A clustering first – route second method for the solution of many-to- many Dial a Ride problem MARIALISA NIGRO, LIVIA MANNINI Engineering Department Roma Tre University Via Vito Volterra 62 Rome, ITALY marialisa.nigro@uniroma3.it , livia.mannini@uniroma3.it MARTA FLAMINI Università Telematica Internazionale UNINETTUNO Corso Vittorio Emanuele II, 39 Rome, ITALY m.flamini@uninettunouniversity.net Abstract: A clustering first-route second method to solve the many-to-many Dial a Ride (DAR) problem has been proposed. The clustering phase is the main novelty of the method, taking into account both space and time variables to realize the clusters. The procedure has been tested on a real network during the organization of the mobility of students between some offices and Departments of “Roma Tre” University (Rome, Italy), obtaining good results in terms of waiting time and number of served users. The computational times (few seconds) promise the achievement of an on line service. Key-Words: - Dial a ride problem, cluster method, clustering first-route second, Greedy Algorithm, Pickup and delivery problem 1 Introduction The Dial a Ride (DAR) systems belong to the demand responsive transit systems, usually adopted for supplying areas of low ridership and/or low population density (low demand value, [6]). The problem of identifying a path for one/more vehicles involved in a DAR system, and more generally the Pickup and delivery problem from which DAR derives, has been widely discussed in literature; for an accurate review see Diana and Dessouky, 2004 [5]. The DAR is a NP-hard problem and the earliest relevant publications date back to 1980’s [12]. Its solution changes if we are in off-line or on-line contexts, if single vehicle or more vehicles are considered, if capacity constraint and/or constraints on the time windows of the generic i-th request are considered [4]. The adopted algorithms are generally heuristic algorithms. The “Tabu search” metaheuristic methods have been used either to solve off-line DAR problems [3] or on-line ones [1]; also Simulated Annealing ([10], [13]), Genetic Algorithms and Evolutionary algorithms ([8], [2]) have been widely adopted. Healy and Moll (1995, [7]) have proposed an extension of classic “local search” algorithm in order to obtain a better quality of solutions. Same idea has been recently followed in [9] with the development of an evolutionary Local Search (ELS) method. Diana and Dessouky (2004, [5]) developed a “regret” insertion heuristic method computationally more complex than a simple insertion heuristic one, but with a better quality of solutions with respect to a “local search” algorithm. In the following paragraphs the analytical formulation of the DAR problem is reported and the new proposed method for the many-to-many case is explained; finally, the results of a real application are shown. 2 Problem definition The analytical formulation is reported below. Given a graph G=[N,A], with N and A respectively equal to the set of nodes and links, once defined the following variables: Recent Researches in Applied Economics and Management - Volume I ISBN: 978-960-474-323-0 464