Abstract
Interest in integrating lot-sizing and cutting stock problems has been increasing over the years. This integrated problem has been applied in many industries, such as paper, textile and furniture. Yet, there are only a few studies that acknowledge the importance of uncertainty to optimise these integrated decisions. This work aims to address this gap by incorporating demand uncertainty through stochastic programming and robust optimisation approaches. Both robust and stochastic models were specifically conceived to be solved by a column generation method. In addition, both models are embedded in a rolling-horizon procedure in order to incorporate dynamic reaction to demand realisation and adapt the models to a multistage stochastic setting. Computational experiments are proposed to test the efficiency of the column generation method and include a Monte Carlo simulation to assess both stochastic programming and robust optimisation for the integrated problem. Results suggest that acknowledging uncertainty can cut costs by up to 39.7%, while maintaining or reducing variability at the same time.

Abstract
Original Equipment Manufacturers (OEMs) have sought new supply chain paradigms that allowed them to focus on core activities, i.e. overall product design and commercialisation. This pursuit led to partnerships with a new generation of tier-1 strategic suppliers acting as integrators. Integrators are not only responsible for system supply, but also for system design. However, critical integrators were not able to live up to their new roles, which led to costly delays in development and production. These failures highlight the ineptitude of current risk management practices employed by OEMs. To support OEMs in implementing a more differentiated and suitable approach to the use of integrators, this paper proposes a mathematical programming model for Supply Chain Design (SCD). Instead of looking at the introduction of integrators as a dichotomous decision, the model suggests the optimal number of integrators, i.e. systems, and individual part suppliers. We propose new measures for integration risk, which build upon current risk assessment practices. Robust optimisation is used to study the effect of uncertainty over baseline risk values. All approaches were tested using both randomly generated instances and real data from a large European OEM in the aerospace industry.