Originally posted by: fcimeson

I'm trying to construct a integer program that has a solution of x2 > x1 when x3 = 1, however cplex seems do something odd with the constraint c1 (x2 - x1 + 99 x3 > -99), perhaps it's a rounding error. Is there a different syntax that I can use to express c1 (x2 - x1 + 99 x3 > -99) to get the desired result? Thanks

Problem File

Maximize
 obj: x1 + x2
Subject To
 c1: x2 - x1 + 99 x3 > -99
 c3: x3 = 1
Bounds
 1 <= x1 <= 2
 1 <= x2 <= 2
Binary
 x3
General
 x1
 x2

Solution

MIP - Integer optimal solution:  Objective =  4.0000000000e+00
Solution time =    0.00 sec.  Iterations = 0  Nodes = 0
Deterministic time = 0.00 ticks  (1.11 ticks/sec)

CPLEX> Incumbent solution
Variable Name           Solution Value
x1                            2.000000
x2                            2.000000

Hi

which API do you use ?

in your example, imply is linearized.

You could also in the lp format use indicators.

Let me quote documentation:

MIP indicator constraints

This rule applies to CPLEX MIP optimizer.

To specify an indicator constraint, enter it among any other constraints in the model, like this:

[constraintname:]  binaryvariable = value  ->  linear constraint

The constraint name, followed by a colon, is optional. The hyphen followed by the greater-than symbol (->), separates the indicator variable and its value from the linear constraint that is controlled. The indicator variable must be declared as a binary variable, and the value it is compared to must be either 0 (zero) or 1 (one).

regards

Originally posted by: fcimeson

Thank you, that is helpful.