf 30883 14504 395 71974 56.3s
0 0 0 0.00% -11527614.11118 inf inf 30680 15865 401 76633 64.5s
0 0 0 0.00% -11527471.22196 inf inf 31284 16465 405 79070 69.8s
0 0 0 0.00% -11527395.95402 inf inf 31229 16980 409 81071 75.2s
0 0 0 0.00% -11527316.65888 inf inf 32100 12986 411 83006 81.1s
0 0 0 0.00% -11527141.27824 inf inf 28744 13832 421 86326 90.0s
0 0 0 0.00% -11526904.19827 inf inf 30467 14570 429 89556 97.2s
0 0 0 0.00% -11526692.91617 inf inf 27476 11189 435 92642 103.8s
0 0 0 0.00% -11526217.62272 inf inf 28778 11853 441 95643 110.2s
0 0 0 0.00% -11526042.22932 inf inf 29523 9730 448 98629 116.9s
0 0 0 0.00% -11525591.15637 inf inf 21970 12043 454 104795 125.7s
0 0 0 0.00% -11525462.37326 inf inf 21858 13684 461 110511 133.8s
Nodes | B&B Tree | Objective Bounds | Dynamic Constraints | Work
Proc. InQueue | Leaves Expl. | BestBound BestSol Gap | Cuts InLp Confl. | LpIters Time
0 0 0 0.00% -11525198.98984 inf inf 20109 13303 468 115982 142.2s
0 0 0 0.00% -11525027.39853 inf inf 26182 14520 476 120505 150.4s
0 0 0 0.00% -11524564.44604 inf inf 24240 13815 483 125479 160.8s
0 0 0 0.00% -11524347.82893 inf inf 20714 14360 488 127468 166.3s
0 0 0 0.00% -11524265.45506 inf inf 23209 14853 492 129924 172.3s
0 0 0 0.00% -11524121.06832 inf inf 25798 15361 494 132013 177.7s
0 0 0 0.00% -11524110.68876 inf inf 24514 12646 501 136267 187.1s
0 0 0 0.00% -11524090.11569 inf inf 19274 13086 505 138311 192.1s
0 0 0 0.00% -11524070.90583 inf inf 21276 13488 511 140291 198.0s
0 0 0 0.00% -11524055.07528 inf inf 23417 13909 515 142270 204.4s
0 0 0 0.00% -11524046.45336 inf inf 25378 14334 519 145468 211.1s
0 0 0 0.00% -11524028.69166 inf inf 18428 12017 529 149498 220.3s
L 0 0 0 0.00% -11524028.69166 -11280420.84095 2.16% 18428 12017 559 149498 375.9s
0.2% inactive integer columns, restarting
Model after restart has 31239 rows, 33398 cols (8609 bin., 0 int., 0 impl., 24789 cont.), and 128168 nonzeros
0 0 0 0.00% -11524028.69166 -11280420.84095 2.16% 6850 0 0 269138 376.6s
0 0 0 0.00% -11524028.69166 -11280420.84095 2.16% 6850 3965 3 279771 384.7s
0 0 0 0.00% -11523938.47525 -11280420.84095 2.16% 22878 5856 3 284202 392.2s
0 0 0 0.00% -11523933.14471 -11280420.84095 2.16% 25779 6819 3 287539 398.4s
0 0 0 0.00% -11523867.12579 -11280420.84095 2.16% 28299 8532 3 293082 406.2s
0 0 0 0.00% -11523864.59742 -11280420.84095 2.16% 21953 10468 3 298176 415.0s
```

The problem just looks really hard to solve, so I tried a few other solvers.

