Name
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. Freitag, T. Jagalski, and C. Ringhofer, Phys. A, 363 (2006), pp. 104-114]. A model was proposed for such a network by [S. Gottlich, 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. Fugenschuh, S. Gottlich, M. Herty, A. Klar, and A. Martin, SIAM J. Sci. Comput., 30 (2008), pp. 1490-1507; S. Gottlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545-559], which demonstrates the modeling and computational advantages of the variational approach. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/120868943 | SIAM JOURNAL ON CONTROL AND OPTIMIZATION |
Keywords | Field | DocType |
continuous supply chain,partial differential equations,variational method,mixed integer programs | Mathematical optimization,Variational method,Queue,Supply chain network,Supply chain,Partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
52 | 1 | 0363-0129 |
Citations | PageRank | References |
1 | 0.39 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ke Han | 1 | 1 | 1.74 |
| Terry L. Friesz | 2 | 227 | 42.12 |
| Tao Yao | 3 | 1 | 0.39 |