A Relax-and-Fix Algorithm for a Maritime Inventory Routing Problem Departamento de Inform´ atica - Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil {mwfriske,buriol}@inf.ufrgs.br Abstract. This work presents a relax-and-ﬁx algorithm for solving a class of single product Maritime Inventory Routing Problem. The prob- lem consists in routing and scheduling a heterogeneous ﬂeet of vessels to supply a set of ports, keeping inventory at production and consumption ports between lower and upper limits. Two sets of constraints are pro- posed both for tightening the problem relaxation and for obtaining better integer solutions. Four MIP-based local searches to improve the solution provided by the relax-and-ﬁx approach are presented. Computational ex- periments were carried out on instances of the MIRPLIB, showing that our approach is able to solve most instances in a reasonable amount of time, and to ﬁnd new best-known solutions for two instances. A new dataset has been created by removing the clustered characteristics of ports from the original instances, and the eﬀectiveness of our method was tested in these more general instances. Keywords: Maritime Inventory Routing Problem, Relax-and-Fix, MIP-Based Local Search 1 Introduction Maritime transportation is the major mode of transportation used when consid- ering large quantities of goods, mainly bulk products. The Maritime Inventory Routing Problem (MIRP) arises when one has to manage both the scheduling of vessels and the inventories at ports. It can be considered a variant of the Inventory Routing Problem, which combines vehicle routing and inventory man- agement. However, MIRP deals with special features of maritime transportation. This work considers the single product MIRP model proposed by [12]. Given a ﬁnite planning horizon, a ﬂeet of heterogeneous vessels, and a set of ports, one must decide for each vessel which ports will be visited, when they will be visited, and the amount of product that should be loaded or discharged when a vessel operates at each port. In this problem variant, ports are grouped in geographi- cal regions, such that each region has only production (loading) or consumption (discharging) ports. Each port has ﬁxed storage and operating capacities, while production/consumption rates may vary along the planning horizon. The in- ventory of ports is supplied by vessels, and by simpliﬁed spot markets when © Springer International Publishing AG 2017 et al. (Eds.), ICCL 2017, LNCS 10572, pp. 270–284, 2017. https://doi.org/10.1007/978-3-319-68496-3_18 T. Bektaş Marcelo W. Friske and Luciana S. Buriol ()