Paolo Carraresi

On some matching problems arising in vehicle scheduling models

Two bipartite matching problems arising in Vehicle Scheduling are considered: the capacitated matching and the multicommodity matching. For the former, given a reasonable cost structure, we can exhibit a polynomial time algorithm, while the general case is conjectured to be NP-hard. The latter problem is shown to be NP-hard. A heuristic algorithm based on Lagrangean relaxation for the capacitated version of the multicommodity matching is also presented together with experimental results.

Network models for vehicle and crew scheduling

Abstract Network models and methods have proven to be rather successful in many application fields. In this survey their use in the solution of Vehicle Scheduling and Crew Scheduling problems in Mass Transit settings is reviewed. An attempt is made to encompass in a unified framework some of the most relevant models on the subject to be found in the literature.

A multi-level bottleneck assignment approach to the bus drivers' rostering problem

Abstract The problem of finding a work assignment for drivers in a given time horizon, in such a way as to have an even distribution of the workload, is considered. This problem is formulated as a Multi-level Bottleneck Assignment Problem (MBA). The MBA problem is studied: it is shown that it is NP-complete and an asymptotically optimal algorithm is presented. Some computational results are illustrated which prove the efficiency of the algorithm.

A new lower bound for the quadratic assignment problem

We introduce a new lower bound for the quadratic assignment problem based on a sequence of equivalent formulations of the problem. We present a procedure for obtaining tight bounds by sequentially applying our approach in conjunction with the A. Assad and W. Xu bound and the N. Christofides and M. Gerrard bound.

Regional mass transit assignment with resource constraints

This paper considers a mass transit system in a regional area. The problem of improving the quality of the service by decreasing the total passenger waiting time is studied. A model to improve the effectiveness of the system without worsening the cost (vehicles and duties) and the passenger assignment is proposed, along with a new definition of passenger assignment to support the proposed model.

RELAXATION APPROACHES TO LARGE SCALE BUS DRIVER SCHEDULING PROBLEMS

The bus driver scheduling (BDS) problem in a transit company consists of establishing, at minimum cost, a list of work-days in which a driver is assigned to each bus in the given time-table and all clauses of the union contract are respected. In this paper we present a general mathematical programming formulation for the BDS problem. Because, in general, the problem is too large to be solved directly, we introduce a relation of the problem and three different solution approaches. Computational results obtained on real life problems indicate that mathematical programming techniques can solve the BDS problem efficiently.

Testing Optimality for Quadratic 0-1 Problems

Abstract: The issue tackled is testing whether a given solution of a quadratic 0-1 problem is optimal. The paper presents an algorithm based on the necessary and sufficient optimality condition introduced by Hirriart-Urruty for general convex problems. A measure of the quality of the solution is provided. Computational results show the applicability of the method. The method is extended to constrained quadratic 0-1 problems such as quadratic assignment and quadratic knapsack .

Testing optimality for quadratic 0–1 unconstrained problems

This paper analyses a necessary and sufficient optimality condition for quadratic pseudo-Boolean unconstrained problems. It is proved that in general testing any necessary and sufficient optimality condition is a difficult task for anyNP-hard problem. Anɛ-optimality condition is derived together with an approximation scheme to test it.

BDS: A system for the Bus Drivers’ Scheduling problem integrating combinatorial optimization and logic programming

The bus driver scheduling problem is the problem of finding a set of duties to be assigned to the drivers in order to satisfy all clauses of the union contract and to meet, at cost, the daily service requirement. The aim of this paper is to present a novel approach to the bus drivers scheduling problem which is based on an integration between combinatorial optimization and logic programming. This integration is supported by Logiform, an expert system shell of the 2nd generation where knowledge is partitioned in two levels: shallow and deep knowledge. The former represents common sense knowledge (thumb rules) and is expressed in first order predicate calculus; the latter is a rigorous and complete theory of the considered phenomenon and is expressed by a mathematical model. A combinatorial optimization model is presented together with a procedure, based on a Lagrangian relaxation approach, which yields a lower bound and a feasible solution. This solution is processed by Logiform in order to satisfy particular union constraints not included in the mathematical model. Logiform also provides and controls interactions between algorithms execution and the operator. The effectiveness of the proposed combinatorial approach is discussed by reporting the experience of using an early version of BDS (not including Logiform) at ATAF, the transit company of Florence.