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Zbl 1159.74317
Sun, Shuyu; Dong, Ming
Continuum modeling of supply chain networks using discontinuous Galerkin methods. (English)
[J] Comput. Methods Appl. Mech. Eng. 197, No. 13-16, 1204-1218 (2008). ISSN 0045-7825

Summary: Using a connectivity matrix, we establish a continuum modeling approach with partial differential equations of conservation laws for simulating materials flow in supply chain networks. A number of existing and new constitutive relationships for modeling velocity are summarized or proposed. To effectively treat strong advection components within the modeling system, we apply discontinuous Galerkin (DG) methods for solving production flow in a supply chain network. In addition, a number of DG properties are analyzed for treating network flow. In particular, a nearly optimal error estimate is obtained using a new estimating technique that utilizes two physical meaningful assumptions on the connectivity matrix. Numerical examples are provided to simulate a single node, a serial supply chain and an entire network as well as to investigate the influence of influx variation and node shut-down to the profiles of work in progress (WIP) and outflux. It is shown that the proposed modeling approach is applicable to a large number of scenarios including re-entrant lines and the proposed DG algorithm is robust and accurate for predicting WIP and outflux behaviors.

MSC 2000:: *74A99 Generalities, etc. of continuum mechanics of solids
74S30 Other numerical methods

Keywords: supply chain network; re-entrant line; connectivity matrix; discontinuous Galerkin method; conservation law; continuum modeling

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