Abstract.
Separated continuous linear programs (SCLP) are a class of continuous linear programs which, among other things, can serve as a useful model for dynamic network problems where storage is permitted at the nodes. Recent work on SCLP has produced a detailed duality theory, conditions under which an optimal solution exists with a finite number of breakpoints, a purification algorithm, as well as a convergent algorithm for solving SCLP under certain assumptions on the problem data. This paper combines much of this work to develop a possible approach for solving a wider range of SCLP problems, namely those with fairly general costs. The techniques required to implement the algorithm are no more than standard (finite-dimensional) linear programming and line searching, and the resulting algorithm is simplex-like in nature. We conclude the paper with the numerical results obtained by using a simple implementation of the algorithm to solve a small problem.
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Received: May 1994 / Accepted: March 2002¶Published online June 25, 2002
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Pullan, M. An extended algorithm for separated continuous linear programs. Math. Program. 93, 415–451 (2002). https://doi.org/10.1007/s10107-002-0307-0
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DOI: https://doi.org/10.1007/s10107-002-0307-0