A hybrid lower bound for multi-processor task scheduling problems in multi-stage hybrid flow shop environment

In this paper, a lower bound for the optimal makespan value have been improved (Hybrid lower bound) which can be used to evaluate the performance algorithm for multi-processor task scheduling problems in multi-stage FSMP(flow shop with multi-processor).So, the values of hybrid lower bounds can be used as an optimal solution when the problems are small size.After applying the hybrid bounds, the result has shown that the bounds are efficient in estimating the optimal makespen value.In addition, the high competence of this program in calculating the lower bound and execution speed are proofed