Improved methods for storing and updating information in the out-of-kilter algorithm
Journal of the ACM (JACM)
Dual algorithms for pure network problems
Operations Research
Reoptimization procedures for networks with side constraints
Computers and Industrial Engineering
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A faster strongly polynomial minimum cost flow algorithm
Operations Research
An efficient implementation of a scaling minimum-cost flow algorithm
Journal of Algorithms
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Dynamic Programming and Stochastic Control
Dynamic Programming and Stochastic Control
Optimal routing in time-varying, stochastic networks: algorithms and implementations
Optimal routing in time-varying, stochastic networks: algorithms and implementations
A Computational Study of Cost Reoptimization for Min-Cost Flow Problems
INFORMS Journal on Computing
Updating Paths in Time-Varying Networks Given Arc Weight Changes
Transportation Science
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A dual ascent reoptimization technique is proposed for updating optimal flows for the minimum cost network flow problem (MCNFP) given any number of simultaneous, heterogeneous changes to the network attributes (i.e. supply at nodes, arc costs and arc capacities) and the optimal solutions to the prior primal and dual problems. Significant savings in computation time can be achieved through the use of reoptimization in place of solving a new MCNFP from scratch as each new problem instance (i.e. set of network attribute updates) arises. The proposed technique can be implemented with polynomial worst-case computational complexity. Extensive numerical experiments were designed and conducted to assess the computational benefits of employing the proposed reoptimization technique as compared with solution from scratch using comparable classic implementations of the original algorithms. This work was motivated by the need for the real-time provision of evacuation instructions to people seeking quick egress from a large sensor-equipped building that has come under attack by natural or terrorist forces, but has broad applicability.