Abstract
We study the problem of scheduling unit jobs on a singlemachine with a common deadline where some jobs may be rejected. Each job has a weight and a profit and the objective is to minimize the sum of the weighted completion times of the scheduled jobs plus the sum of the profits of the rejected jobs. Our main result is an \({O}({n \log n})\)-time algorithm for this problem. In addition, we show how to incorporate weighted tardiness penalties with respect to a common due date into the objective while preserving the \({O}({n \log n})\) time bound. We also discuss connections to a special class of unit-demand auctions. Finally, we establish that certain natural variations of the scheduling problems that we study are NP-hard.
This research was supported by NSF Grant CCFā1217980.
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DomaniƧ, N.O., Plaxton, C.G. (2014). Scheduling Unit Jobs with a Common Deadline to Minimize the Sum of Weighted Completion Times and Rejection Penalties. In: Ahn, HK., Shin, CS. (eds) Algorithms and Computation. ISAAC 2014. Lecture Notes in Computer Science(), vol 8889. Springer, Cham. https://doi.org/10.1007/978-3-319-13075-0_51
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