22,753 research outputs found

    Combining time and position dependent effects on a single machine subject to rate-modifying activities

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    We introduce a general model for single machine scheduling problems, in which the actual processing times of jobs are subject to a combination of positional and time-dependent effects, that are job-independent but additionally depend on certain activities that modify the processing rate of the machine, such as, maintenance. We focus on minimizing two classical objectives: the makespan and the sum of the completion times. The traditional classification accepted in this area of scheduling is based on the distinction between the learning and deterioration effects on one hand, and between the positional effects and the start-time dependent effects on the other hand. Our results show that in the framework of the introduced model such a classification is not necessary, as long as the effects are job-independent. The model introduced in this paper covers most of the previously known models. The solution algorithms are developed within the same general framework and their running times are no worse than those available earlier for problems with less general effects

    Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan

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    2006-2007 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

    Scheduling problems with the effects of deterioration and learning

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    Author name used in this publication: T. C. E. Cheng2006-2007 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

    Optimal Composition Ordering Problems for Piecewise Linear Functions

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    In this paper, we introduce maximum composition ordering problems. The input is nn real functions f1,,fn:RRf_1,\dots,f_n:\mathbb{R}\to\mathbb{R} and a constant cRc\in\mathbb{R}. We consider two settings: total and partial compositions. The maximum total composition ordering problem is to compute a permutation σ:[n][n]\sigma:[n]\to[n] which maximizes fσ(n)fσ(n1)fσ(1)(c)f_{\sigma(n)}\circ f_{\sigma(n-1)}\circ\dots\circ f_{\sigma(1)}(c), where [n]={1,,n}[n]=\{1,\dots,n\}. The maximum partial composition ordering problem is to compute a permutation σ:[n][n]\sigma:[n]\to[n] and a nonnegative integer k (0kn)k~(0\le k\le n) which maximize fσ(k)fσ(k1)fσ(1)(c)f_{\sigma(k)}\circ f_{\sigma(k-1)}\circ\dots\circ f_{\sigma(1)}(c). We propose O(nlogn)O(n\log n) time algorithms for the maximum total and partial composition ordering problems for monotone linear functions fif_i, which generalize linear deterioration and shortening models for the time-dependent scheduling problem. We also show that the maximum partial composition ordering problem can be solved in polynomial time if fif_i is of form max{aix+bi,ci}\max\{a_ix+b_i,c_i\} for some constants ai(0)a_i\,(\ge 0), bib_i and cic_i. We finally prove that there exists no constant-factor approximation algorithm for the problems, even if fif_i's are monotone, piecewise linear functions with at most two pieces, unless P=NP.Comment: 19 pages, 4 figure
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