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21.
Joseph Y.-T. Leung 《Discrete Applied Mathematics》2007,155(8):945-970
We consider the problem of scheduling orders for multiple different product types in an environment with m dedicated machines in parallel. The objective is to minimize the total weighted completion time. Each product type is produced by one and only one of the m dedicated machines; that is, each machine is dedicated to a specific product type. Each order has a weight and may also have a release date. Each order asks for certain amounts of various different product types. The different products for an order can be produced concurrently. Preemptions are not allowed. Even when all orders are available at time 0, the problem has been shown to be strongly NP-hard for any fixed number (?2) of machines. This paper focuses on the design and analysis of efficient heuristics for the case without release dates. Occasionally, however, we extend our results to the case with release dates. The heuristics considered include some that have already been proposed in the literature as well as several new ones. They include various static and dynamic priority rules as well as two more sophisticated LP-based algorithms. We analyze the performance bounds of the priority rules and of the algorithms and present also an in-depth comparative analysis of the various rules and algorithms. The conclusions from this empirical analysis provide insights into the trade-offs with regard to solution quality, speed, and memory space. 相似文献
22.
Editorial: Metal-Enhanced Fluorescence 总被引:1,自引:0,他引:1
23.
24.
Joseph Shipman 《Mathematical Intelligencer》2007,29(4):9-14
Theorems 2 and 3 establish the minimum algebraic conditions necessary for a field to be algebraically closed, and they can
therefore be said to “optimize” the Fundamental Theorem of Algebra. But each specific“degree implication” is a first-order
consequence of the axioms for fields, and could have been discovered two centuries ago; the existence of these finitary relationships
appears to have been unsuspected by practically everyone, with one important exception. 相似文献
25.
26.
Joseph M. Ling 《Discrete and Computational Geometry》2007,37(3):455-469
In this paper we prove four new (infinite) lists of quadratic inequalities, and four cubic inequalities, for the flag f-vectors
of 4-polytopes. These extend and supplement the only four currently known non-linear inequalities, which were proved by Bayer
in 1987. The new lists of inequalities for flag f-vectors yield new lists of inequalities for
f-vectors of 4-polytopes. Using the latter, we managed to improve an estimate discovered by Hoppner and Ziegler concerning
upper bounds of f1 in terms of f0 and f3. 相似文献
27.
This article provides a status report on discrete mathematics in America's schools, including an overview of publications
and programs that have had major impact. It discusses why discrete mathematics should be introduced in the schools and the
authors' efforts to advocate, facilitate, and support the adoption of discrete mathematics topics in the schools. Their perspective
is that discrete mathematics should be viewed not only as a collection of new and interesting mathematical topics, but, more
importantly, as a vehicle for providing teachers with a new way to think about traditional mathematical topics and new strategies
for engaging their students in the study of mathematics. 相似文献
28.
Each convex planar set K has a perimeter C, a minimum width E, an area A, and a diameter D. The set of points (E,C, A1/2, D) corresponding to
all such sets is shown to occupy a cone in the non-negative orthant of R4with its vertex at the origin. Its three-dimensional cross section S in the
plane D = 1 is investigated. S lies in a rectangular parallelepiped in R3. Results of Lebesgue, Kubota, Fukasawa, Sholander, and Hemmi are used to
determine some of the boundary surfaces of S, and new results are given for the other boundary surfaces. From knowledge of S, all inequalities among
E, C ,A, and D can be found. 相似文献
29.
Andrew Bach Xinglong Jiang Joseph Mckenna Kapa Prasad Oljan Repic Wen‐Chung Shieh 《Journal of heterocyclic chemistry》2004,41(4):637-640
An efficient approach has been developed for the synthesis of an isofervenulin analogue 1 employing a one‐pot condensation‐substitution reaction of a chlorocarboethoxytriazine (electrophile) with a urea (nucleophile). The resulting cyclization reaction resulted in the synthesis of a pyrimido‐heterocycle in good yield in either acidic or basic media. The former was assisted by utilizing trimethylsilyl chloride. 相似文献
30.