Hybrid Algorithm for IRP C. Archetti, L. Bertazzi, A. Hertz, M.G. Speranza A Hybrid Algorithm for an Inventory-Routing Problem Claudia Archetti * Luca Bertazzi * Alain Hertz † M. Grazia Speranza * * Department of Quantitative Methods, University of Brescia Contrada Santa Chiara 50, I-25122 Brescia, Italy {archetti, bertazzi, speranza}@eco.unibs.it † GERAD 3000, chemin de la Cte-Sainte-Catherine, Montral (Qc) Canada H3T 2A7 alain.hertz@gerad.ca 1 Introduction The class of inventory routing problems (IRP) includes a variety of different optimization prob- lems that, though often very different from each other, all consider a routing and an inventory component of an optimization problem. Time may be discrete or continuous, demand may be deterministic or stochastic, inventory holding costs may be accounted for in the objective function or not. When the holding costs are not included in the objective function, usually a limited inventory capacity at the customers is available and cannot be exceeded ([7], [6], [8], [9]). The only exact approach for an IRP we are aware of is presented in [1]. The availability of exact solutions for test instances makes it possible the evaluation of the performance of a heuristic algorithm. In this paper we present a metaheuristic for the solution of this IRP that combines a tabu search scheme with ad hoc designed mixed integer programming (MIP) models. In fact, whereas tabu search algorithms have been proved to be very effective for many vehicle routing problems, the complexity of the IRP we studied required, in order to get high quality solutions, a more sophisticated heuristic search of the solution space. The effectiveness of the metaheuristic is proved over a set of benchmark instances with errors that are systematically below 1%. 2 Problem description We consider a distribution network where a product is shipped from a common supplier, denoted by 0, to a set M = {1, 2,...,n} of customers over a time horizon H . At each discrete time t ∈T = {1,...,H } a quantity r 0t is produced at the supplier and a quantity r it is consumed at customer i ∈M. A starting inventory level B 0 at the supplier is given. Each customer i has a given starting inventory I i0 ≤ U i and a maximum capacity U i . If customer i is EU/MEeting 2008 - Troyes, France, October 23–24, 2008 1