Lucio Bianco

A Network Based Model for Traffic Sensor Location with Implications on O/D Matrix Estimates

In this paper, we define and solve the sensor location problem (SLP), that is, we look for the minimum number and location of counting points in order to infer all traffic flows in a transport network. We set up a couple of greedy heuristics that find lower and upper bounds on the number of sensors for a set of randomly generated networks. We prove that solving the SLP implies that the Origin/Destination (O/D) matrix estimation error be always bounded. With respect to alternative sensor location strategies, simulation experiments show that: (i) measurement costs being equal, the O/D estimation error is lower, and (ii) conversely, O/D estimation error being equal, the number of sensors is smaller.

Dynamic Programming Strategies for the Traveling Salesman Problem with Time Window and Precedence Constraints

The Traveling Salesman Problem with Time Window and Precedence Constraints (TSP-TWPC) is to find an Hamiltonian tour of minimum cost in a graph G = (X, A) of n vertices, starting at vertex 1, visiting each vertex i ∈ X during its time window and after having visited every vertex that must precede i, and returning to vertex 1. The TSP-TWPC is known to be NP-hard and has applications in many sequencing and distribution problems. In this paper we describe an exact algorithm to solve the problem that is based on dynamic programming and makes use of bounding functions to reduce the state space graph. These functions are obtained by means of a new technique that is a generalization of the “State Space Relaxation” for dynamic programming introduced by Christofides et al. (Christofides, N., A. Mingozzi, P. Toth. 1981b. State space relaxation for the computation of bounds to routing problems. Networks 11 145–164.). Computational results are given for randomly generated test problems.

The traveling salesman problem with cumulative costs

In this paper, we consider a special case of the time-dependent traveling salesman problem where the objective is to minimize the sum of all distances traveled from the origin to all other cities. Two exact algorithms, incorporating lower bounds provided by a Lagrangean relaxation of the problem, are presented. We also investigate a heuristic procedure derived from dynamic programming that is able to evaluate the distance from optimality of the produced solution. Computational results for a number of problems ranging from 15 to 60 cities are given. They show that problems up to 35 cities can be solved exactly and problems up to 60 cities can be solved within 3% from optimality.

A heuristic procedure for the crew rostering problem

Abstract This paper deals with the problem of planning work schedules in a given time horizon so as to evenly distribute the workload among the drivers in a mass transit system. An integer programming formulation of this problem is given. An iterative heuristic algorithm is described which makes use of a lower bound derived from the mathematical formulation. Furthermore, the algorithm at each iteration solves a multilevel bottleneck assignment problem for which a new procedure that gives asymptotically optimal solutions is proposed. Computational results for both the rostering problem and the multilevel bottleneck assignment problem are given.

A Set Partitioning Approach to the Crew Scheduling Problem

The crew scheduling problem (CSP) appears in many mass transport systems (e.g., airline, bus, and railway industry) and consists of scheduling a number of crews to operate a set of transport tasks satisfying a variety of constraints. This problem is formulated as a set partitioning problem with side constraints (SP), where each column of the SP matrix corresponds to a feasible duty, which is a subset of tasks performed by a crew. We describe a procedure that, without using the SP matrix, computes a lower bound to the CSP by finding a heuristic solution to the dual of the linear relaxation of SP. Such dual solution is obtained by combining a number of different bounding procedures. The dual solution is used to reduce the number of variables in the SP in such a way that the resulting SP problem can be solved by a branch-and-bound algorithm. Computational results are given for problems derived from the literature and involving from 50 to 500 tasks.

Scheduling models for air traffic control in terminal areas

We propose a job-shop scheduling model with sequence dependent set-up times and release dates to coordinate both inbound and outbound traffic flows on all the prefixed routes of an airport terminal area and all aircraft operations at the runway complex. The proposed model is suitable for representing several operational constraints (e.g., longitudinal and diagonal separations in specific airspace regions), and different runway configurations (e.g., crossing, parallel, with or without dependent approaches) in a uniform framework. The complexity and the highly dynamic nature of the problem call for heuristic approaches. We propose a fast dynamic local search heuristic algorithm for the job-shop model suitable for considering one of the different performance criteria and embedding aircraft position shifting control technique to limit the controllers/pilots’ workload. Finally, we describe in detail the experimental analysis of the proposed model and algorithm applied to two real case studies of Milan-Malpensa and Rome-Fiumicino airport terminal areas.

Minimizing total completion time subject to release dates and sequence‐dependentprocessing times

We consider the problem of scheduling jobs with release dates and sequence‐dependentprocessing times on a single machine to minimize the total completion time. We show thatthis problem is equivalent to the Cumulative Traveling Salesman Problem with additionaltime constraints. For this latter problem, we give a dynamic programming formulation fromwhich lower bounds are derived. Two heuristic algorithms are proposed. Performanceanalysis of both lower bounds and heuristics on randomly generated test problems are carriedout. Moreover, the application of the model and algorithms to the real problem of sequencinglanding aircraft in the terminal area of a congested airport is analyzed. Computational resultson realistic data sets show that heuristic solutions can be effective in practical contexts.

Combinatorial aspects of the sensor location problem

In this paper we address the Sensor Location Problem, that is the location of the minimum number of counting sensors, on the nodes of a network, in order to determine the arc flow volume of all the network. Despite the relevance of the problem from a practical point of view, there are very few contributions in the literature and no combinatorial analysis is performed to take into account particular structure of the network. We prove the problem is

EXACT AND HEURISTIC PROCEDURES FOR THE TRAVELING SALESMAN PROBLEM WITH PRECEDENCE CONSTRAINTS, BASED ON DYNAMIC-PROGRAMMING

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