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871.
On the capacitated vehicle routing problem 总被引:1,自引:0,他引:1
We consider the Vehicle Routing Problem, in which a fixed fleet of delivery vehicles of uniform capacity must service known
customer demands for a single commodity from a common depot at minimum transit cost. This difficult combinatorial problem
contains both the Bin Packing Problem and the Traveling Salesman Problem (TSP) as special cases and conceptually lies at the
intersection of these two well-studied problems. The capacity constraints of the integer programming formulation of this routing
model provide the link between the underlying routing and packing structures. We describe a decomposition-based separation
methodology for the capacity constraints that takes advantage of our ability to solve small instances of the TSP efficiently.
Specifically, when standard procedures fail to separate a candidate point, we attempt to decompose it into a convex combination
of TSP tours; if successful, the tours present in this decomposition are examined for violated capacity constraints; if not,
the Farkas Theorem provides a hyperplane separating the point from the TSP polytope. We present some extensions of this basic
concept and a general framework within which it can be applied to other combinatorial models. Computational results are given
for an implementation within the parallel branch, cut, and price framework SYMPHONY.
Received: October 30, 2000 / Accepted: December 19, 2001 Published online: September 5, 2002
Key words. vehicle routing problem – integer programming – decomposition algorithm – separation algorithm – branch and cut
Mathematics Subject Classification (2000): 20E28, 20G40, 20C20 相似文献
872.
E. Casarejos P. Armbruster L. Audouin J. Benlliure M. Bernas A. Boudard R. Legrain S. Leray B. Mustapha S. Czajkowski T. Enqvist B. Fernandez J. Pereira M. Pravikoff F. Rejmund K. -H. Schmidt C. Stephan J. Taieb L. Tassan-Got C. Villagrasa C. Volant W. Wlazlo 《Physics of Atomic Nuclei》2003,66(8):1413-1420
The isotopic production cross sections of heavy residues in relativistic heavy-ion collisions have been investigated in inverse kinematics. The primary reaction products were fully identified in mass and atomic number prior to beta decay using the fragment separator FRS. The huge collection of data obtained helps in the understanding of the two main reaction mechanisms involved: fragmentation and fission. These data provide basic information for future radioactive ion beam facilities and for technical applications like intense neutron sources by means of spallation targets. 相似文献
873.
874.
875.
876.
V. F. Shkar’ V. P. Denisenkov A. M. Grishin A. A. Yalali S. I. Khartsev E. I. Nikolaev V. N. Sayapin 《Physics of the Solid State》2003,45(12):2334-2337
Bismuth iron garnet films prepared through electron-beam and laser-induced evaporation on (001)-oriented substrates of scandium gallium gadolinium garnet are investigated using ferromagnetic resonance. It is assumed that the additional minima observed in the angular dependence of the resonance field can be associated with the magnetic moment of bismuth ions. 相似文献
877.
S. Juodkazis A.V. Rode E.G. Gamaly S. Matsuo H. Misawa 《Applied physics. B, Lasers and optics》2003,77(2-3):361-368
We report on three-dimensional (3D) optical memory recording and reading in glass by femtosecond pulses. Optically induced dielectric breakdown of glass is a mechanism of recording. The formulae of dielectric breakdown presented are applicable, in principle, for any crystalline or amorphous dielectric material. Scaling dependences of the probabilities of multi-photon and impact ionization are given. The measured threshold of an in-bulk dielectric breakdown of silica was reproduced numerically by implementing the ionization potential of Si (8.15 eV) for calculations. Exact measures of focal spot size and pulse duration at the focus allowed us to evaluate the intensity of a pulse during recording of 3D optical memory bits with high accuracy. The readout of the 3D optical memory was carried out by the white-light continuum generated from the previously damaged sites (recorded memory bits). The mechanism of the readout was a four-photon parametric interaction. PACS 42.65.Jx; 42.65.Ky; 42.70.Ce; 42.79.Vb 相似文献
878.
LetC(X,E) andC(Y,F) denote the spaces of continuous functions on the Tihonov spacesX andY, taking values in the Banach spacesE andF, respectively. A linear mapH:C(X,E)→C(Y,F) isseparating iff(x)g(x)=0 for allx inX impliesHf(y)Hg(y)=0 for ally inY. Some automatic continuity properties and Banach-Stone type theorems (i.e., asserting that isometries must be of a certain
form) for separating mapsH between spaces of real- and complex-valued functions have already been developed. The extension of such results to spaces
of vector-valued functions is the general subject of this paper. We prove in Theorem 4.1, for example, for compactX andY, that a linear isometryH betweenC(X,E) andC(Y,F) is a “Banach-Stone” map if and only ifH is “biseparating (i.e,H andH
−1 are separating). The Banach-Stone theorems of Jerison and Lau for vector-valued functions are then deduced in Corollaries
4.3 and 4.4 for the cases whenE andF or their topological duals, respectively, are strictly convex.
Research supported by the Fundació Caixa Castelló, MI/25.043/92 相似文献
879.
If M is an isoparametric hypersurface in a sphere S
n
with four distinct principal curvatures, then the principal curvatures κ1, . . . , κ4 can be ordered so that their multiplicities satisfy m
1 = m
2 and m
3 = m
4, and the cross-ratio r of the principal curvatures (the Lie curvature) equals −1. In this paper, we prove that if M is an irreducible connected proper Dupin hypersurface in R
n
(or S
n
) with four distinct principal curvatures with multiplicities m
1 = m
2 ≥ 1 and m
3 = m
4 = 1, and constant Lie curvature r = −1, then M is equivalent by Lie sphere transformation to an isoparametric hypersurface in a sphere. This result remains true if the
assumption of irreducibility is replaced by compactness and r is merely assumed to be constant.
相似文献
880.
This paper establishes a general ABC inventory classification system as the foundation for a normative model of the maintenance cost structure and stock turnover characteristics of a large, multi-item inventory system with constant demand. For any specified number of inventory classes, the model allows expression of the overall system combined ordering and holding cost in terms of (i) the re-ordering frequencies for the items in each inventory class and (ii) the inventory class structure, that is, the proportion of the total system's items that are in each inventory class. The model yields a minimum total maintenance cost function, which reflects the effect of class structure on inventory maintenance costs and turnover. If the Pareto curve (a.k.a. Distribution-by-value function) for the inventory system can be expressed (or approximated) analytically, the model can also be used to determine an optimal class structure, as well as an appropriate number of inventory classes. A special case of the model produces a simply structured, class-based ordering policy for minimizing total inventory maintenance costs. Using real data, the cost characteristics of this policy are compared to those of a heuristic, commonly used by managers of multi-item inventory systems. This cost comparison, expressed graphically, underscores the need for normative modelling approaches to the problem of inventory cost management in large, multi-item systems. 相似文献