Abstract
The mixed plant location problem (mixed in the sense of allowing capacitated as well as uncapacitated plants) is a difficult and important mixed integer problem. We give a direct dual method, consisting of several phases (each of which appears essential for some data), to resolve a strong relaxed form of the problem with additional constraints over the integer variables (user specified, or derived from the data themselves). When all features of the algorithm are employed, there appears to be no difficulty with problems of 100 plants, even in an inefficient computer implementation. The primal solutions which we derive from the orthogonality conditions and a simple greedy heuristic are almost always much better than those we obtain from a standard relaxed problem in the Lagrangean sense. With an enumeration code in an efficient implementation we would expect to be capable of resolving very large problems (of perhaps up to 500 or 1000 plants) to within practically well acceptable tolerances.
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This paper is a revision of Tech. Rep. 20, Dept. of Statistics. The Wharton School, University of Philadelphia, January 1977. We should like to thank the referee for some valuable suggestions.
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Guignard, M., Spielberg, K. A direct dual method for the mixed plant location problem with some side constraints. Mathematical Programming 17, 198–228 (1979). https://doi.org/10.1007/BF01588244
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DOI: https://doi.org/10.1007/BF01588244