Machine Flexibility for Lot Sizing Problems in Unbalanced Systems

The intense competition driven by the globalized market has forced the development of industrial processes to adapt to increasingly complex environments, leading to the creation of new strategies aimed at improving decision-making. In this highly competitive environment, businesses need to optimize their processes, services, and products to achieve better margins and maintain their position in the market. Research on lot-sizing problems is in line with this trend in the evolution of decision-making processes. The batch sizing problem is to find a production plan that minimizes production costs while meeting the demand for the items. This paper analyzes the benefits of machine flexibility in the context of unbalanced batch sizing problems, in which the number of items is greater than the number of machines. Because all of the known flexibility configurations in the literature, particularly the chain rule configuration, have been proposed for balanced systems (where the number of items is equal to the number of machines), there is still a significant challenge in representing these configurations when the number of items and machines is different. Thus, the main contribution of this work is to propose an approach to construct flexibility configurations for unbalanced systems. In addition, some performance indicators are proposed for evaluating the solutions. A series of computational experiments were carried out to reveal the effectiveness of the proposed methodology