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Differential Multiplant Monopoly on a Freight Network

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  • Terry L. Friesz

    (Pennsylvania State University)

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.

Suggested Citation

  • Terry L. Friesz, 2024. "Differential Multiplant Monopoly on a Freight Network," Networks and Spatial Economics, Springer, vol. 24(4), pages 763-788, December.
    • Handle: RePEc:kap:netspa:v:24:y:2024:i:4:d:10.1007_s11067-024-09654-y
    DOI: 10.1007/s11067-024-09654-y
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    References listed on IDEAS

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    1. repec:bla:jregsc:v:44:y:2004:i:3:p:489-515:2 is not listed on IDEAS
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    3. Bensaid, Bernard & Lesne, Jean-Philippe, 1996. "Dynamic monopoly pricing with network externalities," International Journal of Industrial Organization, Elsevier, vol. 14(6), pages 837-855, October.
    4. Luca Lambertini & Raimondello Orsini, 2007. "Network externalities in a dynamic monopoly," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 15(1), pages 105-117, March.
    5. Terry L. Friesz, 2010. "Dynamic Optimization and Differential Games," International Series in Operations Research and Management Science, Springer, number 978-0-387-72778-3, July-Dece.
    6. Abdullah Dasci & Gilbert Laporte, 2004. "Location and Pricing Decisions of a MultiStore Monopoly in a Spatial Market," Journal of Regional Science, Wiley Blackwell, vol. 44(3), pages 489-515, August.
    7. repec:bla:jregsc:v:44:y:2004:i:3:p:489-515:1 is not listed on IDEAS
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