Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
The Surplus Inventory Matching Problem in the Process Industry
Operations Research
A Column-Generation Approach to the Multiple Knapsack Problem with Color Constraints
INFORMS Journal on Computing
An efficient model and strategy for the steel mill slab design problem
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
The steel mill slab design problem revisited
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
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The steel mill slab design problem from the CSPLIB is a combinatorial optimization problem motivated by an application of the steel industry. It has been widely studied in the constraint programming community. Several methods were proposed to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called the multiple knapsack problem with color constraints, originated from the same industrial problem, was discussed in the integer programming community. In particular, a simple integer program for this problem has been given by Forrest et al. (INFORMS J Comput 18:129---134, 2006). The aim of this paper is to bring these different studies together. Moreover, we adapt the model of Forrest et al. (INFORMS J Comput 18:129---134, 2006) for the steel mill slab design problem. Using this model and a state-of-the-art integer program solver all instances of the steel mill slab library can be solved efficiently to optimality. We improved, thereby, the solution values of 76 instances compared to previous results (Schaus et al., Constraints 16:125---147, 2010). Finally, we consider a recently introduced variant of the steel mill slab design problem, where within all solutions which minimize the leftover one is interested in a solution which requires a minimum number of slabs. For that variant we introduce two approaches and solve all instances of the steel mill slab library with this slightly changed objective function to optimality.