Fluid dynamics models and their applications in transportation and pricing

Kachani, Soulaymane; Perakis, Georgia

doi:10.1016/j.ejor.2004.07.047

Cited by 21 publications

(12 citation statements)

References 33 publications

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“…The fluid dynamics approach to the theory of continuous vehicular traffic flow assumes that flow is strictly a function of density (Kachani and Perakis, 2006), and consequently, the speed is strictly a function of density, V = f(c). The continuous model can be described by a single partial differential equation in the conservation form as given by Eq.…”

Section: Adopted Two-phase Fundamental Diagram Approachesmentioning

confidence: 99%

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Reconstructing freeway travel times with a simplified network flow model alternating the adopted fundamental diagram

Çelikoğlu¹

2013

European Journal of Operational Research

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Section: Adopted Two-phase Fundamental Diagram Approachesmentioning

confidence: 99%

“…Van Woensel et al, 2008;Pillac et al, 2013), supply chains management (e.g. Kachani and Perakis, 2006) and congestion propagation (e.g. Florian et al, 2008;Zhao et al, 2010), where travel time is recognised as an important performance measure for assessing the operating conditions.…”

Section: Introductionmentioning

confidence: 99%

Reconstructing freeway travel times with a simplified network flow model alternating the adopted fundamental diagram

Çelikoğlu¹

2013

European Journal of Operational Research

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“…Continuous flow models have been employed to capture the influence of recurring breakdown (degradation) and repair (regeneration) cycles on the dynamics of discrete entities pertinent to manufacturing, communication networks, and various physical and biological systems [1][2][3]. These models essentially treat the movement of parts, packets, or any discrete entity in a system as a fluid flow, expressed in the form of linear or nonlinear differential equations.…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of the coupled dynamics of machine degradation and repair processes using piecewise affine stochastic differential equations

Tran

Bukkapatnam

2015

International Journal of Non-Linear Mechanics

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This paper introduces an approach to model the coupled dynamics of recurring degradation and restoration processes that take place in real-world systems, such as manufacturing machines, in the form of nonlinear (piecewise affine) differential equations. Unlike previous methods, interactions between degradation and repair dynamics that influence downtime distributions in such manufacturing systems can be explicitly considered and dependencies beyond correlations between the time between failures (TBF) and the time to repair (TTR) can be captured. The periodic solutions of the model capture the progressive evolution of long timescale failure and repair patterns. The distribution of short timescale failure-repair cycles can be captured by providing a class of random perturbations to certain model parameters. We provide sufficient conditions for the existence and stability of the resulting nonlinear stochastic differential equation (n-SDE) model solutions that mimic the breakdown and repair patterns observed in many real-world manufacturing systems, namely, fairly regular (periodic) large breakdown and repair cycles, interspersed with highly right skewed distributions of short cycles. We also define the basin of attraction for the periodic orbit. The n-SDE model was parametrized using real-world data sets acquired from an automotive manufacturing assembly line segment, and the model solutions were compared with actual observations of TBF and TTR patterns, as well as the performance of the process. Our approach reduces the computation time by about 25% when compared to a discrete-event simulation model, which uses conventional TBF and TTR distributions, implemented on a commercial platform. Experimental investigations also suggest that the model can capture the correlations and nonlinear coupled dynamics that exist in real-world operations among TBF and TTR, which are typically ignored in traditional approaches.

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“…McGill and van Ryzin (1999) There is a growing body of work (reviewed by Bitran and Caldentey 2003) in the revenue management literature that addresses the problem of joint pricing and allocation. Several papers in this area use deterministic demand models to capture complex multiproduct, multiresource, or dynamic environments (e.g., Cote et al 2003, Kachani and Perakis 2006, Kuyumcu and Popescu 2006. Ziya et al (2004) analyze demand conditions that ensure regularity in deterministic models.…”

Section: Relation To the Literaturementioning

confidence: 99%

Pricing and Revenue Management: The Value of Coordination

2014

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T he integration of systems for pricing and revenue management must trade off potential revenue gains against significant practical and technical challenges. This dilemma motivates us to investigate the value of coordinating decisions on prices and capacity allocation in a stylized setting. We propose two pairs of sequential policies for making static decisions-on pricing and revenue management-that differ in their degree of integration (hierarchical versus coordinated) and their pricing inputs (deterministic versus stochastic). For a large class of stochastic, price-dependent demand models, we prove that these four heuristics admit tractable solutions satisfying intuitive sensitivity properties. We further evaluate numerically the performance of these policies relative to a fully coordinated model, which is generally intractable. We find it interesting that near-optimal performance is usually achieved by a simple hierarchical policy that sets prices first, based on a nonnested stochastic model, and then uses these prices to optimize nested capacity allocation. This tractable policy largely outperforms its counterpart based on a deterministic pricing model. Jointly optimizing price and allocation decisions for the high-end segment improves performance, but the largest revenue benefits stem from adjusting prices to account for demand risk.

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Fluid dynamics models and their applications in transportation and pricing

Cited by 21 publications

References 33 publications

Reconstructing freeway travel times with a simplified network flow model alternating the adopted fundamental diagram

Reconstructing freeway travel times with a simplified network flow model alternating the adopted fundamental diagram

Modeling and analysis of the coupled dynamics of machine degradation and repair processes using piecewise affine stochastic differential equations

Pricing and Revenue Management: The Value of Coordination

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