Experience-Based Approach to Scheduling Problems With the Learning Effect

The existence of the learning effect in many manufacturing systems is undoubted; thus, it is worthwhile that it be taken into consideration during production planning to increase production efficiency. Generally, it can be done by formulating the specified problem in the scheduling context and optimizing an order of jobs to minimize the given time criteria. To carry out a reliable study of the learning effect in scheduling fields, a comprehensive survey of the related results is presented first. It reveals that most of the learning models in scheduling are based on the learning curve introduced by Wright. However, further study about learning itself pointed out that the curve may be an ldquoSrdquo-shaped function, which has not been considered in the scheduling domain. To fill this gap, we analyze a scheduling problem with a new experience-based learning model, where job processing times are described by ldquoSrdquo-shaped functions that are dependent on the experience of the processor. Moreover, problems with other experience-based learning models are also taken into consideration. We prove that the makespan minimization problem on a single processor is NP-hard or strongly NP-hard with the most of the considered learning models. A number of polynomially solvable cases are also provided.