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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