I've received a task to build a shipping estimative that suggests the best accomodation of goods on as few boxes as possible: • There is a finite set of known retangular box sizes • There are many arbitrary retangular item to be packed inside boxes • The fewer boxes should be used the best. Because shipping two boxes 1x1x1 is way more expensive than one box 1x2x1. This should be the priority here. • It should also be optimized to use the smaller boxes as possible, as a second level priority. (eg.: if presented with a choice between one bigger box and two small, it should choose the bigger box) • Items can be rotated to fit the box, but the rotation have to be limited to increments of 45° at a minimum (in my researches it seems that some configurations allow for a 45 degrees rotation to better fit retangular boxes inside a bigger retangular box), being 90° rotations the standard to be taken.

RectangleBinPack - Source code for performing 2d rectangular bin packing. Skip to content. Features Business. And build software together. 2D Bin Packing Software Downloads. Online algorithms for 2D bin packing with advice. Software execution units which o. 2D bin packing is achieved by Best-Fit.

I think all @msw is saying is that this type of problem is unlikely a good fit for a 'perfect' solution, but rather a better fit for an acceptable solution found in a reasonable amount of time with heuristics based on the rules you've provided. From a mathematical viewpoint, this often means you approach it with a different set of algorithms and tools, so I think he's just recommending that. For example, genetic algorithms, simulated annealing, and other methods of following a gradient descent curve approximating the solution space with respect to your heuristic might provide benefits here. – Oct 9 '14 at 3:50. Bin packing is very computationally difficult. Think of half of the problem: you want to pack product in shipping boxes with no wastage in the box. An optimal solution for that would require going through all possible subsets and all possible 3d arrangements of the product that needs to ship in one truck.

I'll give you the optimal solution for that because I have a friend who does six impossible things before breakfast. Now you just have to get all the boxes on the truck with no wastage. My friend does his second impossible thing and gives you the solution. Unfortunately, with the box sizes you selected above, there is empty space in the truck which could be reduced if you'd chosen different (either larger or smaller) boxes in the first task. If you change the size of one box, at best you'll have to re-pack the truck; at worst, you may have to repack all of the boxes which is just as hard as the problem we started with.

And, as with the first stage, you'd have to try all possible 3d arrangements. I found Skiena's The to be helpful for thinking about what class of algorithms suit which sorts of problems, but I mostly learned that good solutions for even mundane problems blow up in you face with computational difficulty. Most of what you are needing fit into the class of and that article is a good jumping off point. It is worth noting that some of the best algorithms for this are commercial products because this task pops up everywhere in logistics (what's the smallest number of train cars can I get my goods into? There is considerable money to be made if the right heuristics can save a manufacturer 100 train cars a month. Unfortunately, the literature on optimizing heuristics isn't nearly as large as for algorithms. Cracked Cap Polypore Uses.