Hi,

let us go on with

https://www.linkedin.com/pulse/what-optimization-how-can-help-you-do-more-less-zoo-buses-fleischer/

 

and address a new concern : infeasibility!

 

Let us suppose we have a new challenge : use less than 7 buses overall.

Then we write

int nbKids=300;
float costBus40=500;
float costBus30=400;
 
dvar int+ nbBus40;
dvar int+ nbBus30;
 
minimize
 costBus40*nbBus40  +nbBus30*costBus30;
 
subject to
{
 ctAllKidsNeedToGo:
     40*nbBus40+nbBus30*30>=nbKids;
 
 ctMaxTotalBuses:
     nbBus30+nbBus40<=7;
}

ctAllKidsNeedToGo and ctMaxTotalBuses are labels for the constraints.

 

But then the problem gets infeasible since even with 7 buses with 40 seats you can take only 280=7*40 kids which is less than 300 kids.

When we launch this model, we get a conflict

which means we have a conflict within those 2 constraints and

a relaxation

which means that if we relax 7 buses to 8 buses then we have a feasible solution.

This is not very useful for this tiny example but for real models this can be key.

For more see Relaxing infeasible models in the IDE Tutorials in CPLEX documentation

regards

NB:

You can also get that info through flow control in scripting:

int nbKids=300;
float costBus40=500;
float costBus30=400;
 
dvar int+ nbBus40;
dvar int+ nbBus30;
 
minimize
 costBus40*nbBus40  +nbBus30*costBus30;
 
subject to
{
 ctAllKidsNeedToGo:
     40*nbBus40+nbBus30*30>=nbKids;
 
 ctMaxTotalBuses:
     nbBus30+nbBus40<=7;
}

main
{
thisOplModel.generate();
if (!cplex.solve())
{
writeln(thisOplModel.printRelaxation());
writeln(thisOplModel.printConflict());
}
}

gives

 

ctMaxTotalBuses
    relax [-Infinity,7] to [-Infinity,8] value is -Infinity

ctAllKidsNeedToGo
  is in conflict
ctMaxTotalBuses
  is in conflict

 

 

 

 

 

 

 

 

 

#DecisionOptimization
#OPLusingCPLEXOptimizer