The final step in solving our optimization problem is to pass the model to the Gurobi Optimizer. We'll use the Gurobi command-line interface, as it is typically the simplest of our interfaces to use when solving a model stored in a file.
To use the command-line interface, you'll first need to bring up a window that allows you to run command-line programs. On a Linux system, you can use a Terminal window. (Note that the Gurobi Interactive Shell, which was used earlier to test your license, does not directly accept command-line program input).
The name of the Gurobi command-line tool is gurobi_cl. To invoke it, type gurobi_cl, followed by the name of the model file. For example, if our model is stored in the file /opt/gurobi1001/linux64/examples/data/coins.lp, you would type the following command into your command-line window...
> gurobi_cl /opt/gurobi1001/linux64/examples/data/coins.lp
This command should produce the following output...
Set parameter LogFile to value "gurobi.log"
Using license file /opt/gurobi/gurobi.lic
Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (linux64)
Copyright (c) 2023, Gurobi Optimization, LLC
Read LP format model from file /opt/gurobi1001/linux64/examples/data/coins.lp
Reading time = 0.00 seconds
: 4 rows, 9 columns, 16 nonzeros
CPU model: 11th Gen Intel(R) Core(TM) i7-1185G7 @ 3.00GHz, instruction set [SSE2]
Thread count: 4 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 4 rows, 9 columns and 16 nonzeros
Model fingerprint: 0x06e334a4
Variable types: 4 continuous, 5 integer (0 binary)
Coefficient statistics:
Matrix range [6e-02, 7e+00]
Objective range [1e-02, 1e+00]
Bounds range [5e+01, 1e+03]
RHS range [0e+00, 0e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 1 rows and 5 columns
Presolve time: 0.00s
Presolved: 3 rows, 4 columns, 9 nonzeros
Variable types: 0 continuous, 4 integer (0 binary)
Found heuristic solution: objective 26.1000000
Root relaxation: objective 1.134615e+02, 2 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 113.46153 0 1 26.10000 113.46153 335% - 0s
H 0 0 113.3000000 113.46153 0.14% - 0s
H 0 0 113.4500000 113.46153 0.01% - 0s
0 0 113.46153 0 1 113.45000 113.46153 0.01% - 0s
Explored 1 nodes (2 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 4: 113.45 113.3 26.1 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.134500000000e+02, best bound 1.134500000000e+02, gap 0.0000%
Details on the format of the Gurobi log file can be found in the Gurobi Reference Manual. For now, you can simply note that the optimal objective value is 113.45. Recall that the objective is denoted in dollars. We can therefore conclude that by a proper choice of production plan, the Mint can produce $113.45 worth of coins using the available minerals. Moreover, because this value is optimal, we know that it is not possible to produce coins with value greater than $113.45!
It would clearly be useful to know the exact number of each coin produced by this optimal plan. The gurobi_cl command allows you to set Gurobi parameters through command-line arguments. One particularly useful parameter for the purposes of this example is ResultFile, which instructs the Gurobi Optimizer to write a file once optimization is complete. The type of the file is encoded in the suffix. To request a .sol file:
> gurobi_cl ResultFile=coins.sol /opt/gurobi1001/linux64/examples/data/coins.lp
The command will produce a file that contains solution values for the variables in the model:
# Objective value = 113.45 Pennies 0 Nickels 0 Dimes 2 Quarters 53 Dollars 100 Cu 999.8 Ni 46.9 Zi 50 Mn 30
In the optimal solution, we'll produce 100 dollar coins, 53 quarters, and 2 dimes.
If we wanted to explore the parameters of the model (for example, to consider how the optimal solution changes with different quantities of available minerals), we could use a text editor to modify the input file. However, it is typically better to do such tests within a more powerful system, such as the Interactive Shell.
Previous: Coins Tutorial: The Model File
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