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Spatial Temporal Analysis of Fieldwise Flow in Microvasculature
Published on: November 18, 2019
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Spatial price equilibrium networks with flow-dependent arc multipliers.
1Department of Operations and Information Management Isenberg School of Management, University of Massachusetts Amherst, Amherst, MA 01003 USA.
Optimization Letters
|March 21, 2022
Summary
This study introduces advanced spatial price equilibrium models with flow-dependent multipliers for dynamic and static networks. These models enhance understanding of commodity trade and financial investments by accounting for real-world market dynamics.
Area of Science:
- Economics
- Operations Research
- Applied Mathematics
Background:
- Spatial price equilibrium models are crucial for understanding market dynamics, particularly transportation costs.
- Existing frameworks often simplify market interactions, limiting applications in complex scenarios.
Purpose of the Study:
- To develop and analyze static and dynamic spatial price equilibrium networks incorporating flow-dependent arc multipliers.
- To expand the applicability of spatial price equilibrium models to a broader range of economic and financial systems.
Main Methods:
- Formulation of the static model as a variational inequality problem.
- Formulation of the dynamic model as a projected dynamical system.
- Application of the Euler method for time-discretization of continuous-time adjustment processes.
Main Results:
- The static model is analyzed as a variational inequality, and the dynamic model as a projected dynamical system.
- The Euler method is presented and implemented to solve numerical examples with flow-dependent arc multipliers.
- The models successfully address losses and gains in product shipments, inspired by agricultural and financial markets.
Conclusions:
- The developed models offer a more realistic representation of spatial price equilibrium with flow-dependent factors.
- The findings contribute to the literature on generalized networks and commodity trade, with implications for perishable goods and financial investments.
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