Issue on GMPL code

Question

I was trying to solve the following problem, using the GLPSOL solver:

Fred has $5000 to invest over the next five years. At the beginning of each year he can invest money in one- or two-year time deposits. The bank pays 4% interest on one-year time deposits and 9 percent (total) on two-year time deposits. In addition, West World Limited will offer three-year certificates starting at the beginning of the second year. These certificates will return 15% (total). If Fred reinvest his money that is available every year, formulate a linear program to show him how to maximize his total cash on hand at the end of the fifth year.

I came up with the following LP model:

Being x_ij the amount invested in option i at year j, we look to
maximize z = 1,04x₁₅ + 1,09x₂₄ + 1,15x₃₃,
subject to:

• x₁₁ + x₁₂ <= 5000
• x₃₁ = x₃₄ = x₃₅ = 0
• x₁₂ + x₂₂ + x₃₂ <= 1,04 x₁₁
• x₁₃ + x₂₃ + x₃₃ <= 1,04 x₁₂ + 1,09 x₂₁
• x₁₄ + x₂₄ <= 1,04 x₁₃ + 1,09 x₂₂
• x₁₅ <= 1,04 x₁₄ + 1,09 x₂₃ + 1,15 x₃₂
• x_ij >= 0

And tried to write it in GMPL:

/* Variables */
var x{i in 1..3, j in 1..5} >= 0;

/* Objective */
maximize money: 1.04*x[1,5] + 1.09*x[2,4] + 1.15*x[3,3];

/* Constraints */
s.t. x[1,1] + x[2,1] <= 5000;
s.t. x[3,1] = x[3,4] = x[3,5] = 0;
s.t. x[1,2] + x[2,2] + x[3,2] <= 1.04 * x[1,1];
s.t. x[1,3] + x[2,3] + x[3,3] <= 1.04 * x[1,2] + 1.09 * x[2,1];
s.t. x[1,4] + x[2,4] <= 1.04 * x[1,3] + 1.09 * x[2,2];
s.t. x[1,5] <= 1.04 * x[1,4] + 1.09 * x[2,3] + 1.15 * x[3,2];

/* Resolve */
solve;

/* Results */
printf{j in 1..5}:"\n* %.2f %.2f %2.f \n", x[1,j], x[2,j], x[3,j];

end;

However, I'm getting the following error:

inv.mod:14: x multiply declared
Context: ...[ 1 , 5 ] + 1.09 * x [ 2 , 4 ] + 1.15 * x [ 3 , 3 ] ; s.t. x
MathProg model processing error

Does anyone have any thoughts about this?

Answer 1

You have to give a unique name to each constraint. Multiple assignments are not allowed.

This works on my machine:

/* Variables */
var x{i in 1..3, j in 1..5} >= 0;

/* Objective */
maximize money: 1.04*x[1,5] + 1.09*x[2,4] + 1.15*x[3,3];

/* Restrições */
s.t. c1: x[1,1] + x[2,1] <= 5000;
s.t. c2: x[3,1] = 0;
s.t. c3: x[3,4] = 0;
s.t. c4: x[3,5] = 0;
s.t. c5: x[1,2] + x[2,2] + x[3,2] <= 1.04 * x[1,1];
s.t. c6: x[1,3] + x[2,3] + x[3,3] <= 1.04 * x[1,2] + 1.09 * x[2,1];
s.t. c7: x[1,4] + x[2,4] <= 1.04 * x[1,3] + 1.09 * x[2,2];
s.t. c8: x[1,5] <= 1.04 * x[1,4] + 1.09 * x[2,3] + 1.15 * x[3,2];

/* Resolve */
solve;

/* Results */
printf{j in 1..5}:"\n* %.2f %.2f %2.f \n", x[1,j], x[2,j], x[3,j];

end;

It prints:

* 0.00 5000.00  0 

* 0.00 0.00  0 

* 0.00 0.00 5450 

* 0.00 0.00  0 

* 0.00 0.00  0 

Good luck!