Robust and stochastic optimization
The management of production/distribution systems is more and more characterized by demand uncertainty, given the trend towards shorter and shorter product life cycles, the increasing obsolescence risk due to product innovation, and the stiff competition among firms. In many real-life contexts, and especially when dealing with Small and Medium Enterprises, it is impossible to build a reliable stochastic characterization of demand uncertainty. Hence, it is necessary to adopt optimization modeling frameworks able to cope with "uncertainty about uncertainty", which often leads to robust optimization models that, in turn, can be represented in terms of convex programming models; many of these models can be efficiently tackled, e.g., by interior point methods. In other cases, we may formulate a stochastic programming model (with recourse), which poses significant computational challenges, requiring careful strategies to generate scenario and to cope with end-of-horizon effects. Alternative models are being investigated on the basis of real life cases.
Similar issues must be tackled when applying the aforementioned modeling and solution methods to select financial portfolios, especially when adopting asymmetric risk measures. Joint research activities are under way with a financial firm involved in mutual fund management, on strategic asset allocation for institutional clients. The aim is to devise a multistage formulation with asymmetric risk measures, and to compare alternative modeling frameworks and solution methods.