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