Batching decisions in multi-item production systems with learning effect

The average time in the system (or average throughput time) is recognized as a crucial performance measure of manufacturing systems and, in recent years, has become even more relevant as markets have shifted towards mass-customization scenarios, since it directly affects the average inventory in the system. Modern manufacturing systems design paradigms, Industry 4.0 on top, focus on the need to achieve high responsiveness by shortening throughput time as the main lever to maintain cost efficiency and competitiveness in such market scenarios. In the contexts in which the human impact on production operations is not negligible, the learning phenomenon may reasonably affect the average time in the system. This paper analyses the learning effect on this performance measure through batching policies. Here, batching is considered as the possibility to group customized orders presenting similarities in the production processes, thus making it possible the exploitation of learning effect. Both single- and multi-item systems under Markovian arrivals are studied, also deterministic and stochastic processing times are considered. The problem that we pose consists in determining the batch size for each product that minimizes the average time in the system taking into consideration the learning effect, which is included by means of the Plateau model. A solution procedure for each case is discussed and, through numerical experiments, the sensitivity of the model to variations in parameter values is studied.