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- W259633267 abstract "Abstract We consider general properties which describe the structure of schedules for a single machine scheduling problem with linearly deteriorating jobs and the objective to minimize the l p norm. Applying a matrix formulation of the problem, we show that it has unique solutions and for p ≥ 1 it possesses a kind of convexity. We also express the time complexity of the problem as a function of index p of the l p norm and prove that there exist thresholds p ∞ and p 1 such that p ∞ p 1 and the case 1 ≤ p ≤ p ∞ is at least as difficult as the case p =1, while the case p 1 ≤ p ≤ + ∞ is as easy as the case p =+ ∞ . These results imply that the V-shapeness of optimal schedules for the problem, previously known only for p =1, still holds for infinite many p > 1 , while symmetricity of the schedules may hold only for some p ≥ 1 ." @default.
- W259633267 created "2016-06-24" @default.
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- W259633267 date "2015-12-01" @default.
- W259633267 modified "2023-09-25" @default.
- W259633267 title "Structural properties of time-dependent scheduling problems with the l p norm objective" @default.
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- W259633267 doi "https://doi.org/10.1016/j.omega.2015.04.015" @default.
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