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The open shop problem is to find a minimum makespan schedule to process eachjob $J_i$ on each machine $M_q$ for $p_{iq}$ time such that, at any time, eachmachine processes at most one job and each job is processed by at most onemachine. We study a problem variant in which the jobs are located in thevertices of an edge-weighted graph. The weights determine the time needed forthe machines to travel between jobs in different vertices. We show that theproblem 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.

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