Journal of Intelligent Manufacturing

, Volume 28, Issue 3, pp 717–725 | Cite as

A new model for single machine scheduling with uncertain processing time

Article
First Online:
Received:
Accepted:

Abstract

Uncertain single machine scheduling problem for batches of jobs is an important issue for manufacturing systems. In this paper, we use uncertainty theory to study the single machine scheduling problem with deadlines where the processing times are described by uncertain variables with known uncertainty distributions. A new model for this problem is built to maximize expected total weight of batches of jobs. Then the model is transformed into a deterministic integer programming model by using the operational law for inverse uncertainty distributions. In addition, a property of the transformed model is provided and an algorithm is designed to solve this problem. Finally, a numerical example is given to illustrate the effectiveness of the model and the proposed algorithm.

Keywords

Integer programming Uncertainty theory Batch scheduling 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgments

This work was supported by National Natural Science Foundation of China Grant Nos. 11471152 and 61273044, and Fuzzy Logic Systems Institute, Japan (JSPS-the Grant-in-Aid for Scientific Research C; No. 24510219).

References

  1. Agnetis, A., Mirchandani, P. B., Pacciarelli, D., & Pacifici, A. (2004). Scheduling problems with competing agents. Operations Research, 52, 229–242.CrossRefGoogle Scholar
  2. Agnetis, A., Mirchandani, P. B., Acciarelli, P. D., & Pacifici, A. (2007). Multi-agent single machine scheduling. Annals of Operations Research, 150, 3–15.Google Scholar
  3. Agnetis, A., Pascale, G., & Pacciarelli, D. (2009). A Lagrangian approach to single-machine scheduling problem with two competing agents. Journal of Scheduling, 12, 401–415.CrossRefGoogle Scholar
  4. Badiru, A. B. (1992). Computational survey of univariate and multivariate learning curve models. IEEE Transaction Engineering Management, 39, 176–188.CrossRefGoogle Scholar
  5. Chen, F., Huang, J., & Centeno, M. (1999). Intelligent scheduling and control of rail-guided vehicles and load/unload operations in a flexible manufacturing system. Journal of Intelligent Manufacturing, 10, 405–421.CrossRefGoogle Scholar
  6. Chen, X., & Ralescu, D. A. (2011). A note on truth value in uncertain logic. Expert Systems with Applications, 38, 15582–15586.CrossRefGoogle Scholar
  7. Chen, X., Kar, S., & Ralescu, D. A. (2012). Cross-entropy measure of uncertain variables. Information Sciences, 201, 53–60.CrossRefGoogle Scholar
  8. Cheng, T. C., Ng, C. T., & Yuan, J. J. (2006). Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. Theoretical Computer Science, 36, 2273–2281.Google Scholar
  9. Dai, W., & Chen, X. (2012). Entropy of function of uncertain variables. Mathematical and Computer Modelling, 55, 754–760.CrossRefGoogle Scholar
  10. Deng, L., & Zhu, Y. G. (2012). Uncertain optimal control with jump. ICIC Express Letters Part B: Applications, 3(2), 419–424.Google Scholar
  11. Gao, Y. (2012). Uncertain models for single facility location problems on networks. Applied Mathematical Modelling, 36(6), 2592–2599.CrossRefGoogle Scholar
  12. Jiq, C. (2001). Stochastic single machine scheduling with an exponentially distributed due date. Operations Research Letters, 28, 199–203.CrossRefGoogle Scholar
  13. Kacem, I. (2008). Approximation algorithm for the weighted flow-time minimization on a single machine with a fixed non-availability interval. Computers & Industrial Engineering, 54(3), 401–410.CrossRefGoogle Scholar
  14. Lee, K., Choi, B. C., Leung, J. Y., & Pinedo, M. L. (2009). Approximation algorithms for multi-agent scheduling to minimize total weighted completion time. Information Processing Letters, 109, 913–917.CrossRefGoogle Scholar
  15. Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.Google Scholar
  16. Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3, 3–10.Google Scholar
  17. Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.CrossRefGoogle Scholar
  18. Liu, B. (2014). Uncertain random graph and uncertain random network. Journal of Uncertain Systems, 8(2), 3–12.Google Scholar
  19. Liu, B. (2015). Uncertainty theory (4th ed.). Berlin: Springer.Google Scholar
