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  • 1
    Electronic Resource
    Electronic Resource
    Two stage linear programming under uncertainty with 0–1 integer first stage variables (1980)
    Springer
    Mathematical programming 19 (1980), S. 279-288 
    Details
    ISSN: 1436-4646
    Keywords: Mixed-Integer Programming ; Stochastic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Stochastic programs with continuous variables are often solved using a cutting plane method similar to Benders' partitioning algorithm. However, mixed 0–1 integer programs are also solved using a similar procedure along with enumeration. This similarity is exploited in this paper to solve two stage linear programs under uncertainty where the first stage variables are 0–1. Such problems often arise in capital investment. A network investment application is given which includes as a special case a coal transportation problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581648
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Investments in stochastic maximum flow networks (1991)
    Springer
    Annals of operations research 31 (1991), S. 457-467 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Each are (i, j) of the network has capacity ξ ij where ξ ij is a non-negative random variable. The capacity of any arc may be reduced increased by an amountu ij ≥0 at a cost ofc ij u ij . The objective is to maximizev−K∑c ij u ij wherev is the expected maximum flow. This problem is formulated as a two-stage linear program under uncertainty. Each feasible $$\bar u = ||\bar u_{ij} ||$$ generates a constraint $$ - \Sigma \pi _{ij} (\bar u)u_{ij} + \theta \leqslant \rho (\bar u)$$ where $$\pi _{ij} (\bar u)$$ is the probability arc (i, j) is in the minimum cut set and $$\rho (\bar u)$$ the expected value of the maximum flow under $$u = (\bar u)$$ . The formulation is later generalized to include certain conditions under which the increase in capacity of an arc may be a non-deterministic function of the investmentc ij u ij .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02204863
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  • 3
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    Investments in stochastic maximum flow networks (1991)
    Springer
    Details
    Publication Date: 1991-12-01
    Print ISSN: 0254-5330
    Electronic ISSN: 1572-9338
    Topics: Mathematics , Economics
    Published by Springer
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