A note on single-machine group scheduling problem with a general learning function

Conventionally, most research assumes that job processing times are constant from the first job to be processed until the last job to be completed. This assumption might be unrealistic in many situations. For instance, Biskup (1999) pointed out that the skills of workers continuously improve when repeating similar tasks. This phenomenon is known as the "learning effect". However, most studies ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known as "group technology". In this short note, we propose a new group scheduling learning model and show that the single-machine makespan problem is polynomially solvable under the proposed model.