Techniques to Restrict an Interval of a Lower Bound in Fuzzy Scheduling Problems

Section: Research Paper
Issue
Vol. 20 No. 1 (2023): Volume 20 Issue 1
Published
Jun 25, 2025
Pages
1-8

Abstract

In this paper, a fuzzy scheduling problem with triangular fuzzy numbers for processing times and due dates is provided. Each of the n operations is to be performed on a single machine without interruption and then becomes ready for processing at time zero. We generalized some ideas by giving a definition and a theorem to find a relation between the fuzzy lower bound and the fuzzy optimal solution for a problem with number of efficient solutions that minimizes total fuzzy completion time and maximum fuzzy tardiness. Also the results show how to choose the best defuzzification method in fuzzy scheduling

References

  1. Jabbar, A. K., and Ramadan, M. R. (2006). Techniques of Finding Lower Bounds in Multi Objective Functions. AL-Rafidain Journal of Computer Sciences and Mathematics, 3(2), 23-29.
  2. Jia, Z, and Ierapetritou, M. G. (2007). Generate Pareto Optimal Solutions for Scheduling Problems using Normal Boundary Intersection Technique, Computers and Chemical Engineering, 31, 268-280.
  3. Lazarev, A., Arkhipov, D., and Werner, F. (2015). Single Machine Scheduling: Finding the Pareto Set for Jobs with Equal Processing Times with Respect to Criteria Lmax and Cmax. 7th Multidisciplinary International Conference on Scheduling: Theory and Applications, 25-28.
  4. Lowe, J., Thisse, J. F., Ward, J., and Wendell, R. E. (1984). On Efficient Solutions to Multiple-Objective Mathematical Programs. Management Science, 30, 1346-1349.
  5. Nguyen, V. , and. Bao, H. P. (2016). An Efficient Solution to the Mixed Shop Scheduling Problem Using A Modified Genetic Algorithm. Procedia Computer Science, 95, 475-482.
  6. Ramadan, A. M. (2021). On Pareto Set for a Bi-criterion Scheduling Problem Under Fuzziness. Iraqi Journal of Statistical Science, 33, 64-71.
  7. Smith, W. E. (1965) Various Optimizers for Single-Stage Production. Naval Research Logistics Quarterly, 3, 59-66.
  8. Steiner, S., and Radzik, T. (2008). Computing all Efficient Solutions of the Bi-Objective Minimum Spanning Tree Problem. Computers and Operations Research, 35, 198-211.
  9. Van Wassenhove, N., and Gelders, L. F. (1980). Solving a Bi-criterion Scheduling Problem. European Journal of Operational Research, 4, 42-48.
  10. Ward, J. (1989). Structure of Efficient Sets for Convex Objectives. Mathematics of Operations Research, 14, 249-257.
  11. Zinchenko, A. B. (2002). Structure of Pareto Set of Some Vector Problems in Scheduling. Russian Mathematics, 46(7), 79-82.

Authors

Nasyar Hussein Qader

Ministry of Education, General Director of Education in Garmian, Training and Educational Development Institute, Iraq.

ORCID
Rzgar F. Mahmood

Mathematics, College of Science, Garmian University, Kalar, IRAQ

ORCID
Mediya B. Mrakhan

Department of Mathematics, College of Science , Sulaimani University, Sulaimani,Iraq.

Ayad Ramadan

Department. of Mathematics ,College Of Science, University of Sulaimani,Sulaimani,Iraq.

ORCID

Identifiers

Download this PDF file
PDF

Statistics

How to Cite

Hussein Qader, N., ایاد, F. Mahmood, R., ناسیار, B. Mrakhan, M., زگار, Ramadan, A., & میدیا. (2025). Techniques to Restrict an Interval of a Lower Bound in Fuzzy Scheduling Problems. IRAQI JOURNAL OF STATISTICAL SCIENCES, 20(1), 1–8. Retrieved from https://rjps.uomosul.edu.iq/index.php/stats/article/view/20784