Sequencing with learning, forgetting and task similarity

In human–machine workplaces, employee skills change over time due to learning and forgetting effects, which greatly affects efficiency. We model these effects within a simple production system. When a job is processed, due to learning the next job of the same type requires less processing time. Meanwhile, jobs of other types are forgotten, hence their future processing times increase. In our work, the amount of learning and forgetting depends on the full matrix similarity of the two job types and on the size of the jobs processed. We describe a dynamic programming algorithm that minimizes the makespan optimally. More generally, the learning level of a job type has an upper limit above which further learning is lost, and a lower limit below which further forgetting is saved. For this more general problem, we adapt our dynamic programming algorithm to provide tight lower bounds that validate the performance of simple heuristic approaches and genetic algorithms. A computational study demonstrates that these procedures routinely deliver optimal, or very close to optimal, solutions for up to eight job types and 80 jobs. Our work provides what are apparently the first effective procedures for optimization of large-scale production schedules with learning and forgetting effects defined by full matrix similarity. This identifies a critical opportunity for human–machine collaboration to improve productivity and support operational excellence.