## Gurobi

```
(base) oscar@Oscars-MBP models_jump % gurobi_cl fail.mps
Set parameter LogFile to value "gurobi.log"
Using license file /Users/oscar/gurobi.lic
Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (mac64[x86] - Darwin 22.6.0 22G91)
Copyright (c) 2023, Gurobi Optimization, LLC
Read MPS format model from file fail.mps
Reading time = 0.33 seconds
: 147910 rows, 147964 columns, 443732 nonzeros
CPU model: Intel(R) Core(TM) i5-8259U CPU @ 2.30GHz
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 147910 rows, 147964 columns and 443732 nonzeros
Model fingerprint: 0x7c054958
Variable types: 109084 continuous, 38880 integer (38880 binary)
Coefficient statistics:
Matrix range [5e-08, 3e+04]
Objective range [2e-02, 4e+02]
Bounds range [1e+00, 5e+07]
RHS range [1e+00, 5e+07]
Presolve removed 117910 rows and 114756 columns
Presolve time: 1.19s
Presolved: 30000 rows, 33208 columns, 124257 nonzeros
Variable types: 24658 continuous, 8550 integer (8550 binary)
Deterministic concurrent LP optimizer: primal and dual simplex
Showing primal log only...
Concurrent spin time: 0.00s
Solved with dual simplex
Extra simplex iterations after uncrush: 40
Root relaxation: objective -1.153649e+07, 21304 iterations, 1.92 seconds (1.00 work units)
Total elapsed time = 5.29s (DegenMoves)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 -1.154e+07 0 865 - -1.154e+07 - - 5s
0 0 -1.154e+07 0 1462 - -1.154e+07 - - 9s
0 0 -1.154e+07 0 1459 - -1.154e+07 - - 9s
0 0 -1.154e+07 0 1487 - -1.154e+07 - - 10s
0 0 -1.154e+07 0 1487 - -1.154e+07 - - 10s
0 0 -1.154e+07 0 1419 - -1.154e+07 - - 13s
0 0 -1.154e+07 0 1416 - -1.154e+07 - - 13s
0 0 -1.153e+07 0 1427 - -1.153e+07 - - 14s
0 0 -1.153e+07 0 1425 - -1.153e+07 - - 14s
0 0 -1.153e+07 0 1390 - -1.153e+07 - - 16s
0 0 -1.153e+07 0 1395 - -1.153e+07 - - 17s
0 0 -1.153e+07 0 1391 - -1.153e+07 - - 17s
0 0 -1.153e+07 0 1393 - -1.153e+07 - - 17s
0 0 -1.153e+07 0 1448 - -1.153e+07 - - 19s
0 0 -1.153e+07 0 687 - -1.153e+07 - - 25s
0 2 -1.153e+07 0 679 - -1.153e+07 - - 33s
11 16 -1.153e+07 4 1058 - -1.153e+07 - 789 35s
116 215 -1.153e+07 26 880 - -1.153e+07 - 411 40s
482 611 -1.153e+07 106 764 - -1.153e+07 - 151 45s
908 1031 -1.138e+07 199 848 - -1.153e+07 - 101 51s
1144 1371 -1.151e+07 223 701 - -1.153e+07 - 98.4 55s
1863 2012 infeasible 482 - -1.153e+07 - 67.3 60s
2394 2626 -1.148e+07 594 384 - -1.153e+07 - 68.6 66s
2961 2993 -1.153e+07 10 985 - -1.153e+07 - 59.2 70s
3572 3655 -1.153e+07 64 805 - -1.153e+07 - 56.6 76s
H 3920 3905 -1.13678e+07 -1.153e+07 1.46% 55.1 78s
* 3946 3874 1010 -1.14123e+07 -1.153e+07 1.07% 54.8 78s
H 4114 3987 -1.14154e+07 -1.153e+07 1.04% 53.5 81s
