Abstract
The present chapter pertains to a bi-objective scheduling on parallel machines involving total tardiness and number of tardy jobs (NT). The processing time of jobs are uncertain in nature and are represented by triangular fuzzy membership function. The objective of the chapter is to find the optimal sequence of jobs processing on parallel identical machines so as to minimize the secondary criteria of NT with the condition that the primary criteria of total tardiness remains optimized. The bi-objective problem with total tardiness and NT as primary and secondary criteria, respectively, for any number of parallel machines is NP-hard. Following the theoretical treatment, a numerical illustration has also been given to demonstrate the potential efficiency of the proposed algorithm as a valuable analytical tool for the researchers.
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References
Anghinolfi, D., Paolucci, M.: Parallel machine total tardiness scheduling problem. Comput. Oper. Res. 3, 3471–3490 (2007)
Azizoglu, M., Kondacki, S., Omer, K.: Bicriteria scheduling problem involving total tardiness and total earliness penalties. Int. J. Prod. Econ. 23, 17–24 (1991)
Akker Vanden, J.M., Hoogeveen, J.A.: Minimizing the number of tardy jobs. Hand Book of Scheduling. Chap-man and Hall/CRC, Boca Raton, Florida (2004)
Chand, S.: Schneerberger: A note on single machine scheduling problem with minimum weighted completion time and maximum allowable tardiness. Naval Res. Logistic 33, 551–557 (1986)
Chen, C.L., Bulfin, R.L.: Scheduling a single machine to minimize two criteria: Maximum tardiness and number of tardy jobs. IIE Trans. 26, 76–84 (1994)
Gupta, D., Sharma, S., Aggarwal, S.: Bi-objective parallel machine scheduling with uncertain processing time. Adv. Appl. Sci. Res. 3, 1020–1226 (2012)
Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Minimizing maximum lateness in a two machine open shop. Math. Oper. Res. 6, 153–158 (1981)
Moore, J.M.: Sequencing n jobs one machine to minimize the number of tardy jobs. Manage. Sci. 77, 102–109 (1968)
Parkash, D.: Bicriteria scheduling problems on parallel machine. Ph.D. thesis. University of Birekshurg. Virginia (1997)
Shin, S.O., Kim, Y.D.: Scheduling on parallel machines to minimize total tardiness. J. Oper. Res. 177, 629–634 (2007)
Singh, T.P.: Bi-objective in fuzzy scheduling on parallel machines. Arya Bhatta J. Math. Inf. 2, 149–152 (2011)
Yager, R.R.: A procedure for ordering fuzzy subsets of unit interval. Inf. Sci. 24, 143–161 (1981)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 78–98 (1965)
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Sharma, S., Gupta, D., Sharma, S. (2014). Bi-Objective Scheduling on Parallel Machines in Fuzzy Environment. In: Babu, B., et al. Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012. Advances in Intelligent Systems and Computing, vol 236. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1602-5_40
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DOI: https://doi.org/10.1007/978-81-322-1602-5_40
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