A Horizon Decomposition Approach for the Capacitated Lot-Sizing Problem with Setup Times
将Dantzig-Wolfe分解中的水平分解方法应用于带设置时间的容量批量问题，通过划分重叠区间生成子问题，并用分支定价算法在挑战性实例上优于现有求解器。
We introduce horizon decomposition in the context of Dantzig-Wolfe decomposition, and apply it to the capacitated lot-sizing problem with setup times. We partition the problem horizon in contiguous overlapping intervals and create subproblems identical to the original problem, but of smaller size. The user has the flexibility to regulate the size of the master problem and the subproblem via two scalar parameters. We investigate empirically which parameter configurations are efficient, and assess their robustness at different problem classes. Our branch-and-price algorithm outperforms state-of-the-art branch-and-cut solvers when tested to a new data set of challenging instances that we generated. Our methodology can be generalized to mathematical programs with a generic constraint structure.