A fully polynomial time approximation scheme for scheduling on parallel identical two-stage openshops
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A two-stage openshop consists of a machine in the first stage and a machine in the second stage; a job processed on the two-stage openshop means it is processed non-preemptively by each of the two machines, in whichever order. We consider the scheduling problem at the availability of multiple parallel identical two-stage openshops, with the goal to minimize the makespan. By uncovering the important role of the critical job in the optimal schedule on a two-stage openshop, we propose to sort the jobs in the novel critical-job order, and use this order to design a pseudo-polynomial time dynamic programming exact algorithm to solve our scheduling problem with any fixed number of two-stage openshops. Afterwards, using the standard scaling technique, we develop the dynamic programming algorithm into a fully polynomial-time approximation scheme. These results improve previously proposed constant ratio approximation algorithms.
KeywordsScheduling Two-stage openshop Makespan Dynamic programming Fully polynomial-time approximation scheme
JD is supported by the NNSF China Grant No. 11501512 and the Zhejiang Provincial Natural Science Foundation Grant No. LY18A010029; part of his work was done while visiting the University of Alberta. JH is supported by the NNSF China Grants Nos. 11271324 and 11471286; part of his work was done while visiting the University of Alberta. GL is supported by NSERC Canada and the NNSF China Grant No. 61672323.
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