The Operations Research and Discrete Optimization (ORDO) group investigates complex decision-making problems, for which it develops mathematical models and efficient optimization methods. The main research focus is on linear, nonlinear and discrete optimization problems arising from a wide variety of applications. For these problems, the group designs and analyzes exact, approximate and heuristic algorithms. Research is often motivated by important applications, but simplified versions of the problems or abstractions are also investigated from a theoretical point of view.
The group’s expertise encompasses mathematical programming, combinatorial optimization, stochastic programming, robust optimization, bilevel programming and continuous approximation models.

Telecommunication networks
The optimal design and management of telecommunication networks, both wired and wireless, allows to keep up with the increasing demand cost-effectively. The group has been working on telecommunication network optimization for almost 20 years: beside classical network design and management problems, recent attention has been devoted to green networking, Internet traffic engineering with elastic demands, and network virtualization (virtual network embedding, network functions virtualization). Optimization models and heuristic algorithms have been developed for green networking, accounting for different routing protocols and failure resiliency strategies. A bilevel programming approach based on fair flow allocation has been proposed for traffic engineering with elastic demands, and both theoretical properties and formulations have been studied for the network virtualization problems.

Public transportation
Planning and managing public transport services in an efficient way requires the development of sophisticated optimization tools. The group has tackled several problems in this field, in collaboration with some of the main Italian transportation companies. These problems include: designing and managing flexible collective transportation systems, sensor location in road networks, personnel workforce scheduling and disruption management in local public transport. In 2016, this last work has been awarded the best OR application by AIRO.

Health care management
Optimizing health care systems is of capital relevance especially nowadays, since the population aging yields to an ever increasing demand for care services and the health service managers are forced to reduce the public health system expenses. The group has been working for several years on health care service management problems, such as operating theatres management and patients-to-nurse assignment in home care services, with particular attention to the quality of the service offered and focusing on problems where data are uncertain. Robust optimization models and approaches have been developed, whose robust solutions have also been tested on realistic samples so as to evaluate their behavior when facing real life scenarios.

Energy systems
Multi-energy systems (with multiple generation and storage units) allow to achieve remarkable savings in primary energy and in CO2 emissions. The design and operation planning of such systems, which is of interest for smart urban districts, give rise to challenging optimization problems, where demand uncertainty and renewable energy variability must be taken into account. Other energy problems addressed include, for instance, the optimal planning of electric distribution networks considering layout constraints and power losses, and the demand-side management problem of optimizing the residential electrical loads of a group of users. The main contributions are discrete optimization models and algorithms for variants of the first two problems, a framework for the residential load management that accounts also for batteries and renewable sources, and a new derivative-free method for black-box constrained optimization problems arising in this area.

Logistics and Freight distribution
The transportation of goods is a vital and complex activity. In urban areas in particular, this complexity is amplified by the ever-increasing urban population coupled with its consistent demand for rapid delivery of goods and services (e.g., the surge in e-commerce).
The vehicles used for goods transportation are major contributors to congestion, emissions, noise. To counter these nuisances, transportation companies, as well as local authorities, are developing strategies aimed at making logistics activities more sustainable while maintaining their economic viability.
The main research activities of the ORDO group in the field of logistics can be summarized as follows: Investigating of pollution, uncertainty and customer service aspects related to vehicle routing problems. Studying fleet composition problems, with a particular emphasis on the integration of electric vehicles for goods distribution. Exploring combining freight within public transport modes. Integrating local authority policies, e.g., vehicle type access restriction, within urban distribution activities.  Designing logistics networks for humanitarian aid and hazardous material transportation.

Data mining and machine learning
Discrete and nonlinear optimization play an important role in either directly tackling fundamental data mining problems or training supervised machine learning models to perform their tasks. Beside the theoretical investigation of linear classification problems, efficient algorithms have been developed for clustering problems with respect to hyperplanes and for the pervasive problem of fitting piecewise affine models to data.