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Exact solution of network flow models with strong relaxations

2022; Springer Science+Business Media; Volume: 197; Issue: 2 Linguagem: Inglês

10.1007/s10107-022-01785-9

1436-4646

Vinícius Loti de Lima, Manuel Iori, Flávio K. Miyazawa,

Advanced Graph Theory Research

We address the solution of Mixed Integer Linear Programming (MILP) models with strong relaxations that are derived from Dantzig–Wolfe decompositions and allow a pseudo-polynomial pricing algorithm. We exploit their network-flow characterization and provide a framework based on column generation, reduced-cost variable-fixing, and a highly asymmetric branching scheme that allows us to take advantage of the potential of the current MILP solvers. We apply our framework to a variety of cutting and packing problems from the literature. The efficiency of the framework is proved by extensive computational experiments, in which a significant number of open instances could be solved to proven optimality for the first time.