Journal of Combinatorial Optimization

, Volume 26, Issue 3, pp 489–498 | Cite as

Single machine scheduling problems with subcontracting options

  • Weiya Zhong
  • Zhiming Huo


In this paper, we study a scheduling model as follows: there are n jobs which can be processed in house on a single machine or subcontracted to a subcontractor. If a job is subcontracted, its processing cost is different from the in-house cost and its delivery lead time is a stepwise function of the total processing time of outsourced jobs. Two objective functions are studied (1) to minimize the weighted sum of the maximal completion time and the total processing cost and (2) to minimize the weighted sum of the number of tardy jobs and the total processing cost. For the first problem, we prove that it is NP-hard and get a pseudo-polynomial time algorithm. For the second problem, we prove that it is NP-hard and get a pseudo-polynomial time algorithm for a special case.


Scheduling Subcontracting Computational complexity 



This work has been financed by Shanghai Leading Academic Discipline Project (S30104).


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiChina

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