3D inventory tracking data structure and algorithm -

summary of problem:

we need keep track of inventory of solid 3 dimensional rectangles (i believe these called cuboids stand corrected).

each cuboid arrives fixed length, breadth, , depth. let's it's 20x5x5 argument's sake. begin, have 10 of these 20x5x5 cuboids in stock.

then during course of business, smaller / secondary cuboids of variable dimensions cut out these bigger / primary cuboids.

summary of question:

a) data structure best track stock of primary cuboid stock availability.

b) algorithm(s) best determine whether primary cuboid can cater secondary cuboid cut out?

additional details , issues:

the first cut primary cuboid easy calculate / determine. problem comes hand second, third, , on cuts, since need track resulting dimensions of edges , vertices of primary cuboid remaining in stock.

if more 1 primary cuboid meets requirements secondary cuboid, smallest primary cuboid preferable cater fifo depletion of stock. need calculate remaining volume of matching primary cuboids determine smallest one.

this gets tricky because once secondary cuboid has been cut out primary cuboid, primary cuboid's new variable dimensions need tracked (all edges , vertices). need keep track of points on primary cuboid secondary cuboid cut out of (as resulting shape).

so it's both volume problem , "does piece fit in piece" problem.

i should add cuboids measured , cut millimetre precision (in case has implications data structure).

i have incomplete answer you, might helpful:

first of all, here similar question, in 2d.
looking through 1 of answers, mentioned arc project. glance, seems idea there discussed in 2d (maybe) applied issue in 3d.

i think applying idea ac project, constraint of being applied 3 dimensions might work.

in case, think case of balancing between complexity of ds , time take calculate whether or not each cuboid can cut next piece required...