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arXiv · 1603.01191

A fixed-parameter algorithm for a routing open shop problem: unit processing times, few machines and locations

René van Bevern·Artem V. Pyatkin
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Abstract

The open shop problem is to find a minimum makespan schedule to process each job $J_i$ on each machine $M_q$ for $p_{iq}$ time such that, at any time, each machine processes at most one job and each job is processed by at most one machine. We study a problem variant in which the jobs are located in the vertices of an edge-weighted graph. The weights determine the time needed for the machines to travel between jobs in different vertices. We show that the problem with $m$ machines and $n$ unit-time jobs in $g$ vertices is solvable in $2^{O(gm^2\log gm)}+O(mn\log n)$ time.

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René van Bevern, Artem V. Pyatkin. 2016-03-03. A fixed-parameter algorithm for a routing open shop problem: unit processing times, few machines and locations. https://arxiv.org/abs/1603.01191

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