Hi,

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

but let s now deal with a new information : for a given bus size if we take more than 4 then we get a 20% discount.

This moves our function cost from linear to piecewise linear. Let's have a look at how to deal with this in OPL.

We would then write:

int nbKids=300;
float costBus40=500;
float costBus30=400;

// If we take more than 4 buses for a given size, 20% cheaper for additional buses
 
dvar int+ nbBus40;
dvar int+ nbBus30;

pwlFunction pricePerQuantity=piecewise{1->4;0.8};

assert forall(k in 1..4 ) pricePerQuantity(k)==k;
assert forall(k in 5..10) as:abs(pricePerQuantity(k)-4-(k-4)*0.8)<=0.00001;
 
minimize
 costBus40*pricePerQuantity(nbBus40)  +pricePerQuantity(nbBus30)*costBus30;
 
subject to
{
 40*nbBus40+nbBus30*30>=nbKids;
}

which gives 10 buses 30 seats and no 40 seats bus.

Not a huge discount but this gives a strong incentive to change and use more 30 seats buses.

regards

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