On seeking efficient Pareto optimal points in multi-player minimum cost flow problems with application to transportation systems

In this paper, we propose a multi-player extension of the minimum cost flow problem inspired by a transportation problem that arises in modern transportation industry. We associate one player with each arc of a directed network, each trying to minimize its cost function subject to the network flow c...

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Bibliographic Details
Published inarXiv.org
Main Authors Gupta, Shuvomoy Das, Pavel, Lacra
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.05.2019
Subjects
Algorithms
Constraint modelling
Cost engineering
Cost function
Mathematics - Optimization and Control
Minimum cost
Pareto optimum
Transportation applications
Transportation industry
Transportation problem
Transportation systems
Online AccessGet full text
ISSN2331-8422
DOI10.48550/arxiv.1805.11750

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Summary:In this paper, we propose a multi-player extension of the minimum cost flow problem inspired by a transportation problem that arises in modern transportation industry. We associate one player with each arc of a directed network, each trying to minimize its cost function subject to the network flow constraints. In our model, the cost function can be any general nonlinear function, and the flow through each arc is an integer. We present algorithms to compute efficient Pareto optimal point(s), where the maximum possible number of players (but not all) minimize their cost functions simultaneously. The computed Pareto optimal points are Nash equilibriums if the problem is transformed into a finite static game in normal form.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1805.11750