An FPTAS for just-in-time scheduling of a flow shop manufacturing process with different service quality levels

This paper addresses the problem of identifying a profit-maximizing schedule for jobs in a just-in-time production line, where the decision maker can adjust each job's processing time, and thereby its quality level and the profit that can be gained from it. The system comprises two sequential machines with a transition period between them and a setup time after completion of each job on the second machine. We first construct an exact algorithm that maximizes the profit. Since this problem is NP-hard, we construct a fully polynomial time approximation scheme (FPTAS) to address it and evaluate its computational complexity.