# Single-machine common due date total earliness/tardiness scheduling with machine unavailability

## Abstract

Research on non-regular performance measures is at best scarce in the deterministic machine scheduling literature with machine unavailability constraints. Moreover, almost all existing works in this area assume either that processing on jobs interrupted by an interval of machine unavailability may be resumed without any additional setup/processing or that all prior processing is lost. In this work, we intend to partially fill these gaps by studying the problem of scheduling a single machine so as to minimize the total deviation of the job completion times from an unrestrictive common due date when one or several fixed intervals of unavailability are present in the planning horizon. We also put serious effort into investigating models with semi-resumable jobs so that processing on a job interrupted by an interval of machine unavailability may later be resumed at the expense of some extra processing time. The conventional assumptions regarding resumability are also taken into account. Several interesting cases are identified and explored, depending on the resumability scheme and the location of the interval of machine unavailability with respect to the common due date. The focus of analysis is on structural properties and drawing the boundary between polynomially solvable and \(\mathcal {NP}\)-complete cases. Pseudo-polynomial dynamic programming algorithms are devised for \(\mathcal {NP}\)-complete variants in the ordinary sense.

## Keywords

Single-machine Earliness/tardiness Common due date Unrestrictive Machine unavailability Maintenance Resumable Semi-resumable Non-resumable \(\mathcal {NP}\)-complete Dynamic programming## Notes

### Acknowledgements

We thank the anonymous referees and the associate editor for their comments, which helped us improve the paper. The second author has been partially supported by a Google Award. The third author has been supported by Fondation Mathématique Jacques Hadamard under the Gaspard Monge Program for Optimization and Operations Research.

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