Article ID: | iaor20073704 |
Country: | United States |
Volume: | 52 |
Issue: | 4 |
Start Page Number: | 623 |
End Page Number: | 638 |
Publication Date: | Jul 2004 |
Journal: | Operations Research |
Authors: | Degraeve Zeger, Peeters Marc |
Keywords: | programming: integer, inventory |
The co-printing problem is a new variant of the bin-packing problem. It finds its origin in the printing of Tetra-bricks in the beverage industry. Combining different types of bricks in one printing pattern reduces the stock. With each brick, a number of colors are associated, and the total number of colors for the whole pattern cannot exceed a given limit. We develop a branch-and-price algorithm to obtain proven optimal solutions. After introducing a Dantzig–Wolfe reformulation for the problem, we derive cutting planes to tighten the LP relaxation. We present heuristics and develop a branching scheme, avoiding complex pricing problem modifications. We present some further algorithmic enhancements, such as the implementation of dominance rules and a lower bound based on a combinatorial relaxation. Finally, we discuss computational results for real-life data sets. In addition to the introduction of a new bin-packing problem, this paper illustrates the complex balance in branch-and-price algorithms among using cutting planes, the branching scheme, and the tractability of the pricing problem. It also shows how dominance rules can be implemented in a branch-and-price framework, resulting in a substantial reduction in computation time.