Mathematics

  2010 AUG 3 - (VerticalNews.com) -- "This paper considers the online scheduling problem with machine cost. We are given a sequence of independent jobs with positive sizes," researchers in Hangzhou, People's Republic of China report.

  "Jobs come one by one and it is required to schedule jobs irrevocably to a machine as soon as they are given, without any knowledge about jobs that follow later on. No machines are initially provided. When a job is revealed, the algorithm has the option to purchase new machines. The objective is to minimize the sum of the rnakespan and cost of purchased machines. We prove that root 2 is a lower bound of the problem, which significantly improves the previous one of 4/3. We also present a new algorithm with competitive ratio (2 + root 7)/3 approximate to 1.5486, which improves the current best algorithm with competitive ratio (2 root 6+3)/5 approximate to 1.5798," wrote G. Dosa and colleagues, Zhejiang University ...read more

  2010 AUG 3 - (VerticalNews.com) -- "We consider minmax regret bottleneck subset-type combinatorial optimization problems, where feasible solutions are some subsets of a finite ground set of cardinality n. The weights of elements of the ground set are uncertain; for each element, an uncertainty interval that contains its weight is given. In contrast with previously studied interval data minmax regret models, where the set of scenarios (possible realizations of the vector of weights) does not depend on the chosen feasible solution, we consider the problem with solution-induced interval uncertainty structure," scientists in Scarborough, Canada report ...read more

  2010 AUG 3 - (VerticalNews.com) -- "In this paper, we present a generalization of the two phase method to solve multi-objective integer programmes with p> 2 objectives. We apply the method to the assignment problem with three objectives," scientists in France report.

  "We have recently proposed an algorithm for the first phase, computing all supported efficient solutions. The second phase consists in the definition and the exploration of the search area inside of which nonsupported nondominated points may exist. This search area is not defined by trivial geometric constructions in the multi-objective case, and is therefore difficult to describe and to explore. The lower and upper bound sets introduced by Ehrgott and Gandibleux in 2001 are used as a basis for this description," wrote A. Przybylski and colleagues ...read more