In an advertisement model we may have to deal with underdelivery: the delivery of less impressions, visitors, GRPs than contractually agreed upon. So what to do. We can minimize the SUM of this quantity with the possible effect of many orders with small underdelivery numbers (spreading the pain). When minimizing the MAX this effect is even guaranteed. Or we can minimize the NUMber of orders with underdelivery.
In practice, a good approach is to minimize a linear combination of both the SUM and the NUM objectives.