Does this bin-packing variant have a name?

Question

I have what sounds like a typical bin-packing problem: x products of differing sizes need to be packed into y containers of differing capacities, minimizing the number of containers used, as well as minimizing the wasted space.

I can simplify the problem in that product sizes and container capacities can be reduced to standard 1-dimensional units. i.e. this product is 1 unit big while that one is 3 units, this box holds 6 units, that one 12. Think of eggs and cartons, or cases of beer.

But there's an additional constraint: each container has a particular attribute (we'll call it colour ), and each product has a set of colours it is compatible with. There is no correlation between colour and product/container sizing; One product may be colour-compatible with the entire palette, Another may only be compatible with the red containers.

Is this problem variant already described in literature? If so, what is its name?

Geoffrey De Smet Geoffrey De Smet · Accepted Answer · 2014-06-13T08:01:37

I think there is no special name for this variant. Although the coloring constraint first gives the impression it's graph coloring related, it's not. It's simply a limitation on the values for a variable.

In a typical solver implementation, each product (= item) will have a variable to which container it's assigned. The color constraints just reduces the value range for a specific variable. So instead of specifying that all variables use the same value range, make it variable specific. (For example, in OptaPlanner this is the difference between a value range provided by the solution generally or by the entity specifically.) So the coloring constraint doesn't even need to be a constraint: it can be part of the model in most solvers.

Any solver that can handle bin packing should be able to handle this variant. Your problem is actually a relaxation of the Roadef 2012 Machine Reassignment problem, which is about assigning processes to computers. Simply drop all the constraints, except for 1 resource usage constraints and the constraint which excludes certain processes to certain machines. That use case is implemented in many solvers. (Although, in practice it is probably be easier to start from a basic bin packing example such as Cloud Balancing.)

Does this bin-packing variant have a name?

2 Answers