A multiperiod traveling salesman problem: Heuristic algorithms

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Abstract

This paper deals with a particular traveling salesman problem in which the cities must be visited on a periodic basis over a given M-day time period. Two heuristic algorithms, embedding a procedure for finding a shortest path on a layered network, are developed. Computational results are also reported for ten test problems drawn from the literature.

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    Instances t-p11 to t-p23 were introduced by Chao et al. (1995b) and instances t-p24 to t-p34 are taken from Cordeau et al. (1997). Results were given by Christofides and Beasley (1984), Paletta (1992), Chao et al. (1995b), Cordeau et al. (1997), Paletta (2002) and Bertazzi et al. (2004). A detailed description of the instances indicating the number of cities and the planning horizon is given in Table 11.

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    The definition of periodicity may be given in the following ways (Paletta and Triki, 2004): all the sets of possible combinations to a customer can be explicitly stated (Russell and Gribbin, 1991); or the distance in days between two visits to each customer can be specified (Chao et al., 1995; Cordeau et al., 1997). Paletta (1992) introduced additional constraints that determine the maximum and minimum number of days that can elapse between two successive visits. However, in our application, the periodicity does not condition the route generation.

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Paletta is Associate Professor of Operations Research at the Dipartimento di Informatica ed Applicazioni of the Università di Salerno, Italy. His research interests are in the field of discrete optimization. He has published in The European Journal of Operational Research, The International Journal of Control, Mathematical Programming Studies, Annals of Discrete Mathematics and Transportation Science.

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