Developing Tight Lower Bounds for Hybrid Flow Shop Scheduling Problems

In this research, a lower bounding mechanism is pro posed for a group scheduling problem on a hybrid fl ow shop environment. The objective function of the scheduli ng problem is to minimize a linear combination of t otal weighted completion time and total weighted tardiness of all jobs. The underlying assumptions include a sequenc e-dependent setup time for changing the process between differe nt groups of jobs, non-zero release times for jobs, stage skipping allowance for jobs, and unrelated parallel machines in different stages. Since this problem is strongl y NP-hard, nonexact algorithms are the main approaches for dealin g with large-scale instances of this problem. Howev er, a tight lower bound is required to precisely evaluate perfo rmances of such algorithms. We propose a lower bounding mechanism, based on the column generation algorithm that is able to find lower bounds which are remark ably tighter than the bounds from CPLEX. To demonstrate this superiority, seven sample problems are tested with the proposed mechanism as well as CPLEX. The average gap between the lower bounds and upper bounds obtained from CPLEX for these sample problems is 216.5%, while this gap for the proposed lower bounding mechani sm (from the upper bound of CPLEX) is reduced to a remarkably low 13.5%.