S.V. Sevastianov For the $r$-stage open shop problem with identical parallel machines at each stage and the minimum makespan criterion, an approximation scheme is constructed with running time $O(nrm + C(m,\eps))$ , where $n$ is the number of jobs, $m$ is the total number of machines, and $C(m,\eps)$ is a function independent of $n$. CitationDiscrete Appl. Math. … Read more
The two-machine flow shop sequencing problem with arbitrary release dates of jobs and the minimum makespan criterion is considered. The problem is known to be NP-hard, and the best known approximation algorithms are those of Potts (1985) with a worst-case performance ratio of 5/3 and running time $O(n^3 \log n)$, and a polynomial time approximation … Read more
We consider the multi-stage multiprocessor flowshop scheduling problem with uniform machines at each stage and the minimum makespan objective. Using a vector summation technique, three polynomial-time heuristics are developed with absolute worst-case performance guarantees. As a direct corollary, in the special case of the ordinary flowshop problem we come to the best approximation algorithms (both … Read more