Two-machine flowshop scheduling with job class setups to minimize total flowtime

This paper studies the two-machine flowshop scheduling problem with job class setups to minimize the total flowtime. The jobs are classified into classes, and a setup is required on a machine if it switches processing of jobs from one class to another class, but no setup is required if the jobs are from the same class. For some special cases, we derive a number of properties of the optimal solution, based on which we design heuristics and branch-and-bound algorithms to solve these problems. Computational results show that these algorithms are effective in yielding near-optimal or optimal solutions to the tested problems.