A Pseudo-Polynomial Primal-Dual Algorithm for Globally Solving aProduction-Transportation Problem

Authors:
Takahito Kuno;Takahiro Utsunomiya
Affiliations:
Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan;Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
Venue:
Journal of Global Optimization
Year:
1997

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Abstract

In this paper, we propose a primal-dual algorithm for solving a class ofproduction-transportation problems. Among m(≥ 2) sources two factoriesexist, which produce given goods at some concave cost and supply them to nterminals. We show that one can globally minimize the total cost ofproduction and transportation by solving a Hitchcock transportation problemwith m sources and n terminals and a minimum linear-cost flow problem withm+n nodes. The number of arithmetic operations required by the algorithm ispseudo-polynomial in the problem input length.