Journal of the Operational Research Society

, Volume 55, Issue 3, pp 247–256

Makespan minimization in single-machine scheduling with step-deterioration of processing times

Theoretical Paper

DOI: 10.1057/palgrave.jors.2601693

Cite this article as:
Jeng, A. & Lin, B. J Oper Res Soc (2004) 55: 247. doi:10.1057/palgrave.jors.2601693


This paper considers a single-machine scheduling problem of minimizing the maximum completion time for a set of independent jobs. The processing time of a job is a non-linear step function of its starting time and due date. The problem is already known to be 𝒩𝒫-hard in the literature. In this paper, we first show this problem to be 𝒩𝒫-hard in the ordinary sense by proposing a pseudo-polynomial time dynamic programming algorithm. Then, we develop two dominance rules and a lower bound to design a branch-and-bound algorithm for deriving optimal solutions. Numerical results indicate that the proposed properties can effectively reduce the time required for exploring the solution space.


single-machine scheduling step-deterioration makespan dynamic programming branch-and-bound 

Copyright information

© Palgrave Macmillan Ltd 2004

Authors and Affiliations

  1. 1.National Chi Nan UniversityTaiwanRepublic of China