Abstract
In this paper, we consider four single-machine scheduling problems with release times, with the aim of minimizing the maximum lateness. In the first problem we have a common deadline for all the jobs. The second problem looks for the Pareto frontier with respect to the two objective functions maximum lateness and makespan. The third problem is associated with a non-availability constraint. In the fourth one, the non-availability interval is related to the operator who is organizing the execution of jobs on the machine (no job can start, and neither can complete during the operator non-availability period). For each of the four problems, we establish the existence of a polynomial time approximation scheme.
Highlights
The problem we consider is the one-machine scheduling problem with release dates and delivery times
We considered important single-machine scheduling problems under release times and tails assumptions, with the aim of minimizing the maximum lateness
All the jobs are constrained by a common deadline
Summary
The problem we consider is the one-machine scheduling problem with release dates and delivery times. The objective is to minimize the maximum lateness. The problem is defined in the following way. N} of n jobs on a single machine. Each job j ∈ J has a processing time p j , a release time. The machine can only perform one job at a given time. The problem is to find a sequence of jobs, with the objective of minimizing the maximum lateness Lmax = max1≤ j≤n C j + q j where C j is the completion time of job j. We define s j as the starting time of job j , i.e., C j = s j + p j , P =
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