The paper considers a three-machine shop scheduling problem to minimize the makespan, in which the route of a job should be feasible with respect to a machine precedence digraph with three nodes and one arc. For this NP-hard problem that is related to the classical flow shop and open shop models, we present a simple 1.5-approximation algorithm and an improved 1.4-approximation algorithm.
 The Author's Accepted Manuscript version is attached.  Please cite this article as: Quibell, R., Strusevich, V.A., An Approximation Algorithm for the Three-Machine Scheduling Problem with the Routes Given by the Same Partial Order, Computers & Industrial Engineering (2014), doi: http://dx.doi.org/10.1016/j.cie.2014.08.009.  This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.