Classes of Problems
Routing with Profits
The key characteristic of the class of routing problems with profits is that, contrary to what happens in other classical routing problems, it may be decided whether or not serve the given customers. Therefore, two different decisions have to be taken simultaneously: which customers to serve, and in which order they are visited (possibly, subdividing them into more than one route).
The Inventory Routing (IRP) is one of the recent challenging combinatorial optimization problems.
An undirected complete graph describes the transportation network with costs associated with the edges. One vertex represents the depot and the other vertices the customers.
The Split Delivery Vehicle Routing Problem (SDVRP) is the problem of finding a set of routes that minimizes the total traveling cost. In the SDVRP, the traditional assumption made in the Vehicle Routing Problem (VRP) that each customer is visited only once is relaxed.
Solving the road congestion problem is one of the major issues in modern cities as it causes time wasting, pollution, higher industrial costs and huge road maintenance costs. Among possible congestion avoidance methods, traffic assignment is a valuable choice since it does not involve huge investments to expand the road network. Traffic assignments are traditionally devoted to two main perspectives on which the well-known Wardropian principles are inspired: the user equilibrium (user's perspective) and the system optimum (system perspective). User equilibrium is a user-driven traffic assignment where each user chooses the most convenient path selfishly. It guarantees that fairness among users is respected since, when the equilibrium is reached, all users sharing the same origin and destination will experience the same travel time. The main drawback in a user equilibrium is that the system total travel time is not minimized. On the other hand, the system optimum is a system-wide traffic assignment in which drivers are routed on the network minimizing the total travel time. In this assignment, users might experience travel times that are higher than the other users travelling from the same origin to the same destination. Thus, there are drawbacks in using one of the two assignments that can be partially overcome by applying users' fairness considerations while minimizing a system-oriented objective. In the last decade, few attempts have been done to present a users' needs and system efficiency trade-off traffic assignment with non-linear programming techniques as in Jahn et Al. (2005). Our research goal is to develop linear programming approaches to solve the system optimal routing of traffic flows with users’ constraints problem.
Portfolio optimization is the problem of determining, according to some criterion, the optimal proportions of the capital invested in each asset at the beginning of the period.
Multiobjective Combinatorial Problems
Decision makers have often to face different, and usually conflicting, objectives. In these cases, the aggregation of multiple criteria into a single objective function seems a natural approach, but the rules for aggregation may be arbitrary and the resulting problem may be oversimplified. Providing the decision maker with a single “optimal” solution may be not adequate to capture the complexity of the actual decision to be made.