Getting "DUAL_INFEASIBLE" when solving a very simple linear programming problem

Hongyu 0
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I am solving a simple LP problem using Gurobi with dual simplex and presolve. I get the model is unbounded but I couldn't see why such a model is unbounded. Can anyone help to tell me where goes wrong?

I attached the log and also the content in the .mps file.

Thanks very much in advance.

Kind regards,

Hongyu.

The output log and .mps file:

Link to the .mps file: https://studntnu-my.sharepoint.com/:u:/g/personal/hongyuzh_ntnu_no/EV5CBhH2VshForCL-EtPvBUBiFT8uZZkv-DrPtjSFi8PGA?e=VHktwf

Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (mac64[arm])
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 1 rows, 579 columns and 575 nonzeros
Coefficient statistics:
  Matrix range     [3e-02, 5e+01]
  Objective range  [7e-01, 5e+01]
  Bounds range     [0e+00, 0e+00]
  RHS range        [7e+03, 7e+03]
Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0      handle free variables                          0s

Solved in 0 iterations and 0.00 seconds (0.00 work units)
Unbounded model
linear-programming gurobi optimization
1 Answers

The easiest way to debug this is to put a bound on the objective, so the model is no longer unbounded. Then inspect the solution. This is a super easy trick that somehow few people know about.

When we do this with a bound of 100000, we see:

 phi = 100000.0000
 gamma[11] = -1887.4290

(the rest zero). Indeed we can make gamma[11] as negative as we want to obey R0. Note that gamma[11] is not in the objective.

More advice: It is also useful to write out the LP file of the model and study that carefully. You probably would have caught the error and that would have prevented this post.

Erwin Kalvelagen0
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