An approximation algorithm for the three-machine scheduling problem with the routes given by the same partial order

A three-machine scheduling problem to minimize the makespan is considered.The processing routes are given by the same digraph on three nodes and one arc.A simple 1.5-approximation algorithm is presented.An improved 1.4-approximation algorithm is presented and analyzed.The achieved bound compares favorably with known results in the area. 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.

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