Lorenzo Brunetta

An operations research model for the evaluation of an airport terminal: SLAM (simple landside aggregate model)

The Simple Landside Aggregate Model (SLAM) is a model for estimating capacity and delays in airport passenger terminals. SLAM is designed to answer “what if†questions about alternative configurations of the various processing and holding facilities in a terminal. It consists of a network of modules, one for each facility of the terminal. These modules are based on a set of quite simple mathematical formulas to be used for the estimation of the capacity of each facility (in terms of passengers per hour) and the level of service (LOS) associated with it. LOS is quantified both in terms of “space available per facility occupant†and waiting time for being processed.

A branch-and-cut algorithm for the equicut problem

We describe an algorithm for solving the equicut problem on complete graphs. The core of the algorithm is a cutting-plane procedure that exploits a subset of the linear inequalities defining the convex hull of the incidence vectors of the edge sets that define an equicut. The cuts are generated by several separation procedures that will be described in the paper. Whenever the cutting-plane procedure does not terminate with an optimal solution, the algorithm uses a branch-and-cut strategy. We also describe the implementation of the algorithm and the interface with the LP solver. Finally, we report on computational results on dense instances with sizes up to 100 nodes.

A polyhedral approach to an integer multicommodity flow problem

Abstract In this paper we propose a branch-and-cut algorithm for the exact solution of an integer multicommodity flow problem. This NP -hard problem finds important applications in transportation, VLSI design, and telecommunications. We consider alternative formulations of the problem and describe several classes of valid inequalities. We describe lifting procedures to extend a given valid inequality for the problem with k commodities, to that having a larger number of commodities. We introduce a new large class of valid constraints, the multi-handle comb inequalities. The polyhedral structure of the integer multicommodity polytope is studied in the case of unit edge capacities. We prove that this polytope is full dimensional and show that some multi-handle comb inequalities are facet defining. Also, the lifting procedures are facet preserving under certain conditions. A branch-and-cut algorithm for the exact solution of the problem is then outlined, and separation algorithms for the main classes of inequalities studied in the paper are proposed. Computational results on several classes of test problems are finally reported, with a comparison between two different formulations.

The Linear Ordering Problem with cumulative costs

The optimization problem of finding a permutation of a given set of items that minimizes a certain cost function is naturally modeled by introducing a complete digraph G whose vertices correspond to the items to be sorted. Depending on the cost function to be used, different optimization problems can be defined on G. The most familiar one is the min-cost Hamiltonian path problem (or its closed-path version, the Traveling Salesman Problem), arising when the cost of a given permutation only depends on consecutive node pairs. A more complex situation arises when a given cost has to be paid whenever an item is ranked before another one in the final permutation. In this case, a feasible solution is associated with an acyclic tournament (the transitive closure of an Hamiltonian path), and the resulting problem is known as the Linear Ordering Problem (LOP). In this paper we introduce and study a relevant case of LOP arising when the overall permutation cost can be expressed as the sum of terms [alpha]u associated with each item u, each defined as a linear combination of the values [alpha]v of all items v that follow u in the permutation. This setting implies a cumulative (nonlinear) propagation of the value of variables [alpha]v along the node permutation, hence the name Linear Ordering Problem with Cumulative Costs. We illustrate the practical application in wireless telecommunication system that motivated the present study. We prove complexity results, and propose a Mixed-Integer Linear Programming model as well as an ad hoc enumerative algorithm for the exact solution of the problem. A dynamic-programming heuristic is also described. Extensive computational results on large sets of instances are presented, showing that the proposed techniques are capable of solving, in reasonable computing times, all the instances coming from our application.

A General Purpose Algorithm for Three-Dimensional Packing

We present a fast and efficient heuristic algorithm for solving a large class of three-dimensional packing problems with the objective of maximizing the average volumetric utilization of containers that might be of different dimensions. The algorithm is a tree-search algorithm that implicitly explores the solution space. The algorithm relies on the fact that, in practice, (i) the number of different types of objects to pack is limited and known in advance, and (ii) the number of occurrences of those objects is sufficiently high to permit use of a pattern approach to solve, at least partially, the problem. Each node of the search tree is solved using an extension of a pallet-loading heuristic developed by Morabito and Morales to generate the patterns and of a container-loading heuristic developed by Pisinger to treat the objects not packed by the pattern approach. We report on our extensive computations on a new large library of instances derived from real world applications.

