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The Bi-objective Minimum Latency Problem with Profit Collection and Uncertain Travel Times

: This paper introduces a new bi-objective minimum latency problem with proﬁt collection, where routes must be constructed in order to maximize the collected proﬁt and to minimize the total latency. These objectives are usually conﬂicting. Thus, considering some important features, as the segmentation of the customers into two classes, mandatory and optional, and the presence of uncertain travel times, we follow a bi-objective approach, aiming to compute a set of Pareto-optimal alternatives with different trade-offs for a decision-maker to choose from. In order to address this computationally challenging problem, we propose a Multi-Objective Iterated Local Search. Computational results conﬁrm the practicality of the algorithm, in terms of the quality of the solutions, and its computational efﬁciency in terms of time spent. We conclude that the algorithm ﬁnds good-quality solutions for small and medium-size instances.