Minimising weighted completion time on a single machine under uncertain weights
by Hui Wu; Bing Wang
International Journal of Automation and Control (IJAAC), Vol. 16, No. 1, 2022

Abstract: This paper has investigated the single-machine scheduling problem regarding the minimisation of the total weighted completion time, with the known processing times, while weights are uncertain. Uncertainty in weights is modelled using a scenario set, which contains explicitly listed scenarios of weights (the discrete-scenario case) or the Cartesian product of the intervals that contain possible values of weights (the interval-data case). Two main criteria are investigated: minimising the maximum objective function (min-max version) and minimising the maximum regret (min-max regret version). The computational complexity of the min-max (regret) versions of the single-machine scheduling problem in the cases of the discrete scenario as well as interval data is discussed, respectively, and on this basis, the approximation of corresponding NP-hard problems is further analysed.

Online publication date: Fri, 03-Dec-2021

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