In open-pit mines (like the one in the picture), mineral is reached by digging material from the surface. However, most of the time, it is necessary to remove worthless material (waste) to have access to the valuable ore.
If the waste is very expensive to remove, it may not be worth it to dig the ore. But, if the waste is easy (cheap) to remove, it may be worth to dig up all the ore, regardless of the amount of waste you have to extract in the process.
In Chile, the mining industry is a very relevant economic sector. Mining exports account for about 62,5% of the total exports and they are responsible for 13% of the GDP (source). In a joint project with researchers from Chilean universities (AMTC and Dept. of Mathematics, UTFSM), we are developing an algorithm to provide a good (and quick) response to the question of whether to dig up the ore or not.
If you are still interested, you can check out below a presentation explaining the problem and our ideas to deal with it.