H 4151 3946 -1.14163e+07 -1.153e+07 1.03% 53.7 81s
H 4263 3946 -1.14180e+07 -1.153e+07 1.02% 53.4 81s
H 4506 4390 -1.14212e+07 -1.153e+07 0.99% 53.3 86s
H 4560 4265 -1.14305e+07 -1.153e+07 0.91% 53.0 86s
H 4657 4250 -1.14362e+07 -1.153e+07 0.86% 52.9 86s
H 4851 4500 -1.14395e+07 -1.153e+07 0.83% 51.1 89s
H 4891 4265 -1.14797e+07 -1.153e+07 0.47% 51.2 89s
H 4953 4250 -1.14920e+07 -1.153e+07 0.37% 51.3 89s
5089 4422 -1.150e+07 253 824 -1.149e+07 -1.153e+07 0.37% 50.0 92s
H 5146 4421 -1.14920e+07 -1.153e+07 0.37% 49.7 92s
H 5320 1569 -1.15152e+07 -1.153e+07 0.16% 49.7 97s
5321 1551 -1.153e+07 58 687 -1.152e+07 -1.153e+07 0.16% 49.7 104s
5323 1552 -1.152e+07 43 868 -1.152e+07 -1.152e+07 0.06% 49.7 113s
5324 1553 -1.152e+07 103 625 -1.152e+07 -1.152e+07 0.05% 49.6 120s
5327 1555 -1.152e+07 149 425 -1.152e+07 -1.152e+07 0.05% 49.6 129s
5328 1556 -1.152e+07 39 479 -1.152e+07 -1.152e+07 0.05% 49.6 130s
5329 1556 -1.152e+07 199 371 -1.152e+07 -1.152e+07 0.05% 49.6 136s
5331 1558 -1.152e+07 112 343 -1.152e+07 -1.152e+07 0.05% 49.6 143s
5333 1559 -1.152e+07 176 324 -1.152e+07 -1.152e+07 0.05% 49.6 149s
5334 1560 -1.152e+07 136 342 -1.152e+07 -1.152e+07 0.05% 49.6 150s
5336 1561 -1.152e+07 69 312 -1.152e+07 -1.152e+07 0.05% 49.5 161s
5337 1562 -1.152e+07 174 312 -1.152e+07 -1.152e+07 0.05% 49.5 166s
5340 1569 -1.152e+07 14 394 -1.152e+07 -1.152e+07 0.05% 59.8 171s
5348 1574 -1.152e+07 15 400 -1.152e+07 -1.152e+07 0.05% 61.4 177s
5352 1577 -1.152e+07 16 484 -1.152e+07 -1.152e+07 0.05% 61.9 180s
5364 1585 -1.152e+07 17 431 -1.152e+07 -1.152e+07 0.05% 62.8 187s
5376 1594 -1.152e+07 19 523 -1.152e+07 -1.152e+07 0.05% 63.6 191s
5387 1609 -1.152e+07 20 525 -1.152e+07 -1.152e+07 0.05% 64.1 195s
5401 1618 -1.152e+07 21 442 -1.152e+07 -1.152e+07 0.05% 64.5 200s
5442 1626 -1.152e+07 27 435 -1.152e+07 -1.152e+07 0.05% 65.0 205s
5511 1672 -1.152e+07 37 399 -1.152e+07 -1.152e+07 0.05% 65.9 211s
5633 1763 -1.152e+07 57 401 -1.152e+07 -1.152e+07 0.05% 66.0 218s
5836 1760 -1.152e+07 86 251 -1.152e+07 -1.152e+07 0.05% 67.3 223s
5939 1898 -1.152e+07 102 241 -1.152e+07 -1.152e+07 0.05% 69.3 229s
6144 2016 -1.152e+07 128 205 -1.152e+07 -1.152e+07 0.05% 69.8 234s
6375 2111 -1.152e+07 158 187 -1.152e+07 -1.152e+07 0.05% 69.7 239s
6612 2127 -1.152e+07 191 175 -1.152e+07 -1.152e+07 0.05% 69.1 244s
6800 2103 -1.152e+07 221 178 -1.152e+07 -1.152e+07 0.05% 70.2 249s
6914 2155 cutoff 248 -1.152e+07 -1.152e+07 0.05% 71.7 254s
7093 2217 -1.152e+07 23 479 -1.152e+07 -1.152e+07 0.05% 73.5 261s
H 7201 2032 -1.15155e+07 -1.152e+07 0.04% 74.3 261s
^C
Interrupt request received
```

## SCIP

I needed to turn off `heuristics/feaspump`

or it would get stuck.

