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  • Articles  (4)
  • Integer Programming  (4)
  • Springer  (4)
  • American Institute of Physics
  • Blackwell Publishing Ltd
  • Cell Press
  • International Union of Crystallography (IUCr)
  • Oxford University Press
  • 2010-2014
  • 2005-2009
  • 1985-1989
  • 1975-1979  (4)
  • 1945-1949
  • 2005
  • 1978  (4)
  • Computer Science  (4)
  • Natural Sciences in General
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  • Articles  (4)
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  • Springer  (4)
  • American Institute of Physics
  • Blackwell Publishing Ltd
  • Cell Press
  • International Union of Crystallography (IUCr)
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Years
  • 2010-2014
  • 2005-2009
  • 1985-1989
  • 1975-1979  (4)
  • 1945-1949
Year
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  • Computer Science  (4)
  • Natural Sciences in General
  • Mathematics  (4)
  • 1
    Electronic Resource
    Electronic Resource
    The reformulation of two mixed integer programming problems (1978)
    Springer
    Mathematical programming 14 (1978), S. 325-331 
    Details
    ISSN: 1436-4646
    Keywords: Integer Programming ; Formulation ; Models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Two practical problems are described, each of which can be formulated in more than one way as a mixed integer programming problem. The computational experience with two formulations of each problem is given. It is pointed out how in each case a reformulation results in the associated linear programming problem being more constrained. As a result the reformulated mixed integer problem is easier to solve. The problems are a multi-period blending problem and a mining investment problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588974
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  • 2
    Electronic Resource
    Electronic Resource
    An algorithm for the 0/1 Knapsack problem (1978)
    Springer
    Mathematical programming 14 (1978), S. 1-10 
    Details
    ISSN: 1436-4646
    Keywords: Integer Programming ; Reduction Method ; Branch and Bound Method ; Knapsack
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Knapsack problem (maximize a linear function, subject to a unique constraint, all being in integers), although of thenp-complete type, is a well solved case in combinatorial programming. The reason for this is twofold: (i) an upper bound of the objective function is easy to compute (ii) it is quite simple to construct feasible solutions. They give lower bounds of the optimum. This makes it possible to know rapidly the optimal value of many variables, and therefore to reduce the problem. Several studies have appeared recently on the subject [5, 9, 12, 18]. We present a program by which Knapsacks involving up to 60 000 boolean variables were solved in a matter of seconds, on an I.B.M. 370-168.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588947
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  • 3
    Electronic Resource
    Electronic Resource
    A hybrid approach to discrete mathematical programming (1978)
    Springer
    Mathematical programming 14 (1978), S. 21-40 
    Details
    ISSN: 1436-4646
    Keywords: Integer Programming ; Dynamic Programming ; Branch-and-Bound ; Discrete Optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The dynamic programming and branch-and-bound approaches are combined to produce a hybrid algorithm for separable discrete mathematical programs. Linear programming is used in a novel way to compute bounds. Every simplex pivot permits a bounding test to be made on every active node in the search tree. Computational experience is reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588949
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  • 4
    Electronic Resource
    Electronic Resource
    Lifting the facets of zero–one polytopes (1978)
    Springer
    Mathematical programming 15 (1978), S. 268-277 
    Details
    ISSN: 1436-4646
    Keywords: Integer Programming ; Zero–One Programming ; Facets ; Valid Inequalities ; Lifting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We discuss a procedure to obtain facets and valid inequalities for the convex hull of the set of solutions to a general zero–one programming problem. Basically, facets and valid inequalities defined on lower dimensional subpolytopes are lifted into the space of the original problem. The procedure generalizes the previously known techniques for lifting facets in two respects. First, the general zero–one programming problem is considered rather than various special cases. Second, the procedure is exhaustive in the sense that it accounts for all the facets (valid inequalities) which are liftings of a given lower dimensional facet (valid inequality).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609032
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