Browse > Article
http://dx.doi.org/10.11627/jkise.2015.38.3.169

Two-Agent Single-Machine Scheduling with Linear Job-Dependent Position-Based Learning Effects  

Choi, Jin Young (Department of Industrial Engineering, Ajou University)
Publication Information
Journal of Korean Society of Industrial and Systems Engineering / v.38, no.3, 2015 , pp. 169-180 More about this Journal
Abstract
Recently, scheduling problems with position-dependent processing times have received considerable attention in the literature, where the processing times of jobs are dependent on the processing sequences. However, they did not consider cases in which each processed job has different learning or aging ratios. This means that the actual processing time for a job can be determined not only by the processing sequence, but also by the learning/aging ratio, which can reflect the degree of processing difficulties in subsequent jobs. Motivated by these remarks, in this paper, we consider a two-agent single-machine scheduling problem with linear job-dependent position-based learning effects, where two agents compete to use a common single machine and each job has a different learning ratio. Specifically, we take into account two different objective functions for two agents: one agent minimizes the total weighted completion time, and the other restricts the makespan to less than an upper bound. After formally defining the problem by developing a mixed integer non-linear programming formulation, we devise a branch-and-bound (B&B) algorithm to give optimal solutions by developing four dominance properties based on a pairwise interchange comparison and four properties regarding the feasibility of a considered sequence. We suggest a lower bound to speed up the search procedure in the B&B algorithm by fathoming any non-prominent nodes. As this problem is at least NP-hard, we suggest efficient genetic algorithms using different methods to generate the initial population and two crossover operations. Computational results show that the proposed algorithms are efficient to obtain near-optimal solutions.
Keywords
Two-Agent Single-Machine Scheduling; Job-Dependent Position-Based Processing Time; Total Weighted Completion Time; Makespan; Branch-and-Bound Algorithm; Genetic Algorithm;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Agnetis, A., Mirchandani, P.B., Pacciarelli, D., and Pacifici, A., Scheduling problems with two competing agents. Operations Research, 2004, Vol. 52, No. 2, pp. 229-242.   DOI
2 Agnetis, A., Pacciarelli, D., and Pacifici A., Multi-agent single machine scheduling. Annals of Operations Research, 2007, Vol. 150, No. 1, pp. 3-15.   DOI
3 Bachman, A. and Janiak, A., Scheduling jobs with position-dependent processing times. Journal of the Operational Research Society, 2004, Vol. 55, pp. 257-264.   DOI
4 Baker, K.R. and Smith, J.C., A multiple-criterion model for machine scheduling. Journal of Scheduling, 2003, Vol. 6, No. 1, pp. 7-16.   DOI
5 Biskup D., Single-machine scheduling with learning considerations. European Journal of Operational Research, 1999, Vol. 115, No. 1, pp. 173-178.   DOI
6 Biskup, D., A state-of-the-art review on scheduling with learning considerations. European Journal of Operational Research, 2008, Vol. 188, No. 2, pp. 315-329.   DOI
7 Chang, P.C., Chen, S.H., and Mani, V., A note on due-date assignment and single machine scheduling with a learning and aging effect. International Journal of Production Economics, 2009, Vol. 117, No. 1, pp. 142-149.   DOI
8 Cheng, T.C.E. and Wang, G., Single machine scheduling with learning effect considerations. Annals of Operations Research, 2000, Vol. 98, No. 1, pp. 273-290.   DOI
9 Cheng, T.C.E., Ng, C.T., and Yuna, 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, pp. 273-281.   DOI
10 Cheng, T.C.E., Wu, W.H., Cheng, S.R., and Wu, C.C., Two-agent scheduling with position-based deterioration jobs and learning effects. Applied Mathematics and Computation, 2011, Vol. 217, No. 1, pp. 8804-8824.   DOI
11 Ding, G. and Sun, S., Single-machine scheduling problems with two agents competing for makespan. Life System Modeling and Intelligent Computing, 2010, Vol. 6328, pp. 244-255.   DOI
12 Graham, R.L., Lawler, E.L., Lenstra, J.K., and Rinnooy, Kan AHG., Optimization and approximation in deterministic sequencing and scheduling theory : a survey. Annals of Discrete Mathematics, 1979, Vol. 5, pp. 287-326.   DOI
