Cross-selling campaigns seek to offer the right products to the set of customers with the goal of maximizing expected profit, while, at the same time, respecting the purchasing constraints set by investors. In this context, a bi-objective version of this NP-Hard problem is approached in this paper, aiming at maximizing both the promotion campaign total profit and the risk-adjusted return, which is estimated with the reward-to-variability ratio known as Sharpe ratio. Given the combinatorial nature of the problem and the large volume of data, heuristic methods are the most common used techniques. A Greedy Randomized Neighborhood Structure is also designed, including the characteristics of a neighborhood exploration strategy together with a Greedy Randomized Constructive technique, which is embedded in a multi-objective local search metaheuristic. The latter combines the power of neighborhood exploration by using a Pareto Local Search with Variable Neighborhood Search. Sets of non-dominated solutions obtained by the proposed method are described and analyzed for a number of problem instances.
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