Bicriteria scheduling on parallel machines: total tardiness and weighted flowtime in fuzzy environment

This paper pertains to a bicriteria scheduling problem on parallel machines which minimises the weighted flowtime (WFT) with the condition that primary criteria of Tmax remains optimised. The processing times of jobs are in fuzzy environment and are represented by triangular fuzzy numbers. The membership function of fuzzy processing times denotes the grades of satisfaction with respect to completion times of jobs. The objective of this paper is to schedule jobs on parallel, identical machines so as to minimise the secondary criteria of WFT without violating the primary criteria of maximum tardiness (Tmax). Following the theoretical treatment, we provide numerical example(s) to demonstrate that the proposed algorithm has potential as a valuable analytical tool for researchers.