On Single Machine Scheduling Problem with Distinct due Dates under Fuzzy Environment

Document Type: Research Paper


Mathematics Department, College of Science and Arts, Al- Badaya, Qassim University, Saudi Arabia


Single machine, distinct due dates, early (lately) machine problem and fuzzy environment closely to the situation faced by '' just in time '' manufacture. This paper attempts to sequence the jobs on a single machine scheduling problem with distinct due dates under fuzzy environment so as to minimize the total penalty cost. This cost is the composition of all the total earliness and tardiness cost. A method to minimize the total penalty cost due to earliness or lateness of job in fuzzy environment is proposed. A numerical example is given in the sake of the paper to support this study.


Arlk, O. A., (2019). Dissatisfaction levels of earliness and   tardiness durations by relaxing common due date on single machine scheduling problems. Journal of Multidisciplinary Modeling and Optimization, Vol. 2(1), pp. 1-15.

Arlk, O. A., and Toksarl, M. D., (2019). Fuzzy parallel machine scheduling problem under fuzzy job deterioration and learning effects with fuzzy processing times. In Advanced Fuzzy Logic Approaches in Engineering Science, pp. 49-67, IGI Global.

Baker, K. S., and Scudder, G. D., (1990). Sequencing with earliness and tardiness penalties. A Review- Operations Research, Vol. 38, pp. 22-36.

Belkaid, F., Maliki, F., Boudahri, F., and Sari, Z. (2012). A branch and bound algorithm to minimize makespan on identical parallel machines with consumable resources. In Advances in mechanical and electronic engineering (pp. 217-221). Springer, Berlin, Heidelberg.

Belkaid, F., Sari, Z., and Yalaoui, F., (2013). A hybrid genetic algorithm for parallel machine scheduling problem with consumable resources. International Conference of Control, Decision and Information Technologies, pp. 143- 148.

Belkaid, F., Yalaoui, F., and Sari, Z., (2016). An efficient approach for the reentrant parallel machine scheduling problem with consumable resources constraints. International Journal of Information Systems and Supply Chain Management, Vol. 9(3), pp. 1-25.

Ben-Yehoshua, Y., and Mosheiov, G. (2016). A single machine scheduling problem to minimize total early work. Computers & Operations Research, Vol. 73, pp. 115-118.

Bellmann, R., and Zadeh,L., (1970). Decision making in a fuzzy environment. Management Science, Vol.17, pp. 141-164.

Biskup, D., and Feldmann, M., (2001). Benchmarks for scheduling on a single machine against restrictive and unrestrictive common due dates. Computers& Operations Research, Vol. 28(8), pp. 787-801.

Cahon, C. S. Mc., and Lee, E. S., (1992). Fuzzy job sequencing for a job shop. European Journal of Operations Research, Vol. 62, pp.294-301.

Che, A., Wu, X., Peng, J., and Yan, P., (2017). Energy- efficient bi- objective single machine scheduling with power- down mechanism. Computers& Operations Research, Vol. 28, pp. 172-183.

Chiang, J., (2001). Fuzzy linear programming based on statistical confidence interval and interval- valued fuzzy set. European Journal of Operational Research, Vol. 129, pp. 65-86.

Cong, T. C. E., (1995). Optimal due date determining and sequence on  jobs on a single machine. Journal of Operations Research Society, Vol.  35(5), pp.  425-433.

Dubois, D., and Prade, H. (1980). Fuzzy sets and systems: theory and applications, Academic Press, New York.

Duenes, A., and Petrivic, A. A new Approach to multi- objective Single Machine Scheduling Problem Under Fuzziness, CTAC School of Maths and Information Sciences, Coventry, U. K., 1995.

Ertem, M., Ozcelik, F., and Sarac, T., (2019). Single machine scheduling problem with stochastic sequence- dependent setup times. International Journal of Production Research, Vol. 57 (10), pp.  3273-3289.

Gerstl, E., and Mosheiov, G., (2020). Single machine scheduling to maximize the number of on- time jobs with generalized due- dates. Journal of Scheduling, Vol. 23, pp. 289-299.

Gupta, S., and Rambha, M.M.G.I., (2011). Single machine scheduling with distinct due dates under fuzzy environment. International Journal of Enterprise Computing and Business Systems, Vol. 1(2), pp. 1-9.

Ishii, H., and Tada, M., (1995). Single machine scheduling with fuzzy precedence relation. European Journal of Operations Research, Vol. 87, pp. 284-288.

Ishubuchi, H. T.M., and Lee, K. H. (1996). Formulation of fuzzy flow shop scheduling with fuzzy processing time. Proceedings of IEEE International Conference of Fuzzy Systems, pp.  199- 205.

Jadhav, V. S., and Bajaj V. H., (2012). Single machine scheduling problem under processing time and fuzzy due dates. International Journal of Computer Engineering Science, Vol. 2(5), pp. 12-19.

Kaufmann, A., and Gupta, M.M. (1988). Fuzzy Mathematical Models in Engineering and Management Science, Elsevier Science Publishing Company INC, New York,

Koulamas, C., Kyparisis, G. J., (2019). New results for single- machine scheduling with past- sequence- dependent setup times and due date- related objectives. European Journal of Operational Research, Vol. 278, pp. 149-159.

Liaw, C. F., (1999). A branch- and- bound algorithm for the single machine earliness and tardiness-scheduling problem. Computers& Operations Research, Vol. 26(7), pp. 679-693. 

Mohamad, N. H., and Said, F., (2011). Solving single machine scheduling problem with common due date.  Business Management Dynamics, Vol. 1(4), pp. 63-72.

Ponnalagu, K., and Mounika, P., (2018). A study on sequencing problem in two different environments. International Journal of Mathematics and its Applications, Vol. 6(1- D), pp. 835-839.

Senthil kumar, P., and Narayanan, S., (2010). Literature review of single machine scheduling problem with uniform parallel machines, Intelligent Information Management, Vol. 2, pp.457-474.

Stoskov, Y. N., and Egorova, N. G. (2018). Single machine scheduling problem with interval processing times and total completion time objective. Algorithms, Vol. 11(5), pp. 47-66.

Toksari, M. D., and Arık, O. A. (2017). Single machine scheduling problems under position dependent fuzzy learning effect with fuzzy processing times. Journal of Manufacturing Systems, Vol. 45, pp. 159-179.

Wang, T., and Xu, D., (2015). Single machine scheduling with workload- dependent maintenance duration to minimize maximum lateness. Mathematical Problems in Engineering, pp. 1-5

Wu, H., and Wang, B., (2020). Single machine scheduling problem with fuzzy time delays and mixed precedence constraints. Journal of Intelligent & Fuzzy Systems, (preprint), pp. 1-14.

Yazdani, M., Khalili, S. M., Babagolzadeh, M., and Jolai, F., (2017). A single- machine-scheduling problem with multiple unavailability constraints. A mathematical model and an enhanced variable neighborhood search approach. Journal of Computational Design and Engineering, Vol. 4(1), pp. 46-59.

Yue, F., Song, S., Jia, P., Wu, G., and Zhao, H. (2020). Robust single machine scheduling problem with uncertain job due dates for industrial mass production. Journal of Systems Engineering and Electronics, Vol. 31(2), pp. 350- 358.

Zadeh, L. A. (1965). Fuzzy sets. Information Control, Vol.  8(3), pp.  338-353.