Gurobi/Example
We are using the example from the gurobi website
http://www.gurobi.com/documentation/7.0/quickstart_linux/solving_a_simple_model_the.html
to demonstrate how to solve a simple model.
Imagine that it is the end of the calendar year at the United States Mint. The Mint keeps an inventory of the various minerals used to produce the coins that are put into circulation, and it wants to use up the minerals on hand before retooling for next year's coins.
The Mint produces several different types of coins, each with a different composition. The table below shows the make-up of each coin type (as reported in the US Mint coin specifications).
Penny Nickel Dime Quarter Dollar Copper (Cu) 0.06g 3.8g 2.1g 5.2g 7.2g Nickel (Ni) 1.2g 0.2g 0.5g 0.2g Zinc (Zi) 2.4g 0.5g Manganese (Mn) 0.3g
For our example, we'll assume we have 1000 grams of copper and 50 grams of the other minerals. Suppose the Mint wants to use the available materials to produce coins with the maximum total dollar value. Which coins should they produce?
The corresponding gurobi input file looks like
[leonhard@eu-login-10 ~]$ cat coins.lp Maximize .01 Pennies + .05 Nickels + .1 Dimes + .25 Quarters + 1 Dollars Subject To Copper: .06 Pennies + 3.8 Nickels + 2.1 Dimes + 5.2 Quarters + 7.2 Dollars - Cu = 0 Nickel: 1.2 Nickels + .2 Dimes + .5 Quarters + .2 Dollars - Ni = 0 Zinc: 2.4 Pennies + .5 Dollars - Zi = 0 Manganese: .3 Dollars - Mn = 0 Bounds Cu <= 1000 Ni <= 50 Zi <= 50 Mn <= 50 Integers Pennies Nickels Dimes Quarters Dollars End [leonhard@eu-login-10 ~]$
The job is then submitted using the gurobi command line interface:
[leonhard@eu-login-10 ~]$ bsub -n 1 -W 0:10 -R "rusage[mem=512]" "gurobi_cl ResultFile=coins.sol coins.lp" Generic job. Job <60506881> is submitted to queue <normal.4h>. [leonhard@eu-login-10 ~]$ bjobs JOBID USER STAT QUEUE FROM_HOST EXEC_HOST JOB_NAME SUBMIT_TIME 60506881 Leonhard PEND normal.4h eu-login-10 * coins.lp Apr 4 13:21 [leonhard@eu-login-10 ~]$ bjobs JOBID USER STAT QUEUE FROM_HOST EXEC_HOST JOB_NAME SUBMIT_TIME 60506881 Leonhard RUN normal.4h eu-login-10 eu-ms-013-0 * coins.lp Apr 4 13:21 [leonhard@eu-login-10 ~]$ bjobs No unfinished job found
The solution is then written to the file coins.sol:
[leonhard@eu-login-10 ~]$ cat coins.sol # Objective value = 113.45 Pennies 0 Nickels 0 Dimes 2 Quarters 53 Dollars 100 Cu 999.8 Ni 46.9 Zi 50 Mn 30 [leonhard@eu-login-10 ~]$
The LSF logs are written to the corresponding log file lsf.o60506881