An efficient generalized network-simplex-based algorithm for manufacturing network flows |
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Authors: | Prahalad Venkateshan Kamlesh Mathur Ronald H Ballou |
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Institution: | (1) AmTrust Bank, 1801 East 9th Street, Mail-Code OH99-0307, Cleveland, OH 44114, USA;(2) Department of Operations, Weatherhead School of Management, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA |
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Abstract: | Fang and Qi (Optim. Methods Softw. 18:143–165, 2003) introduced a new generalized network flow model called manufacturing network flow model for manufacturing process modeling.
A key distinguishing feature of such models is the assembling of component raw-materials, in a given proportion, into an end-product. This assembling operation cannot be modeled using usual generalized networks (which allow gains and
losses in flows), or using multi-commodity networks (which allow flows of multiple commodity types on a single arc). The authors
developed a network-simplex-based algorithm to solve a minimum cost flow problem formulated on such a generalized network
and indicated systems of linear equations that need to be solved during the course of the network-simplex-based solution procedure.
In this paper, it is first shown how various steps of the network-simplex-based solution procedure can be performed efficiently
using appropriate data structures. Further, it is also shown how the resulting system of linear equations can be solved directly
on the generalized network. |
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Keywords: | Network flows Manufacturing networks Generalized network-simplex method |
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