Maria Grazia Scutellà

Distribution network design: New problems and related models

We study some complex distribution network design problems, which involve facility location, warehousing, transportation and inventory decisions. Several realistic scenarios are investigated. Two kinds of mathematical programming formulations are proposed for all the introduced problems, together with a proof of their correctness. Some formulations extend models proposed by Perl and Daskin (1985) for some warehouse location-routing problems; other formulations are based on flow variables and constraints.

Dynamic Shortest Paths Minimizing Travel Times and Costs

In this paper, we study dynamic shortest path problems, which is to determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum time walk problem (which is to find a walk with the minimum travel time) and the minimum cost walk problem (which is to find a walk with the minimum travel cost). The minimum time walk problem is known to be polynomially solvable for a class of networks called FIFO networks. This paper makes the following contributions: (i) we show that the minimum cost walk problem is an NP-complete problem; (ii) we develop a pseudopolynomial-time algorithm to solve the minimum cost walk problem (for integer travel times); and (iii) we develop a polynomial-time algorithm for the minimum time walk problem arising in road networks with traffic lights.

A Multi-Exchange Neighborhood for Minimum Makespan Parallel Machine Scheduling Problems

We propose new local search algorithms for minimum makespan parallel machine scheduling problems, which perform multiple exchanges of jobs among machines. Inspired by the work of Thompson and Orlin (1989) on cyclic transfer neighborhood structures, we model multiple exchanges of jobs as special disjoint cycles and paths in a suitably defined improvement graph, by extending definitions and properties introduced in the context of vehicle routing problems (Thompson and Psaraftis, 1993) and of the capacitated minimum spanning tree problem (Ahuja et al., 2001). Several algorithms for searching the neighborhood are suggested.We report the results of a wide computational experimentation, on different families of benchmark instances, performed for the case of identical machines. This problem has been selected as a case study to perform a comparison among the alternative algorithms, and to discover families of instances for which the proposed neighborhood may be promising in practice. Based on the results of the experiments, we can suggest which among the many possible variants of the proposed approaches may be more promising for developing local search algorithms based on multi-exchange moves for related problems. Also, on some families of instances, which are very hard to solve exactly, the most promising multi-exchange algorithms were observed to dominate, in solution quality and in computational time, competitive benchmark heuristics.

Polynomially solvable satisfiability problems

Abstract We address the well-known satisfiability problem (SAT), i.e., the problem of checking whether a given propositional formula is satisfiable. Although the general satisfiability problem is NP-complete, some particular cases of SAT are known to be easy. The most important of those cases is HORN-SAT, i.e., the satisfiability problem in the case of Horn clauses: actually, an instance of HORN-SAT can be solved in linear time. Yamasaki and Doshita (1983) have introduced a new subclass of SAT, S0, which is polynomially solvable and which strictly includes HORN-SAT. Here we introduce a family of subclasses of SAT, Γ0, Γ1,…,Γk,…, such that HORN-SAT = Γ0, S0 = Γ1, Γk ⊇ Γk-1, k = 1,2,…, and Γk approaches to SAT as k increases. For each k, Γk is solvable in O(n∗nk) time, where n is the number of propositional letters, m is the number of clauses, and n∗ = O(nm) is the size of the input. An algorithm to check whether a given instance of SAT belongs to Γk, for any k, which runs in O(n∗nk time, is also described.

Flows on hypergraphs

We consider the capacitated minimum cost flow problem on directed hypergraphs. We define spanning hypertrees so generalizing the spanning tree of a standard graph, and show that, like in the standard and in the generalized minimum cost flow problems, a correspondence exists between bases and spanning hypertrees. Then, we show that, like for the network simplex algorithms for the standard and for the generalized minimum cost flow problems, most of the computations performed at each pivot operation have direct hypergraph interpretations.

Polynomial auction algorithms for shortest paths

In this paper we consider strongly polynomial variations of the auction algorithm for the single origin/many destinations shortest path problem. These variations are based on the idea of graph reduction, that is, deleting unnecessary arcs of the graph by using certain bounds naturally obtained in the course of the algorithm. We study the structure of the reduced graph and we exploit this structure to obtain algorithms withO (n min{m, n logn}) andO(n2) running time. Our computational experiments show that these algorithms outperform their closest competitors on randomly generated dense all destinations problems, and on a broad variety of few destination problems.

Directed Hypergraphs as a Modelling Paradigm

We address a generalization of graphs, the directed hypergraphs, and show that they are a powerful tool in modelling and solving several relevant problems in many application areas. Such application areas include Linear Production Problems, Flexible Manufacturing Systems, Propositional Logic, Relational Databases, and Public Transportation Systems.RiassuntoGli ipergrafi orientati costitniscono uno strumento di notevole efficacia nella modellazione e soluzione di diverse classi di problemi decisionali. Essi costituiscono un linguaggio unificante per problemi che nascono in ambienti molto diversi, quali “Sistemi di Produzione”, “Sistemi di Trasporto Pubblico”, “Basi di Dati Relazionali” …Particolarmente importanti sono i concetti di ipercammino e di iperflusso che generlizzano in modo naturale quelli di cammino e di flusso su grafi orientati. fpercammini e iperflussi ottimi possono essere trovati per mezzo di algoritmi specializzati, che generalizzano gli algoritmi di etichettatura per la ricerca di cammini minimi e quelli di tipo “simplesso su reti” per i flussi di costo minimo.Ci si propone di presentare alcuni dei contesti più rilevanti, dal punto di vista delle applicazioni pratiche, in cui possono essere utilizzati modelli e algoritmi basati su ipergrafi orientati. Particolare attenzione sarà rivolta alle applicazioni di tipo economico aziendale.

Large scale local search heuristics for the Capacitated Vertex p-Center Problem

This paper investigates the application of very-large neighborhood search techniques for solving the capacitated vertex

The maximum flow problem: A max-preflow approach

p

The skill vehicle routing problem

-center problem. We characterize a local search neighborhood in terms of path and cyclic exchanges of customers among facilities, and exploit principles borrowed from network optimization theory to efficiently detect cost decreasing solutions in such a neighborhood. We complement the multi-exchange methodology with a local reoptimization mechanism specifically designed to perform facility location adjustments. The validity of the proposed approach is supported by empirical investigation and performance comparisons with the commercial code CPLEX.