Philpott, Andrew B.; Craddock, Mark An adaptive discretization algorithm for a class of continuous network programs. (English) Zbl 0840.90064 Networks 26, No. 1, 1-11 (1995). Summary: An algorithm is derived for a class of continuous-time minimum-cost network flow problems. The algorithm is based on some recent results in the theory of separated continuous linear programs and works with a sequence of discrete approximations to the continuous-time problem. We prove the convergence of the algorithm and present some numerical results which compare its performance against that of linear network flow algorithms applied to a uniform discrete approximation of the continuous-time problem. Cited in 8 Documents MSC: 90B10 Deterministic network models in operations research Keywords:continuous-time minimum-cost network flow; separated continuous linear programs PDFBibTeX XMLCite \textit{A. B. Philpott} and \textit{M. Craddock}, Networks 26, No. 1, 1--11 (1995; Zbl 0840.90064) Full Text: DOI References: [1] Anderson, SIAM J. Control Optim. 21 (1983) [2] Anderson, Networks 19 pp 395– (1989) [3] Bellman, Proc. Nat. Acad. Sci. 39 pp 947– (1953) [4] Bertsekas, Oper. Res. 36 pp 93– (1988) [5] Network programming in continuous time with node storage. Infinite Programming. Proceedings of an International Symposium on Infinite Dimensional Linear Programming ( and , Eds.). Springer-Verlag, New York (1985). [6] Pullan, SIAM J. Control Optim. 31 pp 1558– (1993) [7] Pullan, SIAM J. Control Optim. [8] , and , Computer programs for solving the capacitated transshipment problem. University of Auckland School of Engineering Report 521 (1992). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.