An Algorithm for Resource-Unconstrained Earliness-Tardiness Problem with Partial Precedences

자원 제약이 없는 환경에서 부분 우선순위를 고려한 Earliness-Tardiness 최적 일정계획 알고리즘

  • 하병현 (부산대학교 산업공학과)
  • Received : 2013.05.06
  • Accepted : 2013.05.09
  • Published : 2013.06.30


In this paper, we consider the minimization of the total weighted earliness-tardiness penalty of jobs, regarding the partial precedences between jobs. We present an optimal scheduling algorithm in O(n(n+m log m)) where n is the number of jobs and m is the number of partial precedences. In the algorithm, the optimal schedule is constructed iteratively by considering each group of contiguous jobs as a block that is represented by a tree.


Supported by : 교육부


  1. Cho, S.A., C.H. Cho, D.H. Lee, and C.B. Kim, "Single machine scheduling with maximum allowable tardiness in ET model," Journal of the Korean Operations Research and Management Science Society, Vol.23, No.1(1998), pp.29-41.
  2. Garey, M.R., R.E. Tarjan, and G.T. Wilfong, "One-processor scheduling with symmetric earliness and tardiness penalties," Mathematics of Operations Research, Vol.13, No.2 (1988), pp.330-348.
  3. Kedad-Sidhoum, S., Y.R. Solis, and F. Sourd, "Lower bounds for the earliness-tardiness scheduling problem on parallel machines with distinct due dates," European Journal of Operational Research, Vol.189, No.3(2008), pp.1305-1316.
  4. Kim, S.J. and C.Y. Lee, "Application of genetic algorithm to a job scheduling problem," Journal of the Korean Operations Research and Management Science Society, Vol.17, No.3(1992), pp.1-12.
  5. Kim, S.Y. and R.C. Leachman, "A new approach for resource allocation in project scheduling with variable-duration activities," Journal of the Korean Operations Research and Management Science Society, Vol.19, No.3(1994), pp.139-149.
  6. Kim, Y.D. and C.A. Yano, "Minimizing mean tardiness and earliness in single-machine scheduling problems with unequal due dates," Naval Research Logistics, Vol.41, No.7(1994), pp.913-933.<913::AID-NAV3220410705>3.0.CO;2-A
  7. Park, K.T. and K.H. Kim, "Berth scheduling for container terminals by using a sub-gradient optimization technique," Journal of the Operational Research Society, Vol.53, No.9 (2002), pp.1054-1062.
  8. Vanhoucke, M., E. Demeulemeester, and W. Herroelen, "An exact procedure for the resource-constrained weighted earliness-tardiness project scheduling problem," Annals of Operations Research, Vol.102, No.1-4(2001), pp.330-348.
  9. West, D.B., Introduction to Graph Theory, Prentice-Hall, Inc., Upper Saddle River, NJ, second edition, 2001.
  10. Xie, W. and N.V. Sahinidis, "A branch-and-bound algorithm for the continuous facility layout problem," Journal of the Operational Research Society, Vol.32, No.4-5(2008), pp. 1016-1028.