In the automotive industry, the high customizability of the final products leads to the need for managing large portfolios of variants of the same product, given the different combination of optional components that characterizes each variant. Due to the large number of components and to the variability of the final product demand brought about by such high customizability, planning how many units per variant should be produced in a given period is a critical task. This is especially true in the medium term, when few available components are left. In this paper, a proactive approach that can help find the best set of variants, to which available capacity should be allocated, is proposed. The problem of finding the best set of product variants is rephrased as a product portfolio selection problem and modeled as a multiple-objective multi-dimensional knapsack. A tabu search algorithm has been developed to provide a solution to the problem. The proposed approach has been tested in a real case study from the automotive industry; the results show its effectiveness in terms of providing a good set of trade-off product portfolios among which the product manager can choose.