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Spatial price equilibrium sensitivity analysis

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  • Chao, Gary S.
  • Friesz, Terry L.

Abstract

A direct approach to performing sensitivity analysis for a spatial price equilibrium problem with nonlinear transportation cost, commodity supply and commodity demand functions is presented. The first order derivatives of all decision variables with respect to parameter perturbations are shown to be expressable in a simple from which requires inversion of a matrix whose rank is the number of regions considered. A typical network usually involves several hundred regions and several thousand links; thus, by working with a matrix whose rank depends only on the number of regions rather than the number of links, computer storage is minimized and the necessary matrix inversion is made feasible, enabling us to perform the sensitivity analyses of very large nonlinear equilibrium problems. An example is presented to demonstrate application of the method. The approach taken here is also adaptable to the sensitivity analysis of Wardropian equilibrium problems.

Suggested Citation

  • Chao, Gary S. & Friesz, Terry L., 1984. "Spatial price equilibrium sensitivity analysis," Transportation Research Part B: Methodological, Elsevier, vol. 18(6), pages 423-440, December.
    • Handle: RePEc:eee:transb:v:18:y:1984:i:6:p:423-440
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    Cited by:

    1. José Holguín-Veras & Ning Xu & Miguel Jaller & John Mitchell, 2016. "A Dynamic Spatial Price Equilibrium Model of Integrated Urban Production-Transportation Operations Considering Freight Delivery Tours," Transportation Science, INFORMS, vol. 50(2), pages 489-519, May.
    2. Yang, Chin W. & Hwang, Ming J. & Sohng, Soong N., 2002. "The Cournot competition in the spatial equilibrium model," Energy Economics, Elsevier, vol. 24(2), pages 139-154, March.
    3. Konur, Dinçer & Geunes, Joseph, 2012. "Competitive multi-facility location games with non-identical firms and convex traffic congestion costs," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 373-385.
    4. Cho, Hsun-Jung & Smith, Tony E. & Friesz, Terry L., 2000. "A reduction method for local sensitivity analyses of network equilibrium arc flows," Transportation Research Part B: Methodological, Elsevier, vol. 34(1), pages 31-51, January.

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