{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:40:57Z","timestamp":1777902057029,"version":"3.51.4"},"reference-count":7,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2003,3,1]],"date-time":"2003-03-01T00:00:00Z","timestamp":1046476800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIMULATION"],"published-print":{"date-parts":[[2003,3]]},"abstract":"<jats:p>Production flows through factories are modeled through conservation laws leading to nonlinear hyperbolic partial differential equations (PDEs). For a linear production line, models based on conservation laws can be derived from first principles, using methods from gas dynamics. For reentrant manufacturing, a heuristic model is presented merging a nonlocal state equation relating throughput time to work in progress through Little\u2019s law to produce a nonlinear, nonlocal hyperbolic PDE. These two models can serve as the building blocks of fast simulations of the dynamics of capacity-limited supply chains. The authors present simulations for a chain consisting of a reentrant module, followed and preceded by a linear module. The response of the system to various production scenarios is discussed.<\/jats:p>","DOI":"10.1177\/0037549703255638","type":"journal-article","created":{"date-parts":[[2003,11,12]],"date-time":"2003-11-12T16:35:11Z","timestamp":1068654911000},"page":"157-162","source":"Crossref","is-referenced-by-count":4,"title":["A Mesoscopic Approach to the Simulation of Semiconductor Supply Chains"],"prefix":"10.1177","volume":"79","author":[{"given":"Dan","family":"Marthaler","sequence":"first","affiliation":[{"name":"Department of Mathematics Arizona State University Tempe, AZ 85287-1804"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dieter","family":"Armbruster","sequence":"additional","affiliation":[{"name":"Department of Mathematics Arizona State University Tempe, AZ 85287-1804,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Ringhofer","sequence":"additional","affiliation":[{"name":"Department of Mathematics Arizona State University Tempe, AZ 85287-1804"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2003,3,1]]},"reference":[{"key":"atypb1","unstructured":"1 WWK. 1996. Factory explorer. Portland, OR: WWK ."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.9.3.383"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"3 Armbruster, D., D. Marthaler, and C. Ringhofer. 2002. Kinetic and fluid model hierarchies for supply chains. Preprint, Arizona State University .","DOI":"10.1137\/S1540345902419616"},{"key":"atypb4","unstructured":"4 Helbing, D. 1996. Traffic modeling by means of physical concepts . In Workshop on traffic and granular flow, edited by D. E. Wolf, M. Schreckenberg, and A. Bachem. Singapore: World Scientific."},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"5 LeVeque, R. J. 1992. Numerical methods for conservation laws. Boston: Birkhauser-Verlag .","DOI":"10.1007\/978-3-0348-8629-1"},{"key":"atypb6","unstructured":"6 LeVeque, R. J. 1998. Finite difference methods for differential equations. Draft version for use in AMath 585-6, University of Washington ."},{"key":"atypb7","unstructured":"7 Armbruster, D., D. Marthaler, and C. Ringhofer. 2002. A continuum model for a re-entrant factory. Preprint, Arizona State University ."}],"container-title":["SIMULATION"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549703255638","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549703255638","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T11:18:23Z","timestamp":1777634303000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0037549703255638"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,3]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2003,3]]}},"alternative-id":["10.1177\/0037549703255638"],"URL":"https:\/\/doi.org\/10.1177\/0037549703255638","relation":{},"ISSN":["0037-5497","1741-3133"],"issn-type":[{"value":"0037-5497","type":"print"},{"value":"1741-3133","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,3]]}}}