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Journal of Scheduling

, Volume 21, Issue 4, pp 461–482 | Cite as

Single-machine scheduling with workload-dependent tool change durations and equal processing time jobs to minimize total completion time

  • Zhijun Xu
  • Dehua Xu
Article

Abstract

We consider a single-machine tool change scheduling problem where tool change durations are workload-dependent. The processing times of all the jobs are the same. The objective is to determine the number of tool change activities, the start time and the completion time of each tool change activity jointly and schedule all the jobs to the machine such that the total completion time of the jobs is minimized. For the case where the tool change duration function is concave, we present a linear time optimal algorithm. For the case where the tool change duration function is convex, we convert it into a convex integer quadratic programming problem with fixed dimension and then propose two polynomial time algorithms for it. We also study some special cases for which optimal schedules can be obtained directly. For the case where the tool change duration function is linear, we present all the optimal schedules.

Keywords

Scheduling Tool change Workload-dependent Total completion time 

Notes

Acknowledgements

We thank the referees for their valuable comments which improved the paper substantially. This research was supported by the National Natural Science Foundation of China (71201022).

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of ScienceEast China University of TechnologyNanchangPeople’s Republic of China
  2. 2.Department of MathematicsTongji UniversityShanghaiPeople’s Republic of China
  3. 3.School of International Economics and BusinessNanjing University of Finance & EconomicsNanjingPeople’s Republic of China

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