```
(base) oscar@Oscars-MBP models_jump % scip -s scip.set -f fail.mps
SCIP version 7.0.3 [precision: 8 byte] [memory: block] [mode: optimized] [LP solver: SoPlex 5.0.2] [GitHash: 74c11e60cd]
Copyright (C) 2002-2021 Konrad-Zuse-Zentrum fuer Informationstechnik Berlin (ZIB)
External libraries:
SoPlex 5.0.2 Linear Programming Solver developed at Zuse Institute Berlin (soplex.zib.de) [GitHash: e24c304e]
CppAD 20180000.0 Algorithmic Differentiation of C++ algorithms developed by B. Bell (www.coin-or.org/CppAD)
ZLIB 1.2.11 General purpose compression library by J. Gailly and M. Adler (zlib.net)
GMP 6.2.1 GNU Multiple Precision Arithmetic Library developed by T. Granlund (gmplib.org)
ZIMPL 3.4.0 Zuse Institute Mathematical Programming Language developed by T. Koch (zimpl.zib.de)
PaPILO 1.0.2 parallel presolve for integer and linear optimization [GitHash: e567fef]
bliss 0.73.3p Computing Graph Automorphism Groups by T. Junttila and P. Kaski (http://www.tcs.hut.fi/Software/bliss/)
Ipopt 3.14.1 Interior Point Optimizer developed by A. Waechter et.al. (www.coin-or.org/Ipopt)
reading user parameter file <scip.set>
read problem <fail.mps>
============
original problem has 147964 variables (38880 bin, 0 int, 0 impl, 109084 cont) and 147910 constraints
solve problem
=============
presolving:
(round 1, fast) 55129 del vars, 32414 del conss, 0 add conss, 28092 chg bounds, 0 chg sides, 1080 chg coeffs, 0 upgd conss, 0 impls, 8634 clqs
(round 2, fast) 72942 del vars, 81521 del conss, 0 add conss, 35481 chg bounds, 1080 chg sides, 3240 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 3, fast) 98298 del vars, 98246 del conss, 0 add conss, 38374 chg bounds, 1080 chg sides, 3240 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 4, fast) 102614 del vars, 98246 del conss, 0 add conss, 41965 chg bounds, 1080 chg sides, 3240 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(1.3s) running MILP presolver
(1.4s) MILP presolver (5 rounds): 1082 aggregations, 0 fixings, 4333 bound changes
(round 5, medium) 103696 del vars, 98246 del conss, 0 add conss, 46314 chg bounds, 1080 chg sides, 3240 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 6, fast) 103696 del vars, 99328 del conss, 0 add conss, 46315 chg bounds, 1080 chg sides, 4330 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 7, fast) 103696 del vars, 99328 del conss, 0 add conss, 72211 chg bounds, 1080 chg sides, 4330 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 8, fast) 116644 del vars, 112276 del conss, 0 add conss, 72211 chg bounds, 1080 chg sides, 4330 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(1.7s) running MILP presolver
(1.8s) MILP presolver (4 rounds): 1082 aggregations, 0 fixings, 0 bound changes
(round 9, medium) 117726 del vars, 112276 del conss, 0 add conss, 72211 chg bounds, 1080 chg sides, 4330 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 10, fast) 117726 del vars, 113357 del conss, 0 add conss, 72211 chg bounds, 1080 chg sides, 4330 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 11, exhaustive) 117726 del vars, 113358 del conss, 0 add conss, 72211 chg bounds, 1080 chg sides, 4330 chg coeffs, 3240 upgd conss, 0 impls, 0 clqs
(round 12, exhaustive) 117726 del vars, 113358 del conss, 0 add conss, 72211 chg bounds, 1080 chg sides, 4330 chg coeffs, 4317 upgd conss, 3240 impls, 0 clqs
(2.1s) sparsify finished: 3240/142541 (2.3%) nonzeros canceled - in total 3240 canceled nonzeros, 8640 changed coefficients, 0 added nonzeros
(2.2s) probing: 51/8640 (0.6%) - 0 fixings, 0 aggregations, 0 implications, 0 bound changes
(2.2s) probing aborted: 50/50 successive totally useless probings
(2.3s) symmetry computation started: requiring (bin +, int -, cont +), (fixed: bin -, int +, cont -)
(2.4s) no symmetry present
presolving (13 rounds: 13 fast, 5 medium, 3 exhaustive):
117726 deleted vars, 113358 deleted constraints, 0 added constraints, 72211 tightened bounds, 0 added holes, 1080 changed sides, 12970 changed coefficients
4317 implications, 0 cliques
presolved problem has 36712 variables (8640 bin, 0 int, 0 impl, 28072 cont) and 34552 constraints
4317 constraints of type <varbound>
30235 constraints of type <linear>
Presolving Time: 2.04
time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl.
