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Structural properties of time-dependent scheduling problems with the lp norm objective
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DOI：10.1016/j.omega.2015.04.015.png)
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Abstract
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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(infinity) and p(1) such that p(infinity) < p(1) and the case 1 <= p <= p(infinity) is at least as difficult as the case p=1, while the case p(1) <= p <= + infinity is as easy as the case p= +infinity. 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.
Keywords:
Scheduling
Deteriorating jobs
The l(p) norm
Time complexity
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