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A variational approach for continuous supply chain networks

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Title: A variational approach for continuous supply chain networks
Authors: Han, K
Friesz, TL
Yao, T
Item Type: Journal Article
Abstract: We consider a continuous supply chain network consisting of buffering queues and processors first proposed by [D. Armbruster, P. Degond, and C. Ringhofer, SIAM J. Appl. Math., 66 (2006), pp. 896–920] and subsequently analyzed by [D. Armbruster, P. Degond, and C. Ringhofer, Bull. Inst. Math. Acad. Sin. (N.S.), 2 (2007), pp. 433–460] and [D. Armbruster, C. De Beer, M. Fre- itag, T. Jagalski, and C. Ringhofer, Phys. A, 363 (2006), pp. 104–114]. A model was proposed for such a network by [S. G ̈ottlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559] using a system of coupling ordinary differential equations and partial differential equations. In this article, we propose an alternative approach based on a variational method to formulate the network dynamics. We also derive, based on the variational method, a computational algorithm that guarantees numerical stability, allows for rigorous error estimates, and facilitates efficient computations. A class of network flow optimization problems are formulated as mixed integer programs (MIPs). The proposed numerical algorithm and the corresponding MIP are compared theoretically and numerically with existing ones [A. Fu ̈genschuh, S. Go ̈ttlich, M. Herty, A. Klar, and A. Martin, SIAM J. Sci. Comput., 30 (2008), pp. 1490–1507; S. Go ̈ttlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559], which demonstrates the modeling and computational advantages of the variational approach.
Issue Date: 20-Feb-2014
URI: http://hdl.handle.net/10044/1/26584
DOI: https://dx.doi.org/10.1137/120868943
ISSN: 0363-0129
Publisher: Society for Industrial and Applied Mathematics
Start Page: 663
End Page: 686
Journal / Book Title: SIAM Journal on Control and Optimization
Volume: 52
Issue: 1
Copyright Statement: © 2014 Society for Industrial and Applied Mathematics
Keywords: continuous supply chain
partial differential equations
variational method
mixed integer programs
Publication Status: Published
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering



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