The bilevel standardization problem with uniqueness condition for an optimal customer choice (Q2773615)
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scientific article; zbMATH DE number 1710244
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The bilevel standardization problem with uniqueness condition for an optimal customer choice |
scientific article; zbMATH DE number 1710244 |
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24 February 2002
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facility location
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dynamic programming
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bilevel models
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The bilevel standardization problem with uniqueness condition for an optimal customer choice (English)
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The bilevel uncapacitated facility location problem is described. Two polynomially solvable cases are discovered. The first one corresponds to the case of connected matrices of the input data. The second one corresponds to the case of quasiconvex matrices [see \textit{A. A. Ageev} and \textit{V. L. Beresnev,} Tr. Inst. Mat. 10, 5--17 (1988; Zbl 0699.90072)]. The dynamic programming approach is applied to find an optimal solution for both cases. It is shown that the bilevel problem can be reduced to the multistage uncapacitated facility location problem [see \textit{E. N. Goncharov} and \textit{Yu. A. Kochetov}, Diskretn. Anal. Issled. Oper., Ser. 2 6, No. 1, 12--32 (1999; Zbl 0931.90001)].
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