Y.Y. Li, K.S. Leung, et al.
J Combin Optim
In this paper, we introduce the variable sized bin packing problem with novel packing constraints, called the color constraints. In an instance of this problem, we have n items to be packed into bins of m distinct sizes. Items come with two attributes: color and size. In addition to the usual capacity constraints, we require that each bin contain items with at most p distinct colors, where p is a pre-specified positive integer. Our objective is to minimize the total capacity of the bins used in the packing. This problem arises as a model for the slab design problem in the production planning process of a steel plant. An APTAS and two 3-approximations are presented.