Differential Multiplant Monopoly on a Freight Network

Differential Multiplant Monopoly on a Freight Network | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Differential Multiplant Monopoly on a Freight Network Terry Friesz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4178130/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Nov, 2024 Read the published version in Networks and Spatial Economics → Version 1 posted 11 You are reading this latest preprint version Abstract In this paper we give a mathematical statement of a differential spatial monopoly wherein transactions are facilitated by a freight transportation network that is based on an underlying graph. The monopolist has a presence at every node, and freight services are available for paths connecting stipulated origin-destination (OD) pairs. The monopolist produces a single homogeneous product that may be manufactured and inventoried, as well as sold, at every node. The dynamics take the form of ordinary differential equations that describe flow conservation. We present the necessary conditions of the monopolist's optimal control problem and observe their interpretation is that marginal revenue equals marginal cost at each node for each instant of continuous time. Existence of an optimal solution to the monopolist's problem is proven and a numerical example solved using two algorithms: one implemented in discrete time and the other in continuous time. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 27 Nov, 2024 Read the published version in Networks and Spatial Economics → Version 1 posted Editorial decision: Revision requested 18 Sep, 2024 Reviews received at journal 02 Aug, 2024 Reviews received at journal 29 Jul, 2024 Reviews received at journal 22 Jul, 2024 Reviewers agreed at journal 15 Jun, 2024 Reviewers agreed at journal 14 Jun, 2024 Reviewers agreed at journal 14 Jun, 2024 Reviewers invited by journal 12 May, 2024 Editor assigned by journal 09 Apr, 2024 Submission checks completed at journal 01 Apr, 2024 First submitted to journal 27 Mar, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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