Nagurney Anna, Besik Deniz
Department of Operations and Information Management Isenberg School of Management, University of Massachusetts Amherst, Amherst, MA 01003 USA.
Department of Analytics and Operations Robins School of Business, University of Richmond, Richmond, VA 23173 USA.
Optim Lett. 2022;16(8):2483-2500. doi: 10.1007/s11590-022-01868-8. Epub 2022 Mar 15.
The spatial price equilibrium modeling framework, which emphasizes the importance of transportation costs between markets, has been utilized in agricultural, energy, mineral as well as financial applications. In this paper, we construct static and dynamic spatial price equilibrium networks with flow-dependent arc multipliers, which expand the reach of applications. The static model is formulated and analyzed as a variational inequality problem, whereas the dynamic one is formulated as a projected dynamical system, whose set of stationary points coincides with the set of solutions of the variational inequality. Qualitative results are presented, along with an algorithm, the Euler method, which yields a time-discretization of the continuous-time adjustment processes associated with the product shipments from supply markets to demand markets. The algorithm is implemented and applied to compute solutions to numerical examples with flow-dependent arc multipliers addressing losses and/or gains, inspired by perishable agricultural products, and by financial investments. The results in this paper add to the literature on generalized networks as well as that on commodity trade.
空间价格均衡建模框架强调了市场间运输成本的重要性，已被应用于农业、能源、矿产以及金融领域。在本文中，我们构建了具有流量依赖弧乘数的静态和动态空间价格均衡网络，这扩展了应用范围。静态模型被表述并分析为一个变分不等式问题，而动态模型则被表述为一个投影动力系统，其驻点集与变分不等式的解集重合。给出了定性结果，以及一种算法——欧拉方法，该方法对与产品从供应市场到需求市场运输相关的连续时间调整过程进行时间离散化。该算法被实现并应用于计算具有流量依赖弧乘数的数值示例的解，这些示例考虑了受易腐农产品和金融投资启发的损失和/或收益。本文的结果丰富了关于广义网络以及商品贸易的文献。
