منابع مشابه
The Mixing Set with Divisible Capacities
Given rational numbers C0, . . . , Cm and b0, . . . , bm, the mixing set with arbitrary capacities is the mixed-integer set defined by conditions s + Ctzt ≥ bt, 0 ≤ t ≤ m, s ≥ 0, zt integer, 0 ≤ t ≤ m. Such a set has applications in lot-sizing problems. We study the special case of divisible capacities, i.e. Ct/Ct−1 is a positive integer for 1 ≤ t ≤ m. Under this assumption, we give an extended...
متن کاملThe mixing-MIR set with divisible capacities
We study the set S = {(x, y) ∈ + × Zn : x + Bjyj ≥ bj, j = 1, . . . , n}, where Bj , bj ∈ +−{0}, j = 1, . . . , n, and B1| · · · |Bn. The set S generalizes the mixed-integer rounding (MIR) set of Nemhauser and Wolsey and the mixing-MIR set of Günlük and Pochet. In addition, it arises as a substructure in general mixed-integer programming (MIP), such as in lot-sizing. Despite its importance, a n...
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We give a simple algorithm for linear optimization over the mixing set with divisible capacities, and derive a compact extended formulation from such an algorithm. The main idea is to apply a suitable unimodular transformation to obtain an equivalent problem that is easier to analyze.
متن کاملAn axiomatization of entropy of capacities on set systems
We present an axiomatization of the entropy of capacities defined on set systems which are not necessarily the whole power set, but satisfy a condition of regularity. This entropy encompasses the definition of Marichal and Roubens for the entropy of capacities. Its axiomatization is in the spirit of the one of Faddeev for the classical Shannon entropy. In addition, we present also an axiomatiza...
متن کاملEntropy of capacities on lattices and set systems
We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measures. Capacities on lattices address the general case where the family of subsets is not necessarily the Boolean lattice of all subsets. Our definition encompasses the classical definition of Shannon for probability mea...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky a fysiky
سال: 1933
ISSN: 1802-114X
DOI: 10.21136/cpmf.1933.121896