A Lagrangian Based Branch-and-Bound Algorithm for Production-transportation Problems

Authors:
Takahito Kuno;Takahiro Utsunomiya
Affiliations:
Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan (e-mail: takahito@is.tsukuba.ac.jp;Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan
Venue:
Journal of Global Optimization
Year:
2000

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Abstract

We propose a branch-and-bound algorithm of Falk–Soland's type for solving the minimum cost production-transportation problem with concave production costs. To accelerate the convergence of the algorithm, we reinforce the bounding operation using a Lagrangian relaxation, which is a concave minimization but yields a tighter bound than the usual linear programming relaxation in O(mn log n) additional time. Computational results indicate that the algorithm can solve fairly large scale problems.