Hi,

let us go on with

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

40*nbBus40+nbBus30*30>=nbKids;

is a linear constraint. But sometimes we need more than linear constraints.

Suppose now, we have a contract change and we need to pay 500 more if we use 2 kind of buses instead of 1.

Then we could write

int nbKids=300;
float costBus40=460;
float costBus30=360;

// Contract change : +500 if we use 2 kind of buses
 
dvar int+ nbBus40;
dvar int+ nbBus30;

dvar int+ nbKindOfBuses;
 
minimize
 costBus40*nbBus40  +nbBus30*costBus30+(nbKindOfBuses-1)*(500);
 
subject to
{
 40*nbBus40+nbBus30*30>=nbKids;
 
 nbKindOfBuses==(nbBus40!=0)+(nbBus30!=0);
}

and

nbKindOfBuses==(nbBus40!=0)+(nbBus30!=0);

is allowed and we call this a logical constraint.

regards

NB:

Since we use logical constraints for a zoo, we understand a bit better why we say zoological!

and many other very simple examples at https://www.linkedin.com/pulse/making-decision-optimization-simple-alex-fleischer/