×

zbMATH — the first resource for mathematics

Uncertain models for single facility location problems on networks. (English) Zbl 1246.90083
Summary: In practical location problems on networks, the vertex demand is usually non-deterministic. This paper employs uncertainty theory to deal with this non-deterministic factor in single facility location problems. We first propose the concepts of satisfaction degree for both vertices and the whole network, which are used to evaluate products assignment. Based on different network satisfaction degree, two models are constructed. The solution to these models is based on Hakimi’s results, and some examples are given to illustrate these models.

MSC:
90B80 Discrete location and assignment
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hakimi, S.L., Optimum locations of switching centers and the absolute centers and medians of a graph, Oper. res., 12, 450-459, (1964) · Zbl 0123.00305
[2] Hakimi, S.L., Optimum distribution of switching centers in a communication network and some related graph theoretic problems, Oper. res., 13, 462-475, (1965) · Zbl 0135.20501
[3] Handler, G.Y.; Mirchandani, P.B., Location on networks, theory and applications, (1979), MIT Press Cambridge, MA · Zbl 0533.90026
[4] Labbé, M.; Peeters, D.; Thisse, J.F., Handbooks in OR & MS, (1995), Elsevier Amsterdam
[5] Berman, O.; Larson, R.C.; Chiu, S.S., Optimal server location on a network operating as an M/G/1 queue, Oper. res., 33, 746-771, (1985) · Zbl 0576.90031
[6] Batta, R., Single server queueing-location models with rejection, Transport. sci., 22, 209-216, (1988) · Zbl 0648.90029
[7] Batta, R., A queueing-location model with expected service time dependent queueing disciplines, Euro. J. oper. res., 39, 192-205, (1989) · Zbl 0674.90031
[8] Liu, B.; process, Fuzzy, Hybrid process and uncertain process, J. uncert. syst., 2, 1, 3-16, (2008)
[9] Chen, X.W.; Liu, B., Existence and uniqueness theorem for uncertain differential equations, Fuzzy optim. decision making, 9, 1, 69-81, (2010) · Zbl 1196.34005
[10] Liu, B., Uncertain set theory and uncertain inference rule with application to uncertain control, J. uncert. syst., 4, 2, 83-98, (2010)
[11] Liu, B., Theory and practice of uncertain programming, (2009), Springer-Verlag Berlin · Zbl 1158.90010
[12] Gao, X.; Gao, Y.; Ralescu, D.A., On liu’s inference rule for uncertain systems, Int. J. uncertain. fuzz. knowledge-based syst., 18, 1, 1-11, (2010) · Zbl 1207.68386
[13] Liu, B., Uncertainty theory: A branch of mathematics for modeling human uncertainty, (2010), Springer-Verlag Berlin
[14] Zhu, Y., Uncertain optimal control with application to a portfolio selection model, Cybernet. syst., 41, 7, 535-547, (2010) · Zbl 1225.93121
[15] Liu, B., Uncertainty theory, (2007), Springer-Verlag Berlin
[16] Liu, B., Some research problems in uncertainty theory, J. uncertain syst., 3, 1, 3-10, (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.