A Branch-and-Price Algorithm for the Bin Packing Problem with Conflicts

In the Bin Packing Problem with Conflicts (BPPC), we are given a set V = {1, 2, . . . , n} of items, each item i having a non-negative weight wi, and an infinite number of identical bins of weight capacity W . We are also given a conflict graph G = (V,E), where E is a set of edges such that (i, j) ∈ E when i and j are in conflict. Items in conflict cannot be assigned to the same bin. The aim of the BPPC is to assign all items to the minimum number of bins, while ensuring that the total weight of the items assigned to a bin does not exceed the bin weight capacity and that no bin contains items in conflict.