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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Vydáno v:Mathematical programming Ročník 93; číslo 3; s. 415 - 451
Hlavní autor: Pullan, Malcolm C.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Heidelberg Springer 01.12.2002
Springer Nature B.V
Témata:
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
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-002-0307-0