The Bin Packing Problem with Precedence Constraints

Given a set of identical capacitated bins, a set of weighted items and a set of precedences among such items, we are interested in determining the minimum number of bins that can accommodate all items and can be ordered in such a way that all precedences are satisfied. The problem, denoted as the Bin Packing Problem with Precedence Constraints (BPP-P), has a very intriguing combinatorial structure and models many assembly and scheduling issues. According to our knowledge the BPP-P has received little attention in the literature, and in this paper we address it for the first time with exact solution methods. In particular, we develop reduction criteria, a large set of lower bounds, a Variable Neighborhood Search upper bounding technique and a branch-and-bound algorithm. We show the effectiveness of the proposed algorithms by means of extensive computational tests on benchmark instances and comparison with standard integer linear programming techniques.