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- W1983735711 abstract "We study a scheduling problem with rejection on a set of two machines in a flow-shop scheduling system. We evaluate the quality of a solution by two criteria: the first is the makespan and the second is the total rejection cost. We show that the problem of minimizing the makespan plus total rejection cost is NP-hard and for its solution we provide two different approximation algorithms, a pseudo-polynomial time optimization algorithm and a fully polynomial time approximation scheme (FPTAS). We also study the problem of finding the entire set of Pareto-optimal points (this problem is NP-hard due to the NP-hardness of the same problem variation on a single machine [20]). We show that this problem can be solved in pseudo-polynomial time. Moreover, we show how we can provide an FPTAS that, given that there exists a Pareto optimal schedule with a total rejection cost of at most R and a makespan of at most K, finds a solution with a total rejection cost of at most (1+ɛ)R and a makespan value of at most (1+ɛ)K. This is done by defining a set of auxiliary problems and providing an FPTAS algorithm to each one of them." @default.
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- W1983735711 date "2012-05-01" @default.
- W1983735711 modified "2023-09-27" @default.
- W1983735711 title "Two-machine flow-shop scheduling with rejection" @default.
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- W1983735711 doi "https://doi.org/10.1016/j.cor.2011.05.023" @default.
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