A new solution approach for flow shop scheduling with an exponential time-dependent learning effect

This paper addresses a flow shop scheduling problem with a sum-of-process-times based learning effect. The objective is to find schedules that can minimize the maximum completion time. For constructing a solution framework, we propose a new random-sampling-based solution procedure called Bounds-based Nested Partition (BBNP). In order to enhance the effectiveness of BBNP, we develop a composite bound for guidance. Two heuristic algorithms are conducted with worst-case analysis as benchmarks. Numerical results show that the BBNP algorithm outperforms benchmark algorithms.