Syntax error in linear programming modelling with Glpk

Question

Here is my full problem:

Information:

*Max. total investment: $125

*Pay-off is the sum of the units bought x pay-off/unit

*Cost per investment: Buy-in cost + cost/unit x number of units if you buy at least one unit

*The cost is sum of the costs per investment

Constraints:

*You may not invest in both 2 and 5.

*You may invest in 1 only if you invest at least one of 2 and 3.

*You must invest at least two of 3,4,5.

*You may not invest more than max number of units.

Problem: Maximize profit : pay-off - cost

 xi: # of units i ∈ {1,2,3,4,5}
 yi=1 if xi>0 else yi=0
 cost = sum{i in I} buyInCost_i * yi + cost-unit_i*xi
 pay-off = sum{i in I} (pay-off/unit)_i*xi
 profit = pay-off - cost

 Maximize profit

 Subject to

 y2+y5 <= 1
 y1<= y2+y3
 y3+y4+y5 >= 2
 x1<=5, x2<=4, x3<=5, x4<=7, x5<=3
 cost<=125

My modelling :

 set I;

 /*if x[i]>0 y[i]=1 else y[i]=0 ?????*/
 var y{i in I}, binary;

 param a{i in I};
 /* buy-in cost of investment i */

 param b{i in I};
 /* cost per unit of investment i */

 param c{i in I};
 /* pay-off per unit of investment i */

 param d{i in I};
 /* max number of units of investment i */

 var x{i in I} >=0;
 /* Number of units that is bought of investment i */

 var po := sum{i in I} c[i]*x[i];

 var cost := sum{i in I} a[i]*y[i] + b[i]*x[i];

 maximize profit: po-cost;

 s.t. c1: y[2]+y[5]<=1;
 s.t. c2: y[1]<y[2]+y[3];
 s.t. c3: y[3]+y[4]+y[5]>=2;
 s.t. c4: x[1]<=5 
     x[2]<=4
     x[3]<=5
     x[4]<=7
     x[5]<=3;

 s.t. c5: cost <=125;
 s.t. c6{i in I}: M * y[i] > x[i];   // if condition of y[i] 

 set I := 1 2 3 4 5;
 param a :=
1 25
2 35
3 28
4 20
5 40;

 param b :=
1 5
2 7
3 6
4 4
5 8;

 param c :=
1 15
2 25
3 17
4 13
5 18;

 param d :=
1 5
2 4
3 5
4 7
5 3;

 param M := 10000;

I am getting this syntax error:

      problem.mod:21: syntax error in variable statement 
      Context: ...I } ; param d { i in I } ; var x { i in I } >= 0 ; var po :=
      MathProg model processing error

Can you please help me out?

Answer 1

This answer came from Andrew Makhorin from help-glpk@gnu.org

In MathProg you cannot assign a value to a variable.

If you need to fix a variable at some value, you need to use appropriate equality constraint, e.g.

   var po;

   s.t. foo: po = sum{i in I} c[i]*x[i];

   var cost;

   s.t. bar: cost = sum{i in I} a[i]*y[i] + b[i]*x[i];

Answer 2

There are many errors in your MathProg code. This should work:

set I;

param M;

/*if x[i]>0 y[i]=1 else y[i]=0 ?????*/
var y{i in I}, binary;

param a{i in I};
/* buy-in cost of investment i */

param b{i in I};
/* cost per unit of investment i */

param c{i in I};
/* pay-off per unit of investment i */

param d{i in I};
/* max number of units of investment i */

var x{i in I}, >=0;
/* Number of units that is bought of investment i */

var cost, >= 0;

maximize profit: sum{i in I} c[i] * x[i] - sum{i in I} (a[i] * y[i] + b[i] * x[i]);

s.t. c01: y[2] + y[5]<=1;
s.t. c02: y[1] <= y[2]+y[3];
s.t. c03: y[3]+y[4]+y[5]>=2;
s.t. c04: x[1]<=5;
s.t. c05: sum{i in I} (a[i]*y[i] + b[i]*x[i]) <= 125;
s.t. c6{i in I}: M * y[i] >= x[i];   /* if condition of y[i] */
s.t. c10: x[2]<=4;
s.t. c11: x[3]<=5;
s.t. c12: x[4]<=7;
s.t. c13: x[5]<=3;

data;

set I := 1 2 3 4 5;
param a :=
1 25
2 35
3 28
4 20
5 40;

param b :=
1 5
2 7
3 6
4 4
5 8;

param c :=
1 15
2 25
3 17
4 13
5 18;

param d :=
1 5
2 4
3 5
4 7
5 3;

param M := 10000;