The current main research interests of Roberto Baldacci include Operational Research and Mathematical Programming methodologies and, in particular, the design of effective algorithms for Combinatorial Optimization and Graph Theory problems, and their application to real-world Transportation, Routing and Location problems. His research has been mainly devoted to the study of new general techniques for enumerative methods, and to the definition and evaluation of new algorithms and software implementations for the exact and approximate solution of the following problems:

- Travelling Salesman with additional constraints;
- Vehicle Routing and Scheduling;
- Car Pooling;
- Location;
- Vehicle Routing Applications;
- Telecommunication Network Design;
- Packing;
- Portfolio management;
- Arc Routing.

The main research interests include Operational Research and Mathematical Programming methodologies and, in particular, the design of effective algorithms for Combinatorial Optimization and Graph Theory problems, and their application to real-world Transportation, Routing and Location problems. His research has been mainly devoted to the study of new general techniques for enumerative methods, and to the definition and evaluation of new algorithms and software implementations for the exact and approximate solution of the following problems:

*Vehicle Routing*

The Capacitated Vehicle Routing Problem (CVRP) is the problem of designing the routes for a set of vehicles stationed at a central depot in order to serve a set of customers minimizing the transportation costs and such that a constraint on the capacity of each vehicle is satisfied.

The CVRP is one of the most studied problems in combinatorial optimisation. However, the exact algorithms proposed in the literature are able to solve problems of small dimension only. Moreover, the single constraint on the vehicle capacity represents, with wide approximation only, the real problems characterized by several and difficult constraints that make the VRP one of the most difficult problems among combinatorial optimisation problems. The purpose of the research on the VRP is to develop new mathematical methodologies in order to design new exact and heuristic solution algorithms that are able to handle real constraints.

*Car Pooling*

Car pooling is a transportation service organized by a large company which encourages its employees to pick up colleagues while driving to/from work in order to minimize the number of private cars travelling to/from the company site. The benefits which can be obtained are particularly relevant both in terms of reduction of the use of private cars and of the parking space required. The Car Pooling Problem (CPP) consists in defining the subsets of employees that will share each car and the paths the drivers should follow, so that sharing is maximized and the sum of the path costs is minimized. The purpose of the research on the CPP is to develop new mathematical methodologies in order to design new exact and heuristic solution algorithms that are able to handle real constraints.

*Telecommunication Network
Design*

Telecommunications represent one of the technological area that has had major development during last years and that is subject to changes and huge investments. During this last years Operations Research has developed optimisation and simulation methods on graphs that can be effectively used to solve real problems in this area. In particular, the frame of this research is the one of wide-band telecommunication network, on cable or wireless. The design of such network is a complex task and is generally subject to a number of complex constraints of different type, such as, geographical, technological, organizational, etc. The direct consequence of this fact is that the design of telecommunication network is generally tackled in successive phases.

*Packing problems*

Packing problems find many practical applications in many real world problems, e.g. container and pallet loading. In the Two-Dimensional Bin Packing Problems (2DBPP), Two-Dimensional Strip Packing Problem (2DSPP), and Two-Dimensional Knapsack Problem (2DKP), items are rectangles to be packed with the height parallel to the height of the bins. Bins are finite rectangles in the case of 2DBPP and 2DKP, while in 2DSPP one is given a unique rectangular bin having finite width and infinite height. In 2DBPP one has to pack all the items by minimizing the number of used bins, while in 2DSPP one has to pack all the items in the unique rectangle, by minimizing the overall height of the packing; finally, in 2DKP the aim is to pack a maximum-profit subset of items fit into a unique (finite) bin. Many practical applications are characterized by the additional constraint requiring that items are packed in shelves ("shelf packing"). Moreover, even when not explicitly required by the operational constraints, such a requirement widely simplifies the solution process. Concerning packing problems, the research propose to develop exact and heuristic algorithms for their solution.

*Portfolio
optimization*

Each of the larger fund management companies in the U.E. and the U.S.A. are responsible for the investment of several billion Euro and Dollars. This money is invested on behalf of pension funds, mutual funds and other institutions. The selection of an appropriate portfolio of assets in which to invest is an essential component of fund management. Although, a large proportion of portfolio selection decisions are taken on a qualitative basis, quantitative approaches to selection are becoming more widely adopted. In this context, a relevant financial problem is the periodical rebalance of a portfolio of assets, such that the portfolio's total value exhibits certain characteristics. For performing a periodical rebalance following a quantitative approach, it is necessary to have a model which represents the future state space evolution of the corresponding economy and where the asset values are some given function of a particular state. Since the size of the problem can be very large even for simple financial model (for a practical problems it is easy to have more than one million variables and constraints), the objective is to device different algorithms based on decomposition methods (i.e. Lagrangean relaxation, Dantzig-Wolfe decomposition and Benders' decomposition).