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One and Two Facility Network Design Revisited

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  • Trilochan Sastry

Abstract

The one facility one commodity network design problem (OFOC) with nonnegative flow costs considers the problem of sending d units of flow from a source to a destination where arc capacity is purchased in batches of C units. The two facility problem (TFOC) is similar, but capacity can be purchased either in batches of C units or one unit. Flow costs are zero. These problems are known to be NP-hard. We describe an exact O(n 3 3 n ) algorithm for these problems based on the repeated use of a bipartite matching algorithm. We also present a better lower bound of Ω(n 2 k * ) for an earlier Ω(n 2k ) algorithm described in the literature where k=⌊d/C⌋ and k * =min k,⌊(n−2)/2⌋. The matching algorithm is faster than this one for k≥⌊(n−2)/2⌋. Finally, we provide another reformulation of the problem that is quasi integral. This property could be useful in designing a modified version of the simplex method to solve the problem using a sequence of pivots with integer extreme solutions, referred to as the integral simplex method in the literature. Copyright Kluwer Academic Publishers 2001

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  • Trilochan Sastry, 2001. "One and Two Facility Network Design Revisited," Annals of Operations Research, Springer, vol. 108(1), pages 19-31, November.
    • Handle: RePEc:spr:annopr:v:108:y:2001:i:1:p:19-31:10.1023/a:1016042524674
    DOI: 10.1023/A:1016042524674
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    Cited by:

    1. Rönnberg, Elina & Larsson, Torbjörn, 2009. "Column generation in the integral simplex method," European Journal of Operational Research, Elsevier, vol. 192(1), pages 333-342, January.

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