C Rajendran

In this paper, we propose two new heuristic tie-breaking rules in the implementation of the well-known NEH heuristic for permutation flow-shop scheduling. While implementing this heuristic, it is known that ties do frequently occur when the initial ordering of jobs is obtained and when the choice of the best partial sequence among the sequences having the same makespan is done. In this paper, we propose two heuristic tie-breaking rules called NEHMSWG and NEHMinS-PS. We investigate their performance and that of the best-known heuristic tie-breaking rule, relative to the optimal/best-known upper bounds on the makespan, by considering benchmark permutation flow-shop scheduling problem instances. The results of performance evaluation reveal that the proposed tie-breaking rules are simple and effective, and improve the solutions with respect to many problem instances in comparison to the best known heuristic rule reported in the literature.

In this paper, the permutation flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs is considered, and a simulated annealing algorithm (SA) and two modified SAs (MSA1 and MSA2) are proposed. In the first phase, the proposed algorithms are used to minimise CTV of jobs without any right shifting of completion times of jobs on the last machine (RSCT). As followed in the literature some times, the RSCT (except that of the last job) is attempted in the second phase, and in the third phase, we convert sequences so as to follow the V-shaped property with respect to processing time of jobs on the last machine, followed by RSCT except that of the last job, so that the makespan and the machine utilisation in the shop floor remain the same. We present an extensive computational evaluation of the existing and the proposed heuristic algorithms.