Originally posted by: SystemAdmin

[Simon said:]

Hello!

I'm trying to model a CLSD with Concert Technology and Java. The CLSD is a modified version of the CLSP (cf. [url=http://www.palgrave-journals.com/jors/journal/v54/n5/full/2601525a.html]http://www.palgrave-journals.com/jors/journal/v54/n5/full/2601525a.html[/url]).

I've modeled all constraints except one. The CSLD is based on a TSP and I've problems to model the constraint, which eliminates subtours. The constraint is given formely as follows:

[img]http://www.4ballerz.de/cplex11/constraint3_10.jpg[/img]

with: J is a set of products, T is a set of periods. F[sub]jt[/sub] is a integer variable, Y[sub]ijt[/sub] is a binary varible.

My first approach to model this would be as follows:


for(int j = 0; j < nPeriod; j++)<br />{
for(int t = 0; t < nProduct; t++)<br /> {
IloLinearNumExpr rhs1 = cplex.linearNumExpr();
for(int i = 0; i <nProduct; i++)<br /> {
rhs1.addTerm(1., F_jt[i][t]);
//How to model -J*(1-Y_ijt[i][j][t])
}
cplex.addGe(F_jt[j][t], null);
}
}


But I don't know how to model the expressions [tt]-J*(1-Y[sub]ijt[/sub])[/tt] and [tt]J{i}[/tt].

Can somebody help me?


A second extension, I try to model , is that a product has to start in a specific period. Therefor I initialize the Array [tt]int periodStart[nProduct][/tt] with nProduct = count of products. In every cell is the start period of a product saved.

Now I would extend my objective function and constraints (only one is given as an example) as follows:

[img]http://www.4ballerz.de/cplex11/obj_fun.jpg[/img]


//objective function
IloLinearNumExpr objf_a = cplex.linearNumExpr();
IloLinearNumExpr objf_b = cplex.linearNumExpr();

for(int j=0; j < nProduct;j++)<br />{
for(int t = 0; t < nPeriod; t++)<br /> {
objf_b.addTerm(pv.getO_h_jt()[j][t], I_jt[j][t]);
for(int i = 0; i < nProduct; i++)<br /> {
//The modification to start in a later period is here.
if(j!=i && t > periodStart[j] ) objf_b.addTerm(pv.getO_sc_ij()[i][j], Y_ijt[i][j][t]);
}
}
}

cplex.addMinimize(cplex.sum(objf_a, objf_b));


and

[img]http://www.4ballerz.de/cplex11/constraint3_9.jpg[/img]


for(int t = 0; t < nPeriod; t++)<br />{
for(int k = 0; k < nProduct; k++)<br /> {
IloLinearNumExpr res_3_8a = cplex.linearNumExpr();
IloLinearNumExpr res_3_8b = cplex.linearNumExpr();

for(int i = 0; i < nProduct; i++)<br /> {
if(i!=k && t > periodStart[j] )
res_3_8a.addTerm(1., Y_ijt[i][k][t]);

for(int j = 0; j < nProduct; j++)<br /> {
if(j!=k && t > periodStart[j] )
res_3_8b.addTerm(1., Y_ijt[k][j][t]);;
}
}
cplex.addEq(cplex.sum(res_3_8a, Z_jt[k][t-1]),
cplex.sum(res_3_8b, Z_jt[k][t]));
}
}


Would be this approuch correct?

I know, it's a lot of text, but I hope somebody can help me! Thank you!

Best Regards

Simon

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

[prubin said:]

You first code segment is a bit muddled. Do you really mean j < nPeriod and t < nProduct, or do you have these reversed?&nbsp; Do you really mean addGe(F..., null), or should null be rhs1?<br />
Let's say that we reverse the loop indexing, so that the outer loop indexes of time (t) and the inner loop over product (j).  In the innermost loop (i), add a term to rhs1 only if i j (in other words, insert an if block).  That handles j \in J{i}.  Also, do not forget to add 1 to rhs1 (which you can do when you declare it).

The term -J(1-Y...) should actually be -|J|(1-Y...), where |J| is the cardinality of the set J.  So in this case, I think |J| = nProduct, and you can just add the constant term -nProduct to rhs1 and then add nProduct*Y... to it.

Your approach to the second part looks generally to be on the right track, assuming that the function pv.getO_h_jt() returns a two-dimensional matrix.

/Paul
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

[Simon said:]

Hello!

Thank you, for your answer, Paul!

[quote author=prubin link=topic=537.msg1609#msg1609 date=1220638856]
You first code segment is a bit muddled. Do you really mean j < nPeriod and t < nProduct, or do you have these reversed?&nbsp; <br />

You are right, I've reversed the bounds, it was just a little slip.

[quote author=prubin link=topic=537.msg1609#msg1609 date=1220638856]
Do you really mean addGe(F..., null), or should null be rhs1?


"null" was just a placeholder. Otherwise Eclipse shows me a fault. It should be rhs1.

[quote author=prubin link=topic=537.msg1609#msg1609 date=1220638856]
Let's say that we reverse the loop indexing, so that the outer loop indexes of time (t) and the inner loop over product (j).  In the innermost loop (i), add a term to rhs1 only if i j (in other words, insert an if block).  That handles j \in J{i}.  Also, do not forget to add 1 to rhs1 (which you can do when you declare it).

The term -J(1-Y...) should actually be -|J|(1-Y...), where |J| is the cardinality of the set J.  So in this case, I think |J| = nProduct, and you can just add the constant term -nProduct to rhs1 and then add nProduct*Y... to it.


I've tried to trasfer your hints into code. This is my result:


for(int j = 0; j < nProduct; j++)<br />{
for(int t = 0; t < nPeriod; t++)<br /> {
for(int i = 0; i <nProduct; i++)<br /> {
if(i!=j)
model.addGe(F_jt[j][t], model.diff(model.sum(1, F_jt[i][t]),
model.prod(-nProduct, model.diff(1, Y_ijt[i][j][t]))));
}
}
}


Does it look good? And more important, does it look correct?

Best Regards

Simon
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

[prubin said:]

[quote author=Simon link=topic=537.msg1614#msg1614 date=1220728903]


for(int j = 0; j < nProduct; j++)<br />{
for(int t = 0; t < nPeriod; t++)<br /> {
for(int i = 0; i <nProduct; i++)<br /> {
if(i!=j)
model.addGe(F_jt[j][t], model.diff(model.sum(1, F_jt[i][t]),
model.prod(-nProduct, model.diff(1, Y_ijt[i][j][t]))));
}
}
}



I think you need either to drop the '-' from '-nProduct' or to change the outer model.diff to model.sum.  Otherwise, it looks about right to my (less than discerning) eye.

/Paul

#CPLEXOptimizers
#DecisionOptimization