Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Two-Agent Scheduling with Sequence-Dependent Exponential Learning Effects Consideration

처리순서기반 지수함수 학습효과를 고려한 2-에이전트 스케줄링

  • Received : 2013.11.12
  • Accepted : 2013.12.23
  • Published : 2013.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider a two-agent scheduling with sequence-dependent exponential learning effects consideration, where two agents A and B have to share a single machine for processing their jobs. The objective function for agent A is to minimize the total completion time of jobs for agent A subject to a given upper bound on the objective function of agent B, representing the makespan of jobs for agent B. By assuming that the learning ratios for all jobs are the same, we suggest an enumeration-based backward allocation scheduling for finding an optimal solution and exemplify it by using a small numerical example. This problem has various applications in production systems as well as in operations management.

Keywords

References

  1. Agnetis, A., Mirchandani, P.B., Pacciarelli, D. and Pacifici, A., Scheduling problems with two agents. Operations Research, 2004, Vol. 52, No. 2, p 229-242. https://doi.org/10.1287/opre.1030.0092
  2. Agnetis, A., Pascale, G., and Pacciarelli, D., A Lagrangian approach to single-machine scheduling problems with two competing agents. Journal of scheduling, 2009, Vol. 12, No. 4, p 401-415. https://doi.org/10.1007/s10951-008-0098-0
  3. Bachman, A. and Janiak, A., Scheduling jobs with position- dependent processing times. Journal of the operational research society, 2004, Vol. 55, No. 3, p. 257- 264. https://doi.org/10.1057/palgrave.jors.2601689
  4. Biskup, D., Single-machine scheduling with learning considerations. European Journal of Operational Research, 2000, Vol. 98, No. 1-4, p 273-290.
  5. Biskup, D., A state-of-the-art review on scheduling with learning effects. European journal of operational research, 2008, Vol. 188, No. 2, p 315-329. https://doi.org/10.1016/j.ejor.2007.05.040
  6. Cheng, T.C.E., Ng, C.T. and Yuan, J.J., Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. Theoretical computer science, 2006, Vol. 362, No. 1-3, p 273-281. https://doi.org/10.1016/j.tcs.2006.07.011
  7. Choi, J.Y. and Kim, D.G., A numerical analysis of solution approaches for multi-agent scheduling problems. Proceeding of the 43rd international conference on computers and industrial engineering, 2013.
  8. Graham, R.L., Lawler, E.L., Lenstra, J.K., and Rinnooy, Kan A.H.G., Optimization and approximation in deterministic sequencing and scheduling theory : a survey. Annals of Discrete Mathematics, 1979, Vol. 5, p 287- 326. https://doi.org/10.1016/S0167-5060(08)70356-X
  9. Liu, P., Yi, N., and Zhou, X., Two-agent single-machine scheduling problems under increasing linear deterioration. Applied Mathematical Modelling, 2011, Vol. 35, p 2290- 2296. https://doi.org/10.1016/j.apm.2010.11.026
  10. Mosheiov, G., Scheduling problems with a learning effect. European Journal of Operational Research, 2001, Vol. 132, No. 3, p 687-693. https://doi.org/10.1016/S0377-2217(00)00175-2
  11. Mosheiov, G., A note on scheduling deteriorating jobs. Mathematical and Computer Modeling, 2005, Vol. 41, No. 8-9, p 883-886. https://doi.org/10.1016/j.mcm.2004.09.004
  12. Ng, C.T., Cheng, T.C.C.E., and Yuan, J.J., A note on the complexity of the problem of two-agent scheduling on a single machine. Journal of Combinatorial Optimization, 2006, Vol. 12, No. 4, p 387-394. https://doi.org/10.1007/s10878-006-9001-0
  13. Peng, L., Xiaoye, Z. and Lixin, T., Two-agent singlemachine scheduling with position-dependent processing times. International Journal of Advanced Manufacturing Systems, 2010, Vol. 48, No. 1-4, p 325-331. https://doi.org/10.1007/s00170-009-2259-5
  14. Wan, G., Vakati, S.R., Leung, J.Y.T., and Pinedo, M., Scheduling two agents with controllable processing times. European Journal of Operational Research, 2010, Vol. 205, No. 3, p 528-539. https://doi.org/10.1016/j.ejor.2010.01.005
  15. Wang, J.B. and Wang, J.J., Single-machine scheduling jobs with exponential learning functions. Computers and Industrial Engineering, 2011, Vol. 60, No. 4, p 755-759. https://doi.org/10.1016/j.cie.2011.01.010