Program execution

If you have followed the standard installation procedure of Python and the xpress package, you can run this file with the following command:

python Folio.py

Running the program generates the following output:

Maximizing LP Folio using up to 20 threads and up to 31GB memory, with these control settings:
OUTPUTLOG = 1
NLPPOSTSOLVE = 1
XSLP_DELETIONCONTROL = 0
XSLP_OBJSENSE = -1
Original problem has:
         3 rows           10 cols           19 elements
Presolved problem has:
         3 rows           10 cols           19 elements
Presolve finished in 0 seconds
Heap usage: 396KB (peak 410KB, 85KB system)

Coefficient range                    original                 solved
  Coefficients   [min,max] : [ 1.00e+00,  1.00e+00] / [ 1.00e+00,  1.00e+00]
  RHS and bounds [min,max] : [ 3.00e-01,  1.00e+00] / [ 3.00e-01,  1.00e+00]
  Objective      [min,max] : [ 5.00e+00,  3.10e+01] / [ 5.00e+00,  3.10e+01]
Autoscaling applied standard scaling


   Its         Obj Value      S   Ninf  Nneg   Sum Dual Inf  Time
     0         42.600000      D      2     0        .000000     0
     5         14.066667      D      0     0        .000000     0
Uncrunching matrix
Optimal solution found
Dual solved problem
  5 simplex iterations in 0.00 seconds at time 0

Final objective                       : 1.406666666666666e+01
  Max primal violation      (abs/rel) :       0.0 /       0.0
  Max dual violation        (abs/rel) :       0.0 /       0.0
  Max complementarity viol. (abs/rel) :       0.0 /       0.0
Problem status:
	 Solve status: COMPLETED
	 Sol status:     OPTIMAL
Total return: 14.066666666666665
frac(0) : 30.00 %
frac(1) : 0.00 %
frac(2) : 20.00 %
frac(3) : 0.00 %
frac(4) : 6.67 %
frac(5) : 30.00 %
frac(6) : 0.00 %
frac(7) : 0.00 %
frac(8) : 13.33 %
frac(9) : 0.00 %

The upper half of this display is the log of Xpress: the size of the matrix, 3 rows (i.e. constraints) and 10 columns (i.e. decision variables), and the log of the LP solution algorithm (in this case, `D' for dual Simplex). The lower half is the output produced by our program: the maximum return of 14.067 is obtained with a portfolio consisting of shares 0, 2, 4, 5, and 8. 30% of the total amount are spent in shares 0 and 5 each, 20% in 2, 13.33% in 8 and 6.67% in 4. It is easily verified that all constraints are indeed satisfied: we have 50% of North American shares (0 and 2) and 33.33% of high-risk shares (2 and 8).

It is possible to modify the amount of output that is printed by adding the following line before the start of the optimization:

p.controls.outputlog = 0

This setting disables all output (including warnings) from Xpress, with the exception of error messages. The possible values for the printing level range from 0 to 4.