Scheduling jobs with fixed start and end times
Discrete Applied Mathematics
Sequencing with earliness and tardiness penalties: a review
Operations Research
On the k-coloring of intervals
Discrete Applied Mathematics
Single-machine scheduling with a common due window
Computers and Operations Research
Scheduling single-machine problems for on-time delivery
Computers and Industrial Engineering
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobs
Computers and Operations Research
Parallel Processor Scheduling Problems with Optimal Due Interval Determination
ENC '04 Proceedings of the Fifth Mexican International Conference in Computer Science
Maximizing Weighted number of Just-in-Time Jobs on Unrelated Parallel Machines
Journal of Scheduling
Maximizing the weighted number of just-in-time jobs in flow shop scheduling
Journal of Scheduling
Computers and Operations Research - Articles presented at the conference on routing and location (CORAL)
PPAM'05 Proceedings of the 6th international conference on Parallel Processing and Applied Mathematics
Soft Due Window Assignment and Scheduling on Parallel Machines
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Maximizing the weighted number of on-time jobs in single machine scheduling with time windows
Mathematical and Computer Modelling: An International Journal
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We study the problem of maximizing the weighted number of just-in-time jobs on a single machine with position-dependent processing times. Unlike the vast majority of the literature, we do not restrict ourselves to a specific model of processing time function. Rather, we assume that the processing time function can be of any functional structure that is according to one of the following two cases. The first is the case where the job processing times are under a learning effect, i.e., each job processing time is a non-increasing function of its position in the sequence. In the second case, an aging effect is assumed, i.e., each job processing time is a non-decreasing function of its position in the sequence. We prove that the problem is strongly $$\mathcal{N }\mathcal{P }$$NP-hard under a learning effect, even if all the weights are identical. When there is an aging effect, we introduce a dynamic programming (DP) procedure that solves the problem with arbitrary weights in $$O(n^{3})$$O(n3) time (where $$n$$n is the number of jobs). For identical weights, a faster optimization algorithm that runs in $$O(n\log n)$$O(nlogn) time is presented. We also extend the analysis to the case of scheduling on a set of $$m$$m parallel unrelated machines and provide a DP procedure that solves the problem in polynomial time, given that $$m$$m is fixed and that the jobs are under an aging effect.