Abstract
We present and study a mixed integer programming model that arises as a substructure in many industrial applications. This model provides a relaxation of various capacitated production planning problems, more general fixed charge network flow problems, and other structured mixed integer programs. We analyze the polyhedral structure of the convex hull of this model; among other results, we present valid inequalities that induce facets of the convex hull in the general case, which is NP—hard. We then present an extended formulation for a polynomially solvable case for which the LP always gives an integral solution. Projecting from this extended formulation, we show that the inequalities presented for the general model suffice to solve this polynomially solvable case by linear programming in the original variable space.
This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility is assumed by the authors. This research was also supported by NSF Grant No. DMI-9700285 and by Philips Electronics North America.
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Miller, A.J., Nemhauser, G.L., Savelsbergh, M.W.P. (2001). Facets, Algorithms, and Polyhedral Characterizations for a Multi-item Production Planning Model with Setup Times. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_25
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DOI: https://doi.org/10.1007/3-540-45535-3_25
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