Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Branch-and-Price Algorithms for the One-Dimensional Cutting Stock Problem
Computational Optimization and Applications
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
Optimal Integer Solutions to Industrial Cutting Stock Problems
INFORMS Journal on Computing
Optimal Integer Solutions to Industrial Cutting-Stock Problems: Part 2, Benchmark Results
INFORMS Journal on Computing
An exact algorithm for IP column generation
Operations Research Letters
The class constrained bin packing problem with applications to video-on-demand
Theoretical Computer Science
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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.