Scheduling problems with a learning effect

In many realistic settings, the production facility (a machine, a worker) improves continuously as a result of repeating the same or similar activities; hence, the later a given product is scheduled in the sequence, the shorter its production time. This ‘learning effect’ is investigated in the context of various scheduling problems. It is shown in several examples that although the optimal schedule may be very different from that of the classical version of the problem, and the computational effort becomes significantly greater, polynomial-time solutions still exist. In particular, we introduce polynomial solutions for the single-machine makespan minimization problem, and two for multi-criteria single-machine problems and the minimum flow-time problem on parallel identical machines.