We consider the problem of scheduling a set of n jobs on m identical parallel machines so as to minimize the weighted sum of job completion times. This problem is NP-hard in the strong sense. The best approximation result known so far was a 2 (1 + √ 2)-approximation algorithm that has been derived by Kawaguchi and Kyan back in 1986. The contribution of this paper is a polynomial time approximat...

We consider the problem of scheduling a set of n jobs on m identical parallel machines so as to minimize the weighted sum of job completion times. This problem is NP-hard in the strong sense. The best approximation result known so far was a 1 2 (1 + p 2){approximation algorithm that has been derived by Kawaguchi and Kyan back in 1986. The contribution of this paper is a polynomial time approxim...

Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...

this research presents a new application of the cloud theory-based simulated annealing algorithm to solve mixed model assembly line sequencing problems where line stoppage cost is expected to be optimized. this objective is highly significant in mixed model assembly line sequencing problems based on just-in-time production system. moreover, this type of problem is np-hard and solving this probl...