The number balancing (NBP) problem is the following: given real numbers a1, . . . , an ∈ [0, 1], find two disjoint subsets I1, I2 ⊆ [n] so that the difference | ∑ i∈I1 ai − ∑ i∈I2 ai| of their sums is minimized. An application of the pigeonhole principle shows that there is always a solution where the difference is at most O( √ n 2n ). Finding the minimum, however, is NP-hard. In polynomial tim...

A physically concise polynomial-time iterative algorithm due to Barnes – a variation of Karmarkar projective transformation algorithm – is presented in Matlab for linear programs 0 ,   x b Ax to subject x c Min t . The concerned monotonic convergence of the solution vector and the consequent detection of basic variables are stated. The boundedness of the solution, multiple solutions, and no s...

In this work we study class I interior solutions supported by anisotropic polytropes. The generalized Lane--Emden equation compatible with the embedding condition is obtained and solved for a different set of parameters in both isothermal non--isothermal regimes. For completeness, Tolman mass computed analysed to some extend. As complementary consider impact Karmarkar on functions respectively....

Traditional simplex-basedalgorithms for two-stage stochastic linear programscan be broadly divided into two classes: (a) those that explicitly exploit the structure of the equivalent large-scale linear program and (b) those based on cutting planes (or equivalently on decomposition) that implicitly exploit that structure. Algorithms of class (b) are in general preferred. In 1988, following the w...

in this paper, we propose an iterated greedy algorithm for solving the blocking flow shop scheduling problem with total flow time minimization objective. the steps of this algorithm are designed very efficient. for generating an initial solution, we develop an efficient constructive heuristic by modifying the best known neh algorithm. effectiveness of the proposed iterated greedy algorithm is t...