I work in a company where we are supposed to produce and send pipes using trucks to buyers. Pipes of smaller diameter can be nested inside pipes of larger diameter while sending to minimize number of trucks.
The trucks that carry these pipes are usually 40 feet / 12.192 meters long while the pipes are 12 metres long. Hence, they are placed length wise along the trailer.
The trucks are usually 8 feet / 2.438 metres high and wide ie 8x8.
The outer diameters of pipe that we make are 90, 110, 125, 140, 160, 180, 200, 250 and 315 (all sizes in mm).
A constraint here is that while nesting, pipe of one size can only be nested inside pipe one size greater than the next size. Example, 90 pipe can go into 125 and higher pipe size, 140 pipe can go into 160 or higher pipe size.
I wish to mathematically derive a system for optimum loading of the trucks to minimize the number of trucks to deliver the ordered quantity of various sizes using nesting because we often goof-up with nesting resulting in huge cost implications. Can some one please help?
(Also, I am a naive user. It would also be helpful if you can suggest the appropriate tags that I should put along the question to help people notice the question.)