Optimal Scheduling Algorithms to Minimize Total Flowtime on a Two-Machine Permutation Flowshop with Limited Waiting Times and Ready Times of Jobs

In this research, we consider a two-machine permutation flowshop with ready times and limited waiting times of jobs in a semiconductor fab. In the flowshop, each job has its corresponding ready time (arrival time) at machine 1 (for the first operation) and limited waiting time between the completion time of the first operation on machine 1 and the starting time of the second operation on machine 2. That is, the first operation of each job cannot be started earlier than its ready time on the machine 1, and the second operation of each job has to be started within its corresponding limited waiting time after its first operation is completed on machine 1. In this scheduling problem, the objective is minimizing the total flowtime of jobs to be processed on the two-machine permutation flowshop, and we suggested branch and bound algorithms to give optimal solutions. To boost efficiency of the suggested branch and bound algorithms, we developed several dominance properties and three lower bounding schemes, and we used these in the branch and bound algorithms. In addition, we used the solutions of existing heuristic algorithm as the initial upper bounds of the branch and bound algorithms. To evaluate the performances of the branch and bounds, we executed computational simulation test and showed the results.