Multi-Airport Ground Holding Problem: A Heuristic Approach Based on Priority Rules

In recent years, many sophisticated mathematical models have been proposed to address the problem of reducing congestion at major airports by means of Ground Holding (GH) Policies, i.e., by imposing a ground delay to selected aircraft in order to reduce and possibly to avoid airborne delays and congestion. These models, which are usually optimization models, have found little application in practice so far, probably because they are not easy to understand. In this paper we introduce and analyze a family of simple, easy to understand, heuristics. Each heuristic is based on a specific “priority rule”. The flights are grouped dynamically into a manageable number of classes. Each “priority rule” specifies, for any two flights of different classes, which one has priority over the other. The performances of the proposed heuristics are compared among themselves, and with that of an “optimal” policy, on a set of test problems.

Evaluating terminal management performances using SLAM : The case of Athens international Airport

Abstract Athens in Greece is the city selected to host the 2004 Olympic Games. Many simulations and analyses have been performed in order to properly approach the logistics problems arising from such an event. In this paper we address one of these problems. More precisely, we present a model for analyzing the terminal of Athens International Airport (AIA) under three different scenarios: (i) a historic scenario, based on a typical “busy day”, (ii) a foreseeable scenario with AIA becoming a hub and increasing its traffic volume, and (iii) a traffic intense scenario, as expected during the 2004 Olympic Games. The airport simulation is performed through the OPAL platform. While the airside analysis does not evidence any major cause of congestion, the landside, evaluated through an enhanced version of the simple landside aggregate model (SLAM), shows possible situations of congestion with a consequent degradation in the level of service provided. The use of SLAM allows signaling out the bottlenecks and the corresponding possible causes. A simple modification in the airport policies is sufficient to significantly improve the overall performance.

The flow management problem: recent computational algorithms

Abstract The air traffic flow management problem, together with various policies to address it, is described in this paper. A survey of optimization algorithms for the ground-holding (and ‘free flight’) policies is provided. An exact algorithm, based on the integration of a heuristic algorithm with an integer linear programming model is presented next. This approach provides exact solutions in a much shorter computational time than previous algorithms proposed in the literature. Computational results for large-size instances with over 20 000 flights based on the OAG data for a full day in the USA air traffic network are reported.

Solving the multi-airport Ground Holding Problem

The increasing demand for air traffic in the last years has led to a heavier use of airportsand airways, while their capacities have not grown accordingly. The main drawback of thisphenomenon is a situation of congestion in air traffic networks that produces departure delaysand queues before landing, causes large losses to air companies and affects air traffic safety.A way of reducing congestion is to adopt a Ground Holding policy, i.e., to hold on theground a limited number of flights before departure in order to avoid as much as possibleairborne delay. The Ground Holding Problem (GHP) is that of determining a way of distributingdelays to the flights in such a way as to minimize the overall cost of the delays (bothon the ground and in the air). The importance of Ground Holding policies is well recognizedand optimization models have been proposed: unfortunately, it is very difficult to have real,or -even realistic-, GHP instances to evaluate the quality of one procedure over the others.Given this lack of GHP instances, in this paper we introduce 32 new test cases, up to 5000flights on a network of 10 airports, in which congestion is caused by insufficient capacity inarrival airports. These instances (made accessible via ftp) are solved to computationallycompare a new heuristic algorithm with both a previous heuristic and an exact algorithm.The new algorithm we propose is based on -priority rules-, where the flight priority iscomputed as a cost function.

Solving the feedback vertex set problem on undirected graphs

Abstract Feedback vertex problems consist of removing a minimal number of vertices of a directed or undirected graph in order to make it acyclic. The problem is known to be NP -complete. In this paper we consider the variant on undirected graphs. The polyhedral structure of the feedback vertex set polytope is studied. We prove that this polytope is full dimensional and show that some inequalities are facet defining. We describe a new large class of valid constraints, the subset inequalities. A branch-and-cut algorithm for the exact solution of the problem is then outlined, and separation algorithms for the inequalities studied in the paper are proposed. A local search heuristic is described next. Finally, we create a library of 1400 randomly generated instances with the geometric structure suggested by the applications, and we computationally compare the two algorithmic approaches on our library.