13 Hardy, G., Littlewood, J., and Polya, G. Inequalities. London : Cambridge University Press, 1967.
14 Hillier, F.S. and Lieberman, G.J., Introduction to Operations Research, McGraw Hill, 2015.
15 Knotts, G., Dror, M., and Hartman, B.C., Agent-based project scheduling. IIE Transactions, 2000, Vol. 32, No. 5, pp. 387-401.   DOI
16 Kuo, W.H. and Yang, D.L., Minimizing the makespan in a single-machine scheduling problem with the cyclic process of an aging effect. Journal of the Operational Research Society, 2008, Vol. 59, pp. 416-420.   DOI
17 Lee, W.C., Wang, W.J., Shiau, Y.R., and Wu, C.C., A single-machine scheduling problem with two-agent and deteriorating jobs. Applied Mathematical Modelling, 2010, Vol. 34, No. 10, pp. 3098-3107.   DOI
18 Leung, J.Y.T., Pinedo, M.L., and Wan, G., Competitive two-agent scheduling and its applications Operations Research, 2010, Vol. 58, No. 2, pp. 458-469.   DOI
19 Liu, P., Yi, N., and Zhou, X., Two-agent single-machine scheduling problems under increasing linear deterioration. Applied Mathematical Modelling, 2011, Vol. 35, No. 5, pp. 2290-2296.   DOI
20 Li, D.C. and Hsu, P.H., Solving a two-agent single-machine scheduling problem considering learning effect. Computers and Operations Research, 2012, Vol. 39, No. 7, pp. 1644-1651.   DOI
21 Liu, P., Zhou, X., and Tang, L., Two-agent single-machine scheduling with position-dependent processing times. International Journal of Advanced Manufacturing Technology, 2010, Vol. 48, No. 1, pp. 325-331.   DOI
22 Mitchell, M., An introduction to genetic algorithm, MIT Press, 1996.
23 Mosheiov, G., A note on scheduling deteriorating jobs. Mathematical and Computer Modelling, 2005, Vol. 41, No. 8-9, pp. 883-886.   DOI
24 Mosheiov, G., Parallel machine scheduling with a learning effect. Journal of the Operational Research Society, 2001, Vol. 52, No. 10, pp. 1165-1169.   DOI
25 Ng, C.T., Cheng, T.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, pp. 387-394.   DOI
26 Pessan, C., Bouquard, J.L., and Neron, E., An unrelated parallel machines model for an industrial production resetting problem. European Journal of Industrial Engineering, 2008, Vol. 2, No. 2, pp. 153-171.   DOI
27 Wang, J. and Wang, M., Worst-case analysis for flow shop scheduling problems with an exponential learning effect. Journal of the Operational Research Society, 2012, Vol. 63, pp. 130-137.   DOI
28 Wu, C.C., Yin, Y., and Cheng, S.R., Some single-machine scheduling problems with a truncation learning effect. Computers and Industrial Engineering, 2011a, Vol. 60, No. 4, pp. 790-795.   DOI
29 Wang, J.B. and Xia, Z.Q., Flow-shop scheduling with a learning effect. Journal of the Operational Research Society, 2005, Vol. 56, pp. 1325-1330.   DOI
30 Wu, C.C., Huang, S.K., and Lee, W.C., Two-agent scheduling with learning consideration. Computers and Industrial Engineering, 2011b, Vol. 61, No. 4, pp. 1324-1335.   DOI
31 Wu, W.H., Xu, J., Wu, W.H., Yin, Y., Cheng, I.F., and Wu, C.C., A tabu method for a two-agent singlemachine scheduling with deterioration jobs. Computers and Operations Research, 2013, Vol. 40, No. 8, pp. 2116-2127.   DOI
32 Yin, Y., Cheng, S.R., Cheng, T.C.E., Wu, W.H., and Wu, C.C., Two-agent single-machine scheduling with release times and deadlines. International Journal of Shipping and Transport Logistics, 2013, Vol. 5, No. 1, pp. 75-94.   DOI
33 Yin, Y., Xu, D., Cheng, S.R., and Wu, C.C., A generalization model of learning and deteriorating effects on a single-machine scheduling with past-sequence-dependent setup times. International Journal of Computer Integrated Manufacturing, 2012, Vol. 25, No. 9, pp. 804-813.   DOI