Originally posted by: far123

I have a axle relocation problem, which tries to find the most proper location for each axle to minimize the cost.

96 axles and 96 locations, respectively.

The constraints are very simple.
The only complicating part is the objective, which uses min() function.

Cplex cannot find a solution even with very long running time. Does anyone have experience on handling this kind fo objective function? You can find the OPL model below.

tuple axle{
key int axleId;
float relativeSmallDiam;
float diamError;
}

tuple bogie{
key string bogieId;
{int} locs;
}

{axle} axles = ...;
float rsDiamsj in axles = j.relativeSmallDiam;
float dErrorj in axles = j.diamError;

{int} locations = ...;

{bogie} bogies = ...;

float unitWearCost = 30000/60;

dvar int AxleAlloclocationsaxles in 0..1;

dexpr float TotalTruingAmount = sum(k in bogies)
sum(i in k.locs)
( (sum(j in axles) rsDiams[j]*AxleAllocitem(locations,ord(locations,i))[j] -
min(p in k.locs) sum(q in axles) rsDiams[q]*AxleAllocitem(locations,ord(locations,p))[q])*2
+ sum(j in axles) dError[j]*AxleAllocitem(locations,ord(locations,i))[j]);

minimize unitWearCost * TotalTruingAmount+10;

subject to{
forall(i in locations)
sum(j in axles) AxleAlloc[i][j] == 1;

forall(j in axles)
sum(i in locations) AxleAlloc[i][j] == 1;
}

Thanks...
#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: far123

Could anyone help me with this? I'm stuck.
#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: Ed Chamberlayne

I'm sure someone on this forum can give a better answer but I don't believe you can use a min function on your decision variable - in this case, your AxleAlloc variable. You can use a minl or min function over parameters.
#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: SystemAdmin

A min() in an objective term indeed does not seem to be a good idea.
I did not understand your model in detail but you seem to have
something like
min[A + (min(c in C)xc]) + B.
Have you tried to model the "min(c in C)"-term by an additional
variable, i.e., you have something additionla constraints like
forall(c in C) y <= x[c];
and your objective changes to something like
minA+B-y

It's worth giving it a try.

Hope this wil help.

Best regards
Norbert
#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: SystemAdmin

Nasty formatting ... same mail in a more readable form.
Sorry for double-posting
Norbert

---

A min() in an objective term indeed does not seem to be a good idea.
I did not understand your model in detail but you seem to have
something like
min[A + (min(c in C)x[c]) + B.
Have you tried to model the "min(c in C)"-term by an additional
variable, i.e., you have something additionla constraints like
forall(c in C) y <= x[c];
and your objective changes to something like
minA+B-y

It's worth giving it a try.

Hope this wil help.

Best regards
Norbert
#DecisionOptimization
#OPLusingCPLEXOptimizer