Abstract
The multi-level Simple Plant Location Problem (MLP) are studied. Assumed that cost of transporting unit commodity from one site to other site equal to the sum of edge lengths in the path between these sites. Let p be a number of levels, n – a number of demand sites, m r – a number of feasible facilities on level r, 1 ≤ r ≤ p.
For the MLP on a chain exact algorithms A p andà p are constructed with time complexities(pnm 1• • • m p ) and (n 3∑ pi =1 m r ) respectively. For a case two and three levels algorithms A 2 and A 3 are preferable. In case p ≤ 4 the polynomial algorithm à p is better.
For a case MLP on tree networks (in contrary to the chain problem) the optimal solution with connected regions of servicing can not exist (even in case two levels). Nevertheless in case two-level LP on tree networks we present the polynomial exact algorithm which requires (m 3 n) operations.
This work was supported by the grant 96-01-01591 of the Russian Foundation of Fundamental Research.
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References
Kaufman L., Eede M.V., Haunsen P.A. (1977) A plant and warehouse location problemOper. Res. Quart. V. 28, N 3. P.547–554.
Ro H., Tcha D. (1984) A branch and bound algorithm for the two-level uncapacitated facility location problem with some side constraintsEuropean J. Oper. Res.V. 18, N 3. P.349–358.
Tcha D.W., Lee B. (1984) A branch and bound algorithm for the multi-level uncapacitated facility location problemEuropean J. Oper. Res. V. 18, N 1. P.35–43.
V. S. Mikhalevich, V. A. Trubin, and N. Z. Shor (1986) Optimization Problems of Production- Transportation Planning (in Russian), Nauka, Moscow.
V. A. Trubin and F. A. Sharifov (1992) The simplest multi-level location problem on a tree-like network (in Russian),Kibernet. Sistem. Anal. (Kiev), No. 6, 128–135.
E. Kh. Gimadi (1995) Effective algorithms for solving the multi-level plant location problem (in Russian),Diskretny analyz i issledov. oper. (Novosibirsk), V. 2, N 4. P. 13–31.
M. R. Garey, D. S. Johnson (1979)Computers and Intractability, Freeman, San Francisco.
V. L. Beresnev, E. Kh. Gimadi, and V. T. Dement’ev (1978)Extremal Standardization Problems (in Russian), Nauka, Novosibirsk.
E. Kh. Gimadi and N. I. Glebov (1982)Extremal Problems of Making Solutions (in Russian), Novosibirsk University, Novosibirsk.
E. Kh. Gimadi (1970) Choice of optimal scales in a class of location, unification, and standard-ization problems (in Russian),Upravlyaemye Sistemy 6, 57–70.
E. Kh. Gimadi, V. T. Dement’ev (1973) Certain problems in the selection of optimal paramet-ric series and methods for their solution (standardization problems) (in Russian), in:Problemy Kibernetiki. Vol. 27, Nauka, Moscow, pp. 19–32.
V. L. Beresnev (1979) Algorithms for the minimization of polynomials of Boolean variables (in Russian), in:Problemy Kibernetiki. Vol. 36,Nauka, Moscow, pp. 225–246.
E. Kh. Gimadi (1987) A standardization problem with data of arbitrary sign and with connected quasiconvex and almost quanticonvex matrices (in Russian),Upravlyaemye Sistemy 27, 3–11.
E. Kh. Gimadi (1983) An efficient algorithm for solution of a distribution problem with servicing areas that are connected in relation to an acyclic network (in Russian),Upravlyaemye Sistemy 23,12–23.
E. Kh. Gimadi (1984) The problem of distribution on a network with centrally connected service areas, (in Russian),Upravlyaemye Sistemy 25, 38–47.
E. Kh. Gimadi (1984) The problem of distribution on a network with centrally connected service areas, (in Russian),Upravlyaemye Sistemy 25, 38–47.
A. A. Ageev (1990) A polynomial algorithm for solving the location problem on a series-parallel network (in Russian),Upravlyaemye Sistemy 30, 3–16.
Ageev A.A. (1992) A criterion of polynomial-time solvability for the network location problem IntegerProgramming and Combinatorial Optimization. Proc. IPCO II Conf. Campus Printing, Carnegie Mellon University, P.237–245.
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Gimadi, E.K. (1997). Exact Algorithms for Some Multi-level Location Problems on a Chain and a Tree. In: Operations Research Proceedings 1996. Operations Research Proceedings, vol 1996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60744-8_14
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DOI: https://doi.org/10.1007/978-3-642-60744-8_14
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