A branch-and-bound approach for a two-machine flowshop scheduling problem

This paper presents a branch-and-bound approach for solving a two-machine flow shop scheduling problem, in which the objective is to minimize a weighted combination of job flowtime and schedule makespan. Experimental results show that the algorithm works very well for certain special cases and moderately well for others. In fact, it is able to produce optimal schedules for 500-job problems in which the second machine dominates the first machine. It is also shown that the algorithm developed to provide an upper bound for the branch-and-bound is optimal when processing times for jobs are the same on both machines. The primary reason for developing the branch-and-bound approach is that its results can be used to guide other heuristic techniques, such as simulated annealing, tabu search and genetic algorithms, in their search for optimal solutions for larger problems.