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Open AccessJournal ArticleDOI

Letter to the Editor-Finding Minimal Cost-Time Ratio Circuits

Bennett Fox
- 01 Jun 1969 - 
- Vol. 17, Iss: 3, pp 546-551
TLDR
This note presents an efficient method for the solution of the flow-circulation problem, the basis for which is a search for a way to route flow so that the cost-time trade-off is optimal.
Abstract
In the treatment of routing problems, other authors have used column generators to introduce, into the basis of the master problem, the solution that corresponds to a cycle in a graph with minimal cost-to-time ratio This subproblem is of independent interest and corresponds to deterministic Markov renewal programming; this note presents an efficient method for its solution, intuitive basis for which is a search for a way to route flow so that the cost-time trade-off is optimal This flow-circulation problem is solved parametrically by the out-of-kilter algorithm

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Citations
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Journal ArticleDOI

Fractional programming: Applications and algorithms

TL;DR: This paper surveys applications as well as solution methods in linear, quadratic and concave-convex fractional programming and tries to determine for each method the kind of fractional programs that are solved by it suitably.
Journal ArticleDOI

Status of periodic optimization of dynamical systems

TL;DR: In this article, the problem of periodic optimization of dynamical systems is reviewed and the most interesting results among those available are illustrated, as well as the most significant and open aspects of the problem.
Book ChapterDOI

Fractional Combinatorial Optimization

TL;DR: An instance of a fractional combinatorial optimization problem F consists of a specification of a set, and two functions f : χ → R and g :φ → R.
Journal ArticleDOI

Minimum Convex Cost Dynamic Network Flows

TL;DR: The minimum convex cost dynamic network flow problem is presented, an infinite horizon integer programming problem which involves network flows evolving over time and has applications in periodic production and transshipment, airplane scheduling, cyclic capacity scheduling, and cyclic staffing.
References
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Journal ArticleDOI

Scheduling Parallel Computations

TL;DR: A model for parallel computations is given as a directed graph in which nodes represent elementary operations, and branches, data channels, and an algorithm is given for the determination of the number of initiations of each node in the graph defining a parallel computation.
Journal ArticleDOI

Multichain Markov Renewal Programs

TL;DR: In this article, two methods for computing optimal decision sequences and their cost functions are presented for solving a broad class of shortest-route problems and a third solution technique is shown to apply to certain, but not all, of these Markov renewal programs.
ReportDOI

Finding a cycle in a graph with minimum cost to time ratio with application to a ship routing problem

TL;DR: In this article, the simplex method was used to find a negative cycle in a graph when arc distances are given which may be positive or negative, based on the decomposition principle.
Journal ArticleDOI

Markov-Renewal Programming. II: Infinite Return Models, Example

TL;DR: In this paper, the authors consider finite-return Markov-renewal programs over a Markov renewal process, where the intervals between transitions of a system from state i to state j are independent samples from a distribution that may depend upon both i and j. Given a reward structure and a decision mechanism that influences both the rewards and the Markov renewal process, the problem is to select alternatives at each transition so as to maximize total expected reward.
Journal ArticleDOI

Markov Renewal Programming by Linear Fractional Programming

TL;DR: In this article, the multichain case is handled by a decomposition approach, with particular attention given to the resolution of tied policies that minimize expected cost per unit time, and a linear fractional programming approach is used to solve the multi-chain case.