52.1s| 1 | 0 | 46718 | - | 623M | 0 | 36k| 34k| 34k| 0 | 0 | 1 | 0 |-1.153649e+07 | -- | Inf | unknown
65.0s| 1 | 0 | 46727 | - | 630M | 0 | 36k| 34k| 34k| 4 | 1 | 2 | 0 |-1.153649e+07 | -- | Inf | unknown
68.0s| 1 | 0 | 46990 | - | 634M | 0 | 36k| 34k| 34k| 125 | 2 | 3 | 0 |-1.153649e+07 | -- | Inf | unknown
70.6s| 1 | 0 | 47228 | - | 638M | 0 | 36k| 34k| 34k| 248 | 3 | 4 | 0 |-1.153649e+07 | -- | Inf | unknown
73.6s| 1 | 0 | 47285 | - | 641M | 0 | 36k| 34k| 34k| 270 | 4 | 5 | 0 |-1.153649e+07 | -- | Inf | unknown
76.5s| 1 | 0 | 47364 | - | 645M | 0 | 36k| 34k| 34k| 309 | 5 | 6 | 0 |-1.153649e+07 | -- | Inf | unknown
79.6s| 1 | 0 | 47393 | - | 650M | 0 | 36k| 34k| 34k| 321 | 6 | 7 | 0 |-1.153649e+07 | -- | Inf | unknown
82.9s| 1 | 0 | 47723 | - | 654M | 0 | 36k| 34k| 34k| 442 | 7 | 8 | 0 |-1.153649e+07 | -- | Inf | unknown
86.1s| 1 | 0 | 47904 | - | 657M | 0 | 36k| 34k| 35k| 511 | 8 | 9 | 0 |-1.153649e+07 | -- | Inf | unknown
89.7s| 1 | 0 | 48032 | - | 661M | 0 | 36k| 34k| 35k| 545 | 9 | 10 | 0 |-1.153649e+07 | -- | Inf | unknown
93.4s| 1 | 0 | 48055 | - | 664M | 0 | 36k| 34k| 35k| 557 | 10 | 11 | 0 |-1.153649e+07 | -- | Inf | unknown
95.6s| 1 | 0 | 48172 | - | 668M | 0 | 36k| 34k| 35k| 627 | 11 | 12 | 0 |-1.153649e+07 | -- | Inf | unknown
96.4s| 1 | 0 | 48172 | - | 669M | 0 | 36k| 34k| 35k| 627 | 11 | 13 | 0 |-1.153649e+07 | -- | Inf | unknown
97.8s| 1 | 0 | 48175 | - | 673M | 0 | 36k| 34k| 35k| 629 | 12 | 13 | 0 |-1.153649e+07 | -- | Inf | unknown
^Cpressed CTRL-C 1 times (5 times for forcing termination)
99.8s| 1 | 0 | 48253 | - | 676M | 0 | 36k| 34k| 35k| 673 | 13 | 14 | 0 |-1.153649e+07 | -- | Inf | unknown
```

## Comments

They all struggle to solve this problem. So

- The LP relaxation is very close to optimal
- The solver has a hard time finding a feasible solution
- The first feasible solution found is very close to optimal

You can probably make much better progress if you:

- Provide a feasible starting point
- Consider other formulations of your problem. What is it modeling and how?