An extended algorithm for separated continuous linear programs

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 opt...

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Bibliographic Details
Published in:Mathematical programming Vol. 93; no. 3; pp. 415 - 451
Main Author: Pullan, Malcolm C.
Format: Journal Article
Language:English
Published: Heidelberg Springer 01.12.2002
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Exact sciences and technology
Linear programming
Mathematical programming
Operational research and scientific management
Operational research. Management science
Production planning
Simplex method
Breakpoint
simplex-like algorithm
Simplex method
Linear programming
continuous linear programming
linear optimal control
Optimal control (mathematics)
Mathematical programming
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary: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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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-002-0307-0