Optimization Letters

, Volume 6, Issue 1, pp 87–98

Single-machine scheduling with nonlinear deterioration


  • Ji-Bo Wang
    • School of ScienceShenyang Aerospace University
    • School of Management Science and EngineeringDalian University of Technology
Original Paper

DOI: 10.1007/s11590-010-0253-3

Cite this article as:
Wang, J. & Wang, M. Optim Lett (2012) 6: 87. doi:10.1007/s11590-010-0253-3


In this paper, we consider the single-machine scheduling problems with nonlinear deterioration. By the nonlinear deterioration effect, we mean that the processing times of jobs are nonlinear functions of their starting times. We show that even with the introduction of nonlinear deterioration to job processing times, single machine makespan minimization problem remains polynomially solvable. We also show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to job normal processing times. A heuristic algorithm utilizing the V-shaped property is proposed, and computational experiments show that it performs effectively and efficiently in obtaining near-optimal solutions.


SchedulingSingle machineDeteriorating jobsMakespanTotal completion time

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© Springer-Verlag 2010