GLPK/Conditional Constraints

Constraints depending on a parameter

Sometimes constraints shall only be active if a condition is met which can be expressed by a parameter.

The following is not legal GMPL:

if (flag) {
    s.t. c : x <= 5;
} else {
    s.t. c : x <= 3;
}

But we can model it in GMPL as follows:

/*
 * This model demonstrates how to let the existence of simple constraints
 * depend on a parameter.
 */

/* This flag controls if constraint c0 or contraint c1 is active */
param flag := 1;

var x;

maximize obj: x;

s.t. c0{i in {1} : flag == 0} : x <= 3;
s.t. c1{i in {1} : flag == 1} : x <= 5;

solve;

display x;

end;

We can do the same for indexed conditions:

/*
 * This model demonstrates how to let the existence of indexed constraints
 * depend on a parameter.
 */

/* This flag controls if constraint c0 or contraint c1 is active */
param flag := 0;

set I := {1..3};
var x{I}, <= 10; 

maximize obj: sum{i in I} x[i];

s.t. c0{i in I : i < 3 && flag == 0} : x[i] <= 3;
s.t. c1{i in I : i > 1 && flag == 1} : x[i] <= 5;

solve;

display x;

end;

Constraints depending on a binary variable

If the relevance of constraints shall depend on a binary variable, we can use a BigM approach:

/*
 * This model demonstrates how to let the relevance of indexed constraints
 * depend on a binary variable.
 */

/* Big M, chosen as small as possible */
param M := 7;

set I := {1..3};
var x{I}, <= 10; 

/* Binary variable controlling which constraint is active */
var y, binary;

maximize obj: sum{i in I} x[i];

s.t. c0{i in I : i < 2} : x[i] <= 3 + M * y;
s.t. c1{i in I : i > 1} : x[i] <= 5 + M * (1 - y); 

solve;

display x, y;

end;