Originally posted by: Chrisontherun

I encountered trouble when posting big-M constraints in CPLEX on C# environment, here's my case:

the constraint I want to post can be read as
(Complete[i]-Due[i])/M <= lateness[i]

where Complete[i] and Due[i] denotes complete and due time of job i, and lateness[i], which is a binary variable, is set to be 1 when job i is late(that is, Complete[i]-Due[i] < 0 ) and 0 other wise, M represents a sufficiently large number. To impletement this, I code as follows:

ILinearNumExpr a = cp.LinearNumExpr(); 

for (

int i = 0; i < nbJobs; i++) 
{ a.AddTerm(1 / 100000.0, complete[i]); a.AddTerm(-1, lateness[i]); cplex.AddLe(a, Due[i] / 100000.0); 
}

it can be seen that M is give the value of 100000.0 which is considerably larger than any of Complete[i] and Due[i]. the objective is to minimize the number of late jobs by

ILinearNumExpr b = cp.LinearNumExpr(); 

for (

int i = 0; i < nbJobs; i++) 
{ b.AddTerm(1, lateness[i]); 
} cplex.AddMinimize(b);

The output shows that even jobs are late, the value of corresponding lateness[i] stays 0. What shocked me is that as I decrease the value of M (from 100000.0 to 1000.0), the number of lateness[i] with value 1 increases as they are not constrained by the big-M constraints posted above. I'm not sure if have missed anything or is there anything wrong with the constraint. Can anybody give me some suggestion?
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Originally posted by: SystemAdmin

My guess is that your M is so big here that you are suffering from bad numerics.
It might be better to rewrite the big-M constraints into something that uses indicator constraints. For example

// If the job is not late (lateness[i] == 0) then it must complete before its due time.
cplex.IfThen(cplex.Eq(lateness[i], 0), cplex.Le(Complete[i], Due[i]));

This expresses exactly the same constraint but leaves it to CPLEX to decide how to handle it best.
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Originally posted by: Chrisontherun

thank you for your advice, I think it addressed my problem pretty well :)
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