Arc flow formulations based on dynamic programming: Theoretical foundations and applications
نویسندگان
چکیده
Network flow formulations are among the most successful tools to solve optimization problems. Such correspond determining an optimal in a network. One particular class of network is arc flow, where variables represent flows on individual arcs For $\mathcal{NP}$-hard problems, polynomial-sized models typically provide weak linear relaxations and may have too much symmetry be efficient practice. Instead, with pseudo-polynomial size usually strong The interest has grown considerably last twenty years, which they been used many open instances hard A remarkable advantage possibility practical-sized directly by Mixed Integer Linear Programming solver, avoiding implementation complex methods based column generation. In this survey, we present theoretical foundations formulations, showing relation between their Dynamic (DP). This allows better understanding strength these through link obtained Dantzig-Wolfe decomposition. DP also new perspective relate state-space relaxation for models. We dual point view contrast that paths cycles. To conclude, review main solution applications several domains such as cutting, packing, scheduling, routing.
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ژورنال
عنوان ژورنال: European Journal of Operational Research
سال: 2022
ISSN: ['1872-6860', '0377-2217']
DOI: https://doi.org/10.1016/j.ejor.2021.04.024