  20. Mohammad, D. A., Doraid, D., & Mahmoud, A. B. (2012). Dynamic programming model for multi-stage single-product Kanban-controlled serial production line. Journal of Intelligent Manufacturing, 23, 37–48.CrossRefGoogle Scholar
  21. Mor, B., & Sheiov, G. (2011). Single machine batchscheduling with two competing agents to minimize total flow time. European Journal of Operational Research, 215, 524–531.CrossRefGoogle Scholar
  22. Moslemipour, G., & Lee, T. S. (2012). Intelligent design of a dynamic machine layout in uncertain environment of flexible manufacturing systems. Journal of Intelligent Manufacturing, 23, 1849–1860.CrossRefGoogle Scholar
  23. Omar, L., Virgilio, L., & Israel, V. (2008). Intelligent and collaborative Multi-Agent System to generate and schedule production orders. Journal of Intelligent Manufacturing, 19, 677–687.CrossRefGoogle Scholar
  24. Peng, J., & Liu, B. (2004). Parallel machine scheduling models with fuzzy processing times. Information Sciences, 166, 59–66.CrossRefGoogle Scholar
  25. Rothblum, G., & Sethuraman, J. (2008). Stochastic scheduling in an in-forest. Discrete Optimization, 5, 457–466.CrossRefGoogle Scholar
  26. Seo, D. K., Klein, C. M., & Jang, W. (2005). Single machine stochastic scheduling to minimize the expected number of tardy jobs using mathematical programming models. Computers & Industrial Engineering, 48(2), 153–161.CrossRefGoogle Scholar
  27. Wang, D., Gen, M., & Cheng, R. (1999). Scheduling grouped jobs on single machine with genetic algorithm. Computers & Industrial Engineering, 36(2), 309–324.CrossRefGoogle Scholar
  28. Wang, I., Yang, T., & Chang, Y. (2012). Scheduling two-stage hybrid flow shops with parallel batch, release time, and machine eligibility constraints. Journal of Intelligent Manufacturing, 23, 2271–2280.CrossRefGoogle Scholar
  29. Wang, X. S., Gao, Z. C., & Guo, H. Y. (2012). Uncertain hypothesis testing for two experts’ empirical data. Mathematical and Computer Modelling, 55, 1478–1482.CrossRefGoogle Scholar
  30. Yang, X., & Gao, J. (2013). Uncertain differential games with application to capitalism. Journal of Uncertainty Analysis and Applications, 1, 7.CrossRefGoogle Scholar
  31. Yang, X., & Gao, J. (2014). Uncertain core for coalitional Game with uncertain payoffs. Journal of Uncertain Systems, 8(2), 13–21.Google Scholar
  32. Yao, K., & Li, X. (2012). Uncertain alternating renewal process and its application. IEEE Transactions on Fuzzy Systems, 20(6), 1154–1160.CrossRefGoogle Scholar
  33. Zhang X., Li, L., & Meng, G. (2014). A modified uncertain entailment model. Journal of Intelligent & Fuzzy Systems, to be published.Google Scholar
  34. Zhang, X., & Li, X. (2014). A semantic study of the first-order predicate logic with uncertainty involved. Fuzzy Optimization and Decision Making, to be published.Google Scholar
  35. Zhang, X., Ning, Y., & Meng, G. (2012). Delayed renewal process with uncertain interarrival times. Fuzzy Optimization Decision Making, 12, 79–87.Google Scholar
  36. Zhang, X., & Chen, X. (2012). A new uncertain programming model for project problem. INFORMATION: An International Interdisciplinary Journal, 15(10), 3901–3911.Google Scholar
  37. Zhang, X., & Meng, G. (2013). Maximal united utility degree model for fund distributing in higher school. Industrial Engineering & Management Systems, 12(1), 35–39.Google Scholar
  38. Zhou, J., & Liu, B. (2003). New stochastic models for capacitated location-allocation problem. Computers & Industrial Engineering, 45, 111–125.CrossRefGoogle Scholar
  39. Zhou, S. Y., & Chen, R. Q. (2005). A genetic algorithm: Weighted single machine scheduling problems to maximize the whole-set orders. Systems Engineering, 5, 22–24.Google Scholar
  40. Zhou, S. Y., & Sheng, P. F. (2006). A genetic algorithm for maximizing the weighted number of whole set order. Industrial Engineering and Management, 6, 75–79.Google Scholar
  41. Zhou, J., & Liu, B. (2007). Modeling capacitated location-allocation problem with fuzzy demands. Computers & Industrial Engineering, 53, 454–468.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Kai Hu
    • 1
  • Xingfang Zhang
    • 1
  • Mitsuo Gen
    • 2
    • 3
  • Jungbok Jo
    • 4
  1. 1.School of Mathematical SciencesLiaocheng UniversityLiaochengChina
  2. 2.Tokyo University of ScienceTokyoJapan
  3. 3.Japan and Fuzzy Logic Systems InstituteIizukaJapan
  4. 4.Division of Computer and Information EngineeringDongseo UniversityBusanSouth Korea

Personalised recommendations