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 Mac 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
invoke it, type
gurobi_cl, followed by the name of the model file.
For example, if our model is stored in the file
/Library/gurobi752/mac64/examples/data/coins.lp, you would type the following command into your
This command should produce the following output...
Read LP format model from file /Library/gurobi752/mac64/examples/data/coins.lp
Reading time = 0.01 seconds : 4 rows, 9 columns, 16 nonzeros Optimize a model with 4 rows, 9 columns and 16 nonzeros 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 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) Root relaxation: objective 1.134615e+02, 3 iterations, 0.00 seconds Nodes | Current Node | Objective Bounds | Work Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time 0 0 113.46154 0 1 -0.00000 113.46154 - - 0s H 0 0 113.4500000 113.46154 0.01% - 0s Explored 0 nodes (3 simplex iterations) in 0.00 seconds Thread count was 8 (of 8 available processors) Solution count 2: 113.45 -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
> gurobi_cl ResultFile=coins.sol coins.lpThe 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 30In 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. We'll now describe the Gurobi Interactive Shell, which provides an environment for creating, modifying, and experimenting with optimization models.