• mathematical models
• lean manufacturing
• operations

Purpose – The purpose of the doctoral thesis is to support and to facilitate the introduction of lean concepts, in the industry.
Design/methodology/approach – Starting from the operating techniques included in the lean toolbox, a comprehensive set of twelve mathematical models for operations management is developed. Since Lean Thinking encompasses the whole organization, the models cover several processes performed by an organization. In particular there are: (i) three models dealing with logistic issues, (ii) five models concerning manufacturing issues, and (iii) four models concerning Total Predictive Maintenance.
Findings – The models extend the capabilities of the classical lean tools by means of advanced mathematical techniques such as: fuzzy logic, multi criteria decision making, multivariate statistic and Markov processes.
Practical implications – To assure the possibility to adopt the models in real industrial situations, a great effort has been made to maintain all of them as simple and straightforward as possible. Furthermore, all of them have been designed to be easily implemented in industrial information systems, and have been validated by means of industrial applications of relevance.
Originality/value – The twelve models here presented provide practitioners with innovative operating tools, which integrate different techniques and overcomes most of the limits of the classical lean tools.