Optimization Letters

, Volume 6, Issue 1, pp 87–98

Single-machine scheduling with nonlinear deterioration

Original Paper

DOI: 10.1007/s11590-010-0253-3

Cite this article as:
Wang, JB. & Wang, MZ. 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

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.School of ScienceShenyang Aerospace UniversityShenyangChina
  2. 2.School of Management Science and EngineeringDalian University of TechnologyDalianChina