Comparing Linear and Non-Linear Modelling Approaches of Learning Effects in 2-Stage Flow-Shop Scheduling Problems

Scheduling problems deal with the allocation and sequencing of a set of jobs to a set of production resources (machines, workers) to optimize one or more objective functions. In the literature, traditional deterministic approaches consider that processing times of jobs are fixed, constant and known at the initial time of scheduling. However, this assumption is not realistic particularly in hand-intensive manufacturing, where processing times may vary according to workers' learning about the production process. To deal with this, this paper considers the problem of jobs scheduling with learning effect in the processing times. In contrast with previous works in the literature, it is not the processing time that changes per se, but the resource (worker) that improves his/her productivity by decreasing the actual job processing time. This paper considers the flow-shop configuration in which all jobs are processed by a set of different workers following the same production routing. It reviews linear and non-linear modelling approaches of the learning effect in processing times, in order to gain insights about the actual impact of such different modelling approaches. A computational comparison of exact solutions based on mathematical modelling of the flow-shop problem is presented for the case of two workers. Experiments were run using random-generated instances. Several insights are drawn regarding the behavior of the different models.