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**A survey of results for sequencing problems with controllable processing times.**
*(English)*
Zbl 0693.90056

This paper reviews algorithms and complexity results for scheduling problems in which the processing time of a job is a decision variable. For each job, an upper and lower bound on its processing time is specified and a processing cost, which is a linear decreasing function of processing time, is given. In addition to the processing cost, a schedule cost (maximum completion time, maximum lateness or total weighted completion time, for example) is associate with completion times of the jobs. Most results relate to the problem of scheduling a single machine to minimize the processing plus schedule cost. Throughout the paper, a typical algorithm first selects a processing order of the jobs and then solves a linear program to fix the processing times; this linear program can often be solved very efficiently. For some problems, this type of algorithm provides an exact solution; for others, it is a heuristic and worst-case performance bounds are available.

Reviewer: C.N.Potts

### MSC:

90B35 | Deterministic scheduling theory in operations research |

68Q25 | Analysis of algorithms and problem complexity |

68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |

### Keywords:

controllable processing time; upper bound; complexity results; lower bound; maximum completion time; maximum lateness; total weighted completion time; single machine; heuristic; worst-case performance
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\textit{E. Nowicki} and \textit{S. Zdrzałka}, Discrete Appl. Math. 26, No. 2--3, 271--287 (1990; Zbl 0693.90056)

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### References:

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