J. Comb. Optim. | 2021
Single-machine online scheduling of jobs with non-delayed processing constraint
Abstract
This paper introduces a new environment of online scheduling in which jobs are scheduled under the non-delayed processing (NDP) constraint, where NDP means that the available jobs cannot be delayed for processing when some machine is idle. We study in this paper the single-machine online scheduling to minimize the maximum weighted completion time (\n $${\\textit{WC}}_{\\mathrm{max}}$$\n ) or the maximum delivery completion time (\n $$L_{\\mathrm{max}}$$\n ) under the NDP constraint. For the first problem, we establish a lower bound 2 and provide an online algorithm which has a competitive ratio of $$(3+\\sqrt{5})/2\\approx 2.618$$\n . We present a 3/2-competitive best possible online algorithm